### Séminaires de l’année 2013

# Séminaire de la Fédération PHYSTAT-SUD : Ludwik Leibler

## Vitrimers

### Ludwik Leibler, Matière Molle et Chimie, ESPCI, Paris

Glass-workers shape marvelous objects without using moulds or precise temperature control because glass is a unique material that transforms from liquid to solid in a very progressive way. Can we imagine other compounds that offer similar opportunities? I will present the concept of solidification by molecular-networks topology freezing and introduce vitrimers, organic materials that behave just like glass. Beside opening new perspectives in chemistry and physics of glass formation and catalytically controlled exchange reactions, discovery of vitrimers could profoundly affect many industries that rely on polymers and composites.

# Séminaire du LPTMS: J. Bonart

## Impurties in trapped one-dimensional quantum liquids

### Julius Bonart, LPTHE

Recent experiments with cold atoms on impurity dynamics immersed in trapped 1D quantum liquids have revealed an interesting interplay between the dynamic polaronic impurity mass shift and the renormalization of the optical potential. We show that the influence of the external trap on the Bose gas leads to a steeper effective potential for the impurity. We propose a framework in which this potential renormalization and the mass shift can be quantitatively understood by using a semi-classical theory of density wave excitations in the Luttinger liquid. Then we present more rigorous results on the impurity dynamics which are obtained via the non equilibrium formalism of a quantum Brownian particle. We show that the obtained theoretical results reproduce well recent experimental data.

# Soutenance HDR : Alberto Rosso

## La physique des extrêmes : de la diffusion anormale aux systèmes désordonnés

### Alberto Rosso

# Physics-Biology interface seminar : Jean-François Joanny

**Properties of the actin cortex and dynamics of cytokinesis**

### Jean-François Joanny (Institut Curie - Paris)

In this talk I discuss first the properties of the actin cortical layer in contact with the plasma membrane of a cell using the hydrodynamic theory of active gels: within this framework, the cortical layer can be viewed as an active prewetting layer.

I then discuss cytokinesis which is last stage of cell division when the two daughter cells separate. Cytokinesis proceeds by the formation of an actin contractile ring at the equator of teh cell and by contraction of this ring. The ring formation induces tension gradients in the cortical layer and a cortical flow. Using active gel theory, it is shown numerically that cytokinesis can only be completed if the activity gradient is large enough and that the radius of the contractile ring decreases linearly with time in agreement with experiments.

# Séminaire du LPTMS: Christian Hagendorf

### Spin chains with dynamical lattice supersymmetry

### Christian Hagendorf, Université de Genève

Starting from simple observations about the spectrum of the spin-1/2 XXZ and XYZ Heisenberg chains at particular anisotropy I will show how to construct a representation of the N=(2,2) supersymmetry algebra on the lattice. The supercharges are dynamical: they change the number of sites. The construction generalises to higher spin. In particular, it allows to identify lattice precursors of the N=(2,2) superconformal minimal models. The supersymmetry allows to prove the existence of zero-energy ground states which have often rich properties related to enumerative combinatorics. I will discuss in detail the case of the Fateev-Zamolodchikov chain at spin one whose ground-state components are related to the weighted enumeration of alternating sign matrices.

# Séminaire exceptionnel du LPTMS : David Saad

### David Saad (Aston University)

**Polymer physics for route optimisation on the London underground**

Optimizing paths on networks is crucial for many applications, from subway traffic to Internet communication. As global path optimization that takes account of all path-choices simultaneously is computationally hard, most existing routing algorithms optimise paths individually, thus providing sub-optimal solutions. This work includes two different aspects of routing. In the first [1] we employ the cavity approach to study analytically the routing of nodes on a graph of given topology to predefined network routers and devise the corresponding distributive optimisation algorithm. In the second [2] we employ the physics of interacting polymers and disordered systems (the replica method) to analyse macroscopic properties of generic path-optimisation problems between arbitrarily selected communicating pairs; we also derive a simple, principled, generic and distributive routing algorithm capable of considering simultaneously all individual path choices.

Two types of nonlinear interactions are considered with different objectives: 1) alleviate traffic congestion at both cyber and real space and provide better route planning; and 2) save resources by powering down non-essential and redundant routers/stations at minimal cost. This saves energy and man-power, and alleviates the need for investment in infrastructure. We show that routing becomes more difficult as the number of communicating nodes increases and exhibits interesting physical phenomena such as ergodicity breaking. The ground state of such systems reveals non-monotonic complex behaviours in average path-length and algorithmic convergence, depending on the network topology, and densities of communicating nodes and routers.

We demonstrate the efficacy of the new algorithm [2] by applying it to: (i) random graphs resembling Internet overlay networks; (ii) travel on the London underground network based on Oyster-card data; and (iii) the global airport network. Analytically derived macroscopic properties give rise to insightful new routing phenomena, including phase transitions and scaling laws, which facilitate better understanding of the appropriate operational regimes and their limitations that are difficult to obtain otherwise.

[1] C. H. Yeung, D. Saad, The Competition for Shortest Paths on Sparse Graphs, Phys. Rev. Lett., 108, 208701 (2012).

[2] C. H. Yeung, D. Saad and K. Y. M. Wong, From the Physics of Interacting Polymers to Optimizing Routes on the London Underground, submitted (2012).

# Séminaire du LPTMS: A. de Luca

## Insights into the many-body localization transition from the structure of wave functions.

### Andrea de Luca, LPT ENS

# Physics-Biology interface seminar : Carsten Janke

## Encoding functional information into the microtubule cytoskeleton

### Carsten Janke Institut Curie - Orsay

Our team is interested in the functions of tubulin posttranslational modifications. Tubulin, the building block of the microtubules, is modified by a range of very special posttranslational modifications, such as enzymatic generation of glutamate or glycine side chains, enzymatic removal and re-addition of a C-terminal tyrosine. These modifications take place once the tubulin has polymerized into microtubules, which suggests that they encode information important for the functional specification or the fine-tuning of specific microtubule functions.

While the modifications have been known for a long time, functional studies have remained difficult because nothing was known about the enzymes responsible for these modifications. The recent discovery of most of these enzymes in our team has allowed us to start functional and mechanistic studies that gave us first insights into the divergent roles of tubulin posttranslational modifications. In my presentation, I will give an overview of our first results, our ongoing projects and interests.

# Séminaire du LPTMS: V. Bapst

## On the Quantum Annealing of Quantum Mean-Field Models

### Victor Bapst, LPT ENS

In this talk I will present analytical results on the quantum annealing of quantum mean-field models. I will first explain the connection between static and dynamic properties of the model using results obtained on a toy model, the fully-connected ferromagnetic p-spin model. For p=2 this corresponds to the quantum Curie-Weiss model which exhibits a second-order phase transition, while for p>2 the transition is first order. Focusing on the latter case, I will detail the link between phase transitions, metastable states and residual excitation energy on both finite and divergent time-scales. Then, I will present a study of the thermodynamics of a more realistic optimization problem subject to quantum fluctuations: the quantum coloring problem on random regular graphs. Using the quantum cavity method, that allows to solve such models in the thermodynamic limit, we determined the order of the quantum phase transition that occurs when the transverse field is varied and unveiled the rich structure of the quantum spin-glass phase. In particular, I will explain why the quantum adiabatic algorithm would fail to solve typical instances of this problem efficiently because of entropy induced crossings within the quantum spin-glass phase.

# Journal Club du LPTMS: Kabir Ramola

## Watersheds are Schramm-Loewner Evolution Curves

#### Kabir Ramola, Post-Doc LPTMS

SLE has grown in prominence over the last decade and has helped unify several aspects of critical phenomena, percolation theory and conformal field theory. This paper discusses an interesting real world application of this somewhat technical subject.

http://prl.aps.org/abstract/PRL/v109/i21/e218701

E. Daryaei, N. A. M. Arau´jo, K. J. Schrenk, S. Rouhani, and H. J. Herrmann

Abstract of the article : We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner evolution (SLE) curves, being described by one single parameter κ. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE_{κ}, with κ=1.734±0.005, being the only known physical example of an SLE with κ<2. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore, it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic conformal field theory with a central charge c≈-7/2.

# Séminaire du LPTMS: Michel Bauer

## Mesures non-destructives en mécanique quantique, martingales et variables échangeables

### Michel Bauer, IPhT Saclay

Plus de 80 ans après la découverte des lois de la mécanique quantique, celles-ci continuent de susciter l'étonnement. La notion de mesure, en particulier, reste très mystérieuse, et ce terme recouvre aujourd'hui des processus très variés. Nous décrirons des expériences récentes très simples et belles, qui permettent de lever légèrement un coin du voile. Après quelques remarques sur les mesures en mécanique quantique, nous montrerons pourquoi l'interprétation de ces expériences est étroitement liée à des piliers de la théorie des probabilités, et en particulier au théorème de convergence des martingales. En conclusion, nous montrerons que le théorème de deFinetti sur les variables aléatoires échangeables est une piste pour expliquer la robustesse de la mesure en mécanique quantique et suggère des liens avec la notion "d'éléments de réalité".

# Physics-Biology interface seminar : Stefan Hell

## Nanoscopy with focused light

### Stefan Hell (Max Planck Institute for Biophysical Chemistry & German Cancer Research Center (DKFZ))

**SPECIAL DATE & TIME****Joint seminar with Laboratoire Aimé Cotton hosted by François Treussart**

# Journal Club du LPTMS: Ricardo Marino

## Temporal Effects in the Growth of Networks

### Ricardo Marino, PhD student LPTMS

This article explores a very interesting model in random graphs for preferential attachment with time-decaying properties, ideal for problems in which "popularity" decays over time (for instance, article citations).

**http://prl.aps.org/abstract/PRL/v107/i23/e238701**

**Matúš Medo, Giulio Cimini, and Stanislao Gualdi**

**Abstract of the article :** We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either heterogeneity or decay in isolation, we propose a simple analytically treatable model that combines these two factors. Depending on the input assumptions, the resulting degree distribution shows an exponential, log-normal or power-law decay, which makes the model an apt candidate for modeling a wide range of real systems.

# Séminaire du LPTMS: Serguei Nechaev

## From elongated spanning trees to vicious random walks

### Serguei Nechaev, LPTMS

Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r^{-nu} log r with nu = (k^2-1)/2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent nu is converting into the scaling exponent for the reunion probability (at a given point) of k (1+1)-dimensional vicious walkers, tilde{nu} = k^2/2. Some consequences and generalizations of this result will be also discussed.

# Séminaire du LPTMS: Charles Grenier

## Characterization and decoherence of minimal excitations

### Charles Grenier, CPhT Ecole Polytechnique

The recent years saw the developments of quantum optics experiments with electrons propagating along the edge channels of two-dimensional electron gases in the quantum Hall regime [1]. In this context, the realization of single electron sources is necessary to observe analogues of the fundamental results of quantum optics, such as the Hong-Ou-Mandel effect. In the electronic context, these experiments would provide unprecendented insights on the behavior of electron gases at the single-particle level [2]. In this talk, I will present a theoretical study of the single electron coherence properties of two different types of voltage pulses [3,4]. By combining bosonization and the Floquet scattering approach, the effect of interactions on a periodic source of voltage pulses is computed exactly [5]. When such excitations are injected into one of the channels of a system of two copropagating quantum Hall edge channels, they fractionalize into pulses whose characteristics reflects the properties of interactions. We show that the dependence of fractionalization induced electron/hole pair production in the pulses amplitude contains clear signatures of the fractionalization of the individual excitations. We propose an experimental setup combining a source of Lorentzian pulses [3] and an Hanbury Brown and Twiss interferometer to measure interaction induced electron/hole pair production and more generally to reconstruct single electron coherence of these excitations before and after their fractionalization.

[1] Y. Ji, et al, Nature 422, 415 (2003)

[2] P. Degiovanni, et al, Phys. Rev. B 80, 241307(R) (2009)

[3] L. Levitov, et al, J. Math. Phys. 37, 4845 (1996); D. A. Ivanov, et al, Phys. Rev. B 56, 6839 (1997); J. Keeling, et al, Phys. Rev. Lett. 97, 116403 (2006)

[4] J. Dubois, et al, preprint ArXiv:1212.3921

[5] Ch. Grenier, et al, ArXiv:1301.6777

# Séminaire de la Fédération PHYSTAT-SUD : Aris Moustakas

## Power optimization on a random wireless network: A statistical physics approach

### Aris Moustakas (National and Capodistrian University of Athens, Dept of Physics)

The efficient use of transmitted power is important in modern day wireless networks. Not only is the battery life of transmitting devices thus extended, but also the interference caused to neighboring transmitters is minimized. There are iterative methods to obtain the optimal power per node in a network, however it is known that depending on the strength of the interference, the problem may be infeasible. However, the properties of the optimal power vector in a random network, as well as the convergence to it are not well understood. In this work we study power optimization in a simple network with randomness. We show that the problem can be mapped to an Anderson model and we analyze its properties, such as the average power per transmitter, its probability of failure, the tails of its power distribution and dynamics using ideas from the theory of disordered metals.

*café/thé seront servis à 14h00*

# Physics-Biology interface seminar : Jean-François Allemand

## In vitro & in vivo single molecule approaches to DNA replication

### Jean-François Allemand (École normale supérieure)

DNA replication is an essential step of the cell cycle. Despite many biochemical studies, physical approaches can still bring new informations on some process of DNA replication.

In vitro, using micromanipulation tools, we have shown that force can trigger some DNA polymerases into an exonuclease mode where, instead of synthesizing DNA, the polymerase goes backward and removes nucleotides. This can lead to a mechanical method for DNA sequencing.

In vivo, in E. coli, using single molecule fluorescence techniques we have quantified the real time composition of the replisome, the machinary that copies DNA. We observed a time variation of the composition of the replisome with a number of DNA polymerases that varies from 2 to 3. We will see how these fluctuations are related to the synthesis of the so called Okazaki fragments. We will describe what happens to this scenario when the replication is blocked under specific conditions.

# Soutenance de thèse : Jason Sakellariou

## Inverse inference in the asymmetric Ising model

# Journal Club du LPTMS: Dario Villamaina

## Dario Villamaina, post-doc LPTMS

I will present some recent applications of non-equilibrium fluctuation theory to one-dimensional diffusive models.

### Spontaneous Symmetry Breaking at the Fluctuating Level (Phys. Rev. Lett. 107, 180601 (2011) )

http://prl.aps.org/abstract/PRL/v107/i18/e180601

Abstract: Phase transitions not allowed in equilibrium steady states may happen, however, at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While small fluctuations result from the sum of weakly correlated local events, for currents above a critical threshold the system self-organizes into a coherent traveling wave which facilitates the current deviation by gathering energy in a localized packet, thus breaking translation invariance. This results in Gaussian statistics for small fluctuations but non-Gaussian tails above the critical current. Our observations, which agree with predictions derived from hydrodynamic fluctuation theory, strongly suggest that rare events are generically associated with coherent, self-organized patterns which enhance their probability.

# Séminaire du LPTMS: Kabir Ramola

## Columnar Order and Ashkin-Teller Criticality in the Hard Square Lattice Gas

### Kabir Ramola, LPTMS Orsay

The lattice gas model of particles with nearest and next-nearest-neighbour exclusion on a square lattice (hard squares) undergoes a transition from a fluid phase at low density to a columnar ordered phase at high density. The high-activity series for this model is a singular perturbation series in powers of 1/z, where z is the fugacity associated with each particle. We show that the different terms of the series need to be regrouped to get a Mayer-like series for a polydisperse system of interacting vertical rods. We also analyse the nature of the phase transition as a function of density in this system. We argue that the critical properties of the model are that of a more general Ashkin-Teller model. We employ Monte Carlo simulations to study the correlations between various quantities in the system to get a fairly precise estimate of the position of the transition on the Ashkin-Teller critical line.

# Séminaire du LPTMS: David Mukamel

## Long-Range correlations in driven, non-equilibrium systems

### David Mukamel, Weizmann

Systems driven out of thermal equilibrium often reach a steady state which under generic conditions exhibits long-range correlations. As a result these systems sometimes share some common features with equilibrium systems with long-range interactions, such as the existence of long range-order and spontaneous symmetry breaking in one dimension, ensemble inequivalence and other properties. Some models of driven systems will be presented, and features resulting from the existence of long-range correlations will be discussed.

# Séminaire de la Fédération PHYSTAT-SUD : Peter Sollich

## Uniﬁed study of glass and jamming rheology in soft particle systems

### Peter Sollich, King's College London

Authors: Atsushi Ikeda, Ludovic Berthier, and Peter Sollich

Abstract: We explore numerically the shear rheology of soft repulsive particles at large volume fraction. The interplay between viscous dissipation and thermal motion results in multiple rheological regimes encompassing Newtonian, shear-thinning and yield stress regimes near the ‘colloidal’ glass transition when thermal ﬂuctuations are important, crossing over to qualitatively similar regimes near the ‘jamming’ transition when dissipation dominates. In the crossover regime, glass and jamming sectors coexist and give complex ﬂow curves. Although glass and jamming limits are characterized by similar macroscopic ﬂow curves, we show that they occur over distinct time and stress scales and correspond to distinct microscopic dynamics. We propose a simple rheological model describing the glass to jamming crossover in the ﬂow curves, and discuss the experimental implications of our results. Time permitting a systematic comparison of the model to data for a number of paradigmatic experimental systems will be described.

# Journal Club du LPTMS: Pierpaolo Vivo

## Pierpaolo Vivo, CNRS researcher LPTMS

### The statistical properties of the city transport in Cuernavaca (Mexico) and random matrix ensembles

I present the results of the two papers listed below on an interesting real-life system, namely the bus transportation in the Mexican city of Cuernavaca. In Cuernavaca there is no covering company responsible for organizing the city transport. Consequently, constraints such as a time table that represents external influence on the transport do not exist. Moreover, each bus is the property of the driver. The drivers try to maximize their income and hence the number of passengers they transport. This leads to competition among the drivers and to their mutual interaction. In the paper (1) below, the statistics of empirical inter-arrivals of buses was found to conform to the spacing distribution of Gaussian Unitary Ensemble (GUE) of random matrices. In the paper (2), a simple but rich model of self-avoiding walks with Poissonian rates is put forward to explain the empirical data, whose connection with GUE can be then analytically elucidated.

References:

1. M. Krbalek and P. Seba, The statistical properties of the city transport in Cuernavaca (Mexico) and random matrix ensembles, J. Phys. A: Math. Gen. 33, L229 (2000)

2. J. Baik, A. Borodin, P. Deift and T. Suidan, A model for the bus system in Cuernavaca (Mexico), J. Phys. A: Math. Gen. 39, 8965 (2006)

# Séminaire du LPTMS: G. Biroli

## Difference between Ergodicity, Level Statistics and Localization Transitions on the Bethe Lattice

### Giulio Biroli, IPhT Saclay

Random Matrix Theory was initially developed to explain the eigen-energy distribution of heavy nuclei. It has become clear by now that its domain of application is much broader and extends to very different fields such as number theory and quantum chaos, just to cite a few. In particular, it has been conjectured---and proved or verified in some special cases---that quantum ergodic (or chaotic) systems are characterized by eigen-energies statistics in the same universality class of random matrices and by eigen-functions that are delocalized over the configuration space. On the contrary, non-ergodic quantum systems, such as integrable models, are expected to display a Poisson statistics of energy levels and localized wave-functions. Starting from Anderson's pioneering papers, similar properties have also been studied for electrons hopping in a disordered environment. Remarkably, also in this case, similar features of the energy-level statistics have been found. All that has lead to the conjecture that delocalization in configuration space, ergodicity and level statistics are intertwined properties.

In this talk we revisit the old problem of non-interacting electrons hopping on a Bethe lattice with on-site disorder. By using numerical simulations, the cavity method and mapping to directed polymers in random media we unveil the existence of an intermediate phase in which wave-functions are delocalized but the energy-level statistics is Poisson. This new phase, in which the system is non-ergodic but delocalized, may play an important role in several fields from random matrix theory to strongly interacting quantum disordered systems, in particular it could be related to the non-ergodic metallic phase conjectured to exist in the context of Many-Body Localization.

# Physics-Biology interface seminar : Andrea De Martino

## MicroRNAs: a selective channel of communication between competing RNAs

### Andrea De Martino (Sapienza Universita' di Roma)

It has recently been suggested that the competition for a finite pool of microRNAs (miRNA) gives rise to effective interactions among their common targets (competing endogenous RNAs or ceRNAs) that could prove to be crucial for post-transcriptional regulation (PTR). I shall discuss a minimal model of PTR where the emergence and the nature of such interactions can be characterized in detail at steady state. Sensitivity analysis shows that binding free energies and repression mechanisms are the key ingredients for the cross-talk between ceRNAs to arise. Interactions emerge in specific ranges of repression values, can be symmetrical (one ceRNA influences another and vice-versa) or asymmetrical (one ceRNA influences another but not the reverse) and may be highly selective, while possibly limited by noise. Finally, I will show that non-trivial correlations among ceRNAs can emerge in experimental readouts due to transcriptional fluctuations even in absence of miRNA-mediated cross-talk, so that more refined analyses will be needed to identify signatures of cross-talk in the transcriptome.

# Séminaire du LPTMS: Camille Aron

## Strongly Correlated Electrons Driven by an Electric Field

### Camille Aron, Rutgers University

Strongly correlated many-body systems driven out of equilibrium are attracting a lot of interest, motivated by new experimental realizations in non-linear transport in devices, heterostructures and cold atoms. Theoretically, the challenge is to understand the interplay between the strong correlation and the finite drive. In this talk, I will focus on the Hubbard model driven by a constant electric field. First, I will introduce some theoretical tools to address the non-equilibrium steady states, bypassing the transient dynamics. At the dynamical mean-field level, I will describe how the lattice problem can be self-consistently mapped to a multi-lead Anderson impurity model. Afterwards, I will discuss the fate of Mott physics in the non-linear regime by detailing two key far-from-equilibrium phenomena:

- the dimensional crossover towards a lower dimensional equilibrium system;

- the dielectric breakdown of the Mott insulator.

References:

C. Aron, G. Kotliar, C. Weber, PRL 108, 086401 (2012)

C. Aron, PRB 86, 085127 (2012)

C. Aon, C. Weber, G. Kotliar, arXiv:1210.4926 (2012)

# Séminaire du LPTMS: Chase Broedersz

## Actively stressed marginal networks

### Chase Broedersz, Princeton University

The mechanical properties of cells are regulated in part by internal stresses generated actively by molecular motors in the cytoskeleton. Experiments on reconstituted intracellular F-actin networks with myosin motors show that such active contractility dramatically affects network elasticity. There is also experimental evidence that cytoskeletal networks in living cells may be unstable or only marginally stable in the absence of motor activity. We study the impact of active stresses on the mechanics of disordered, marginally stable networks using a simple model for networks of fibers with linear bending and stretching elasticity. Motor activity controls the elasticity in an anomalous fashion close to the point of marginal stability by coupling to critical network fluctuations. In addition, such motor stresses can stabilize initially floppy networks, extending the range of critical behavior to a broad regime of network connectivities below the marginal point. Away from this regime, or at high stress, motors give rise to a linear increase in stiffness with stress. The remarkable mechanical response of these actively stressed networks is captured by a simple, constitutive scaling relation, which highlights the important role of nonaffine strain fluctuations as a susceptibility to motor stress.

# Séminaire de la Fédération PHYSTAT-SUD : Tomohiro Sasamoto

**Fluctuations in the 1D Kardar-Parisi-Zhang equation and discrete analogues**

**Tomohiro SASAMOTO **(Chiba University, Japan)

The Kardar-Parisi-Zhang (KPZ) equation is a non-linear stochastic partial differential equation which describes surface growth phenomena. Recently its one-dimensional version has attracted much attention because of several exciting experimental and theoretical developments [1].

In this talk we discuss the replica analysis of the KPZ equation and its discrete analogues. Starting from the basics of the KPZ equation and the replica analysis, we explain how one can utilize it for the analysis of the KPZ equation [2], where are the tricky parts, and how they are regularized in discrete models like q-TASEP [3].

References:

[1] K.A. Takeuchi, M. Sano, T. Sasamoto and H. Spohn, Growing interfaces uncover universal fluctuations behind scale invariance, Sci. Rep. 1 (2011) 34.

[2] T. Imamura and T. Sasamoto, Exact solution for the stationary KPZ equation, Phys. Rev. Lett. 108 (2012) 190603.

[3] A. Borodin, I. Corwin and T. Sasamoto, From duality to determinants for q-TASEP and ASEP, arXiv:1207.5035.

# Physics-Biology interface seminar : Chase Broedersz

## Localization and condensation of the parB-DNA complex in the bacterial chromosome

### Chase Broedersz (Princeton University)

The molecular machinery responsible for faithful segregation of the chromosome in bacteria such as Caulobacter crescentus and Bacillus subtilis includes the ParABS a.k.a. Spo0J/Soj partitioning system. In Caulobacter, prior to division, hundreds of ParB proteins bind to the chromosome near the origin of replication, and localize to one pole of the cell. Subsequently, the ParB-DNA complex is translocated to the far pole by the binding and retraction of the ParA spindle-like apparatus. Remarkably, the localization of ParB proteins to specific regions of the chromosome appears to be controlled by only a few centromeric parS binding sites. Although lateral interactions between DNA-bound ParB are likely to be important for their localization, the long-range order of ParB domains on the chromosome appears to be inconsistent with a picture in which protein-protein interactions are limited to neighboring DNA-bound proteins. We propose a simple model to study the localization and condensation of the ParB-DNA complex, which includes both lateral and 3D protein-protein interactions among DNA-bound ParB proteins. Our model shows how such interactions can condense and organize the chromosome spatially, and can control both the localization and the long-range order of the DNA-bound proteins. Interestingly, the condensed ParB-DNA complex adopts a topology in which loops of DNA extend outside the cluster exposed for transcription; this structure may have implications for expression levels of genes in the vicinity of the parS site.

# Journal Club du LPTMS: Andrey Lokhov

## Andrey Lokhov: Ph.D. Student LPTMS

### Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models

##### M. Ekeberg, C. Lovkvist, Y. Lan, M. Weigt, E. Aurell, Phys. Rev. E 87, 012707 (2013)

Spatially proximate amino acids in a protein tend to coevolve. A protein’s 3D structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction, but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.

# Séminaire du LPTMS: P. Soulé et P.-E. Larré

**Wave pattern generated by an obstacle moving in a one-dimensional polariton condensate**

### Pierre-Elie Larré, LPTMS

Motivated by recent experiments on generation of wave patterns in polariton condensates, we analyze superfluid and dissipative characteristics of the one-dimensional flow of a nonresonantly-pumped polariton condensate past a localized obstacle. We consider the response of the condensate flow in the weak-perturbation limit, but also by means of the Whitham averaging theory in the nonlinear regime. One of the results of this work is the identification of a new time-dependent regime separating two types of stationary flows (a mostly viscous one and another one dominated by Cherenkov radiation).

I will also present results obtained by including polarization effects in the description of the polariton condensate, and I will argue that similar effects in presence of an acoustic horizon offer possibilities for demonstrating Hawking-like radiation in polariton condensates.

## Many-body study of a quantum point contact in the fractional quantum Hall regime

### Paul Soulé, LPTMS

Fractional Quantum Hall (FQH) fluids have a low-energy effective theory localized at their edges. The edge states are expected to form a very special one-dimensional strongly interacting electronic system, a chiral Luttinger liquid. Depending on FQH phases, a variety of 1D models has been proposed. But only poor experimental agreements have been found yet.

Using exact diagonalizations in the cylinder geometry we identify the edge modes in the presence of a parabolic confining potential at Landau level filling factors v=1/3 and v=5/2. If we change the sign of the potential we can access both the tunneling through the bulk of the fluid and the tunneling between spatially separated droplets, and measure numerically Luttinger parameters in both cases. These phenomena are at the basis of tunneling experiments in quantum point contact devices of two-dimensional electron gases.

P. Soulé, T. Jolicoeur, Phys. Rev. B 86, 115214 (2012)

P. Soulé, T. Jolicoeur, in preparation

# Physics-Biology interface seminar: Emmanuèle Helfer

## Polymerization of actin branched networks controls the organization of WASH domains at the surface of endosomes

### Emmanuèle Helfer (Laboratoire d'Enzymologie et de Biochimie Structurales - Gif-sur-Yvette)

Sorting of cargoes in endosomes occurs through their selective enrichment into sorting platforms, where transport intermediates are generated. The WASH complex, which is recruited from the cytosol to endosomes, activates the Arp2/3 complex and hence actin polymerization onto such sorting platforms.

Here, we analyzed the role of actin polymerization in the physiology of endosomal domains containing WASH using quantitative image analysis. Using a novel colocalization method that is insensitive to the heterogeneity of size and shape of endosomes, we show that preventing the generation of branched actin networks induces endosomal accumulation of the WASH complex. Moreover, we found that actin depolymerization induces a dramatic decrease in the recovery of endosomal WASH after photobleaching. These results suggest a built-in turnover, where the actin network, i.e. the product of the WASH complex, contributes to the dynamic cytosol/endosome exchange of the WASH complex. Our data also suggest a role of actin in the lateral compartmentalization of endosomes: discrete WASH domains coalesce upon actin depolymerization or Arp2/3 depletion. Thus, branched actin networks are involved in the regulation of WASH domain size.

I will finally discuss the potential role of lipid repartitioning in these sorting platforms and of the ensuing line tension that could develop at the domain boundary. This may provide a dynamin-independent contribution to membrane scission.

# Journal Club du LPTMS: Dmitry Petrov

## Dmitry Petrov, CNRS researcher LPTMS

### Title: Quantum annealing with more than one hundred qubits

#### Authors: Sergio Boixo, Troels F. Ronnow, Sergei V. Isakov, Zhihui Wang, David Wecker, Daniel A. Lidar, John M. Martinis, and Matthias Troyer

The paper is not publicly available as it is submitted to Nature, but I explained Matthias our Journal Club idea and he sent me the preprint asking to keep it for our private use. I will put the preprint on our coffee table together with the D-Wave Systems wikipedia page. Enjoy.

Abstract:

At a time when quantum effects start to pose limits to further miniaturisation of devices and the exponential performance increase due to Moore's law, quantum technology is maturing to the point where quantum devices, such as quantum communication systems, quantum random number generators and quantum simulators, may be built with powers exceeding the performance of classical computers. A quantum annealer, in particular, finds solutions to hard optimisation problems by evolving a known initial configuration towards the ground state of a Hamiltonian that encodes an optimisation problem. Here, we present results from experiments on a 108 qubit D-Wave One device based on superconducting flux qubits. The correlations between the device and a simulated quantum annealer demonstrate that the device performs quantum annealing: unlike classical thermal annealing it exhibits a bimodal separation of hard and easy problems, with small-gap avoided level crossings characterizing the hard problems. To assess the computational power of the quantum annealer we compare it to optimised classical algorithms. We discuss how quantum speedup could be detected on devices scaled to a larger number of qubits where the limits of classical algorithms are reached.

See also

http://en.wikipedia.org/wiki/D-Wave_Systems

http://www.nytimes.com/2013/03/22/technology/testing-a-new-class-of-speedy-computer.html?pagewanted=all&_r=2&

http://www.nature.com/nature/journal/v473/n7346/full/nature10012.html

http://arxiv.org/abs/1302.5843

http://arxiv.org/abs/1102.1296

# Séminaire du LPTMS: Sébastien Balibar

## La Plasticité Géante d'un Cristal Quantique

### Sébastien Balibar, Laboratoire de Physique Statistique de l'ENS

Nous avons découvert [1] que les cristaux d'hélium 4 présentent une plasticité géante à très basse température si l'on élimine toutes leurs impuretés. Ils ne résistent pratiquement pas au cisaillement dans une direction particulière, même sous contrainte extrêmement faible (1 nanobar) et au voisinage du zéro absolu (0.01 Kelvin). Ce phénomène est un exemple spectaculaire de "plasticité" car c'est une conséquence du mouvement libre des dislocations dans une direction que nous avons identifiée, ce qui réduit l'un des coefficients élastiques d'environ 80% même sous l'effet de contraintes extrêmement faibles (1 nanobar). On notera cependant que, contrairement à la plasticité classique, il s'agit d'un effet réversible. Il disparaît dès que des traces d'impuretés s'attachent aux dislocations ou si la température augmente ce qui induit des collisions entre les dislocations en mouvement et les phonons thermiques.

Ce dernier phénomène nous a permis[2] de mesurer la densité de ces dislocations et leur longueur libre qui est très grande (50 à 200 microns) ce qui prouve que les dislocations sont peu connectées entre elles, plus probablement alignées parallelement les unes aux autres.

Toutes ces observations récentes [1,2] démontrent que ces cristaux ne sont vraisemblablement pas "supersolides" comme cela avait été proposé en 2004, et qu'au contraire, leurs apparentes anomalies de rotation sont des artefacts dus à la plasticité géante que nous avons mise en évidence.

[1] A. Haziot, X. Rojas, A. Fefferman, J. Beamish and S. Balibar, Phys. Rev. Lett. 110, 035301 (2013)

[2] A. Haziot, A. Fefferman, J. Beamish, and S. Balibar, Phys. Rev. B 90, 060509(R) (2013).

# Séminaire du LPTMS: Christophe Texier

## Distribution du temps de Wigner dans des cavités chaotiques

### Christophe Texier, LPTMS

The Wigner time delay captures temporal aspect of the scattering process. Due to its relation with the density of states of the open system (here a chaotic cavity), it is also of great interest for the study of coherent electronic transport in mesoscopic devices.

Using the joint distribution for proper time-delays of a chaotic cavity derived by Brouwer, Frahm & Beenakker [Phys. Rev. Lett. **78**, 4737 (1997)], we obtain, in the limit of large number of channels *N*, the large deviation function for the distribution of the Wigner time-delay (the sum of proper times) by a Coulomb gas method.

We show that the existence of a power law tail originates from narrow resonance contributions, related to a (second order) freezing transition in the Coulomb gas.

# Physics-Biology interface seminar : Karen Perronet

**Cinétique de traduction de ribosomes individuels par microscope de fluorescence**

**Karen Perronet (**Laboratoire Charles Fabry, Institut d'Optique)

**Karen Perronet (**Laboratoire Charles Fabry, Institut d'Optique)

Le ribosome est le moteur moléculaire traduisant le code génétique de l’ARNm en protéine. La dynamique de ce processus asynchrone primordial est encore mal connue, surtout chez les eucaryotes. Pouvoir suivre des ribosomes individuels pendant la traduction est donc un enjeu important.

Nous présentons dans ce séminaire différentes stratégies permettant d’étudier la vitesse d’élongation de ribosomes individuels par microscopie de fluorescence en réflexion totale.

Nous avons tout d’abord utilisé des ribosomes procaryotes mutants que nous avons marqués avec un nano-cristal semi-conducteur fluorescent. Nous avons ainsi pu mesurer la vitesse globale de traduction d’une protéine.

Nous avons ensuite hybridé des oligonucléotides fluorescents sur l’ARNm, les départs des marqueurs signalant alors le passage des ribosomes à leurs emplacements. Nous avons alors utilisé des ribosomes eucaryotes, encore très peu étudiés à l’échelle de la molécule unique. Les ribosomes sont initialement immobilisés sur l’ARNm grâce à une IRES, structure secondaire spécifique permettant une initiation non canonique du ribosome. Puis suite à l’injection d’un système de traduction in-vitro, ils peuvent traduire la protéine et atteindre les oligonucléotides marqués, qu’ils détachent grâce à leur activité hélicase. Ces dissociations se traduisent par une disparition du signal de fluorescence des marqueurs qui diffusent hors de l’onde évanescente. Nous avons ainsi pu observer la distribution des durées de traduction jusqu’à des endroits spécifiques de l’ARNm. Nous avons pu extraire deux durées caractéristiques pour l’élongation. La première (typ. 40 s) est associée au premier cycle d’élongation, ralentie par le fait que le ribosome doit s’extraire de l’IRES. La seconde (~1s) correspond à un cycle d’élongation normal.

# Séminaire du LPTMS: Edouard Hannezo

## Epithelial sheet morphologies

### E. Hannezo, Institut Curie

Understanding morphogenesis during the development of the embryo requires an understanding of how mechanical forces coordinate to generate the macroscopic shape of organs. Although it is acknowledged that adhesion and mechanical forces play a crucial role in determining the morphology of a cell, a precise model remains elusive. We propose a simple theoretical model based on adhesion and acto-myosin generated forces to study the morphology of epithelial cells and the 3D topology of epithelial sheets.

# Séminaire de la Fédération PHYSTAT-SUD : Jesper Jacobsen

## Critical manifolds for percolation and Potts models from graph polynomials

### Jesper Jacobsen (Labo. de Physique Théorique de l'Ecole Normale Supérieure, Paris)

The first parameter to be fixed when studying a phase transition is the critical temperature. Somewhat surprisingly, this parameter is only known analytically for the simplest two-dimensional models (Ising model), or for more complicated models (Potts and O(n) vector models) on the simplest possible lattices. The known critical temperatures are invariably given by simple algebraic curves. Some of these results have very recently been proved mathematically by the technique of discrete holomorphicity.

For Potts and (bond or site) percolation models on any desired two-dimensional lattice we define a graph polynomial whose roots turn out to give very accurate approximations to the critical temperatures, or even yield the exact result in the exactly solvable cases. This polynomial depends on a basis (unit cell) and its embedding into the infinite lattice. As the size of the basis is increased the approximation becomes increasingly accurate. This, on the one hand, gives strong evidence that the critical temperature for the lattices with no known analytical solution may not be algebraic numbers, and that conformal invariance will not have any counterpart in finite size (discrete holomorphicity). On the other hand, the method determines the critical temperature to unprecedented accuracy, typically 12-13 significant digits for bond percolation thresholds. It also shows that the phase diagram of the Potts model in the antiferromagnetic regime has an intricate and highly lattice-dependent structure.

# Séminaire du LPTMS: Marie-Hélène Genest

## Supersymmetry and dark matter at the LHC

### Marie-Hélène Genest, LPSC Grenoble

The presence of Cold Dark Matter in the universe has been evinced by a number of astrophysical experiments. Direct and indirect detection experiments are looking for evidences of the presence of this elusive new particle. In a completely complementary approach, one can look for the production of such weakly interacting massive particles (WIMPs) at the LHC, either by looking for direct production of such WIMPs or by looking for supersymmetry, an appealing theory beyond the Standard Model of particles which provides a natural Cold Dark Matter candidate.

# Physics-Biology interface seminar : Claire Wilhelm

## Magnetic living cells: New tools for cell imaging, tissue engineering and cell therapies

### Claire Wilhelm (Université Paris 7)

Recent advances in cell therapy and tissue engineering opened new windows for regenerative medicine, but still necessitate innovative techniques to create and image functional tissues. One promising approach is to associate magnetic nanoparticles with cells in order to supply them with sufficient magnetization to be detectable by MRI or manipulated by magnetic forces, while maintaining cell viability and functionalities. A few years ago, we proposed the use of anionic iron oxide nanoparticles as efficient agents for cell internalisation without impacting cell functions. Recently we examined the influence of the amount of internalized iron and the state of nanoparticle aggregation on the capacity for mesenchymal stem cell differentiation and MRI single cell tracking. We then demonstrated that high resolution Magnetic Resonance Imaging (MRI) allowed combining cellular-scale resolution with the ability to detect two cell types simultaneously at any tissue depth. In parallel, we addressed the challenge to create a functional tissue from stem cells in vitro. The aim was to confine stem cells in three dimensions at the millimetric scale by using home-designed miniaturized magnetic devices, in order to create cellular patterns for stem cell differentiation and tissue engineering.

Finally magnetic nanoparticles show also great promises for antitumor cell therapies, in particular using the magnetic hyperthermia modality. Cellular internalization of magnetic nanoparticles localizes the source of heat in the internal volume of the cell, with direct application for tumor cell therapies. The combination of cell-derived vesicles with magnetic nanoparticles creates multifunctional bio-inspired nanovectors with promising potential for diagnosis and therapy.

# Séminaire exceptionnel du LPTMS : Andrey Yanovsky

## Effect of winding edge currents

### Andrey Yanovsky (B. Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine)

Some degrees of freedom “interact”' with the velocity winding of trajectories, e.g. spin. We discuss the connection between spintronics and winding: namely its relation to Spin-hall effect and Thomas precession. Further we discuss persistent currents for particles with internal degrees of freedom. The currents arise because of winding properties essential for the chaotic motion of the particles in a confined geometry. The currents do not change the particle concentrations or thermodynamics, similar to the skipping orbits in a magnetic field. One of the possible realization are persistent currents in conditions of “extrinsic”' spin Hall effect. The effect is classical in contrast to similar currents predicted for conditions of quantum “intrinsic” spin Hall effect. An analytical solution has been found in an Ornstein-Uhlenbeck process. Weak dependence of the winding currents on the form of confined potential has been uncovered. The results can be of interest beyond the scope of phenomena associated with the spin Hall effect.

*S. Ouvry, L .Pastur, A. Yanovsky, **Physics Letters A 377 (2013), pp. 804-809*

# Séminaire du LPTMS: Véronique Terras

## Algberaic Bethe Ansatz approach to correlation functions of integrable systems: a review

### Véronique Terras, ENS Lyon

This is a review of recent results concerning the computation, in the algebraic Bethe Ansatz framework, of correlation functions of integrable systems. On the simple example of the XXZ spin 1/2 Heisenberg chain, I will explain how to obtain exact representations for the form factors and correlations functions on the lattice, both in finite volume and at the thermodynamic limit. I will then explain how these representations can be used to derive the large distance asymptotic behavior of the two-point functions at the thermodynamic limit and in the critical regime of the chain. I will finally discuss how the method can be applied to more complicated models, such as the exactly solvable solid-on-solid model.

# Journal Club du LPTMS : François Landes

**François Landes **(PhD student LPTMS)

She, Z., Aurell, E. & Frisch, U. The inviscid Burgers equation with initial data of Brownian type. Communications in Mathematical Physics 148, 623–641 (1992). Freely available at : http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104251047

Title: The inviscid Burgers equation with initial data of Brownian type.

Authors: Zhen-su She, Erik Aurell and Uriel Frisch.

In my presentation (aimed mainly at the sutdents) I will introduce Burgers' equation, its link with Navier-Stokes and the phase-diffusion equation, and show how its inviscid limit can be simply solved using a Cole-Hopf transform. In this limit, at long times, the velocity field develops shocks (singularities), which have interesting statistical properties (e.g. they are scale-free distributions). I will motivate the use of non-smooth, random initial conditions, then present a few results obtained with this kind of initial condition.

# Physics-Biology interface seminar : David Dulin

## Dynamics of transcription and error incorporation in a viral RNA-dependent RNA polymerase

### David Dulin (Delft University of Technology)

RNA-dependent RNA polymerases (RdRPs) are essential enzymes that govern transcription and replication in RNA viruses. While RNA elongation forms an important therapeutic target against viral infection, little is known about elongation dynamics at the single-molecule level. Here, we study the well-established RdRP model system of P2 from the double-stranded RNA bacteriophage Φ6 using high-throughput single-molecule force-spectroscopy combined with theoretical modeling. We show that P2 elongation dynamics is irregular, with rapid transcription repeatedly interrupted by pauses whose durations vary from seconds to thousands of seconds. Exploiting the discriminatory power offered by our large datasets, together with specifically-adapted analysis, we introduce a stochastic dynamical model of P2 transcriptional elongation. Our results imply that the majority of pauses result from nucleotide misincorporation, providing a direct link between RdRP dynamics and error rates—rates that offer potential drug targets, as they must be finely tuned to confer both genome stability between generations and adaptability to bypass host defense systems.

# Séminaire du LPTMS : Bernard Hellfer

## Opérateurs d'Aharonov-Bohm et Partitions Spectrales Minimales

### Bernard Hellfer (Dept Math Paris Sud)

"Si l'effet d'Aharonov-Bohm fut au départ une expérience dans un domaine non-borné non simplement connexe interprêté par le scattering, l'étude des propriétés spectrales de l'opérateur d'Aharonov-Bohm dans un domaine borné apparaît dans beaucoup d'autres questions en particulier dans l'étude du diamagnétisme et du paramagnétisme. Une situation très particulière correspond au cas où les flux créés aux pôles sont des multiples impairs de Pi. Nous discuterons de ce cas en liaison avec la question des parties spectrales minimales, question qui apparaît comme situation limite en dynamique des populations."

# Séminaire de la Fédération PHYSTAT-SUD : Rémi Monasson

## Cross-talk and transitions between spatial charts in a neuronal model of the hippocampus

### Rémi Monasson (LPTENS, Paris)

Understanding the mechanisms by which space gets represented in the brain is a fundamental problem in neuroscience. The experimental discovery of so-called "place cells" and "grid cells", encoding specific positions in space, provide essential elements in this context. How a spatial chart i.e. a relation between different points in space, may be built and memorized? In this talk I will present a model of neural network capable of storing several spatial charts. This model may be solved with the help of the techniques of Statistical Physics of Disordered Systems. We will discuss the different possible phases of the system and the essential features of its dynamics (activated diffusion in one chart and transitions between charts), in relation with recent experiments.

# Physics-Biology interface seminar : Michael Murrell

## Mechanical Force Generation and Turnover in the Cell Cytoskeleton

### Michael Murrell (University of Wisconsin, Madison)

Myosin II motors drive contractility of the cortical actin network, enabling shape change and cytoplasmic flows underlying diverse physiological processes ranging from cell division and migration to tissue morphogenesis. Yet, despite its importance, the mechanisms that describe contractility and the generation of mechanical forces within the cortex are not well understood. We recapitulate contractility in vitro, through the development of a minimal model of the cell actomyosin cortex by coupling a two-dimensional, cross-linked F-actin network decorated by myosin thick filaments to a model cell membrane. Myosin motors generate both compressive and tensile stresses on F-actin and consequently, induce large bending fluctuations. Over a large range of crosslinking, we show the extent of network contraction corresponds exactly to the extent of individual F-actin shortening via buckling. This demonstrates an essential role of buckling in facilitating local compression to enable mesoscale network contraction of up to 80% strain. Buckled F-actin at high curvatures are prone to severing and thus, compressive stresses mechanically coordinate contractility with F-actin severing, the initial step of F-actin turnover. Finally, the F-actin curvature acquired by myosin-induced stresses can be further constrained by adhesion of the network to a membrane, accelerating filament severing but inhibiting the long-range transmission of the stresses necessary for network contractility. Thus, the extent of membrane adhesion can regulate the coupling between network contraction and F-actin severing. These data demonstrate the essential role of the non-linear response of Factin to compressive stresses in potentiating both myosin-mediated contractility and filament dynamics.

# Séminaire du LPTMS: Rodolfo Jalabert

## Scattering Phase of Quantum Dots: Emergence of Universal Behavior

### Rodolfo Jalabert, Institut de Physique et Chimie des Materiaux de Strasbourg

In a coherent conductor like a quantum dot, the transmission phase is of key importance in determining the transport properties. Unlike the conductance, the transmission phase is not directly measurable. Nevertheless, phase-sensitive experiments have been performed by embedding a quantum dot in one of the arms of an Aharonov-Bohm interferometer. These experiments, observing in-phase behavior between consecutive Coulomb-blockade resonances, have remained unexplained for more than a decade. We provide a solution of this puzzle by showing that wave-function correlations existing in chaotic ballistic quantum dots are responsible for the emergence of large universal sequences of in-phase resonances in the short wavelength limit [1]. In quantum dots with at least one hundred electrons the description of Coulomb blockade physics within a constant charging energy model allows for an effective one-particle description. Smaller dots require going beyond mean-field approaches by including the effect of electronic correlations. We develop a numerical method, using the Density Matrix Renormalization Group algorithm, in order to obtain the transmission phase of a strongly interacting system. We demonstrate that electronic correlations do not generically lead to the in-phase behavior and that small dots are always in the mesoscopic regime of random relative transmission phases [2].

[1] R.A. Molina, R.A. Jalabert, D. Weinmann, and Ph. Jacquod; Phys. Rev. Lett. 108, 076803 (2012).

[2] R.A. Molina, P. Schmitteckert, D. Weinmann, R.A. Jalabert, and Ph. Jacquod; arXiv:1212.2114 (2012).

# Journal Club du LPTMS : Guillaume Roux

## "Quantum quenches through experimental examples"

### Guillaume Roux (LPTMS)

"The subject of quantum quenches is introduced through two recent experimental results:

http://fr.arxiv.org/abs/1111.0776 Nature 481, 484 (2012)

http://fr.arxiv.org/abs/1211.0545 Science 339, 52 (2013)

The program will be to briefly recall the physics of cold atoms loaded in an optical lattice, to focus on some general questions concerning the time-evolution of closed quantum many-body systems (thermalization, relaxation and non-equilibrium physics), and to explain in more details the results obtained in these two experiments. "

# Séminaire du LPTMS: Max Atkin

## From Instantons to Large Deviations in Hermitian Random Matrices

### Max Atkin (University of Bielefeld)

The typical fluctuations of the largest eigenvalue of a Hermitian random matrix about its mean has been known for a long time to be given by the Tracy-Widom distribution. More recently interest has focused on the 'atypical' fluctuations in which an eigenvalue appears very far from the bulk spectrum. This problem has been attacked using saddle point methods, loop equations and, to a much lesser extent, orthogonal polynomials. In this talk we review recent progress in the orthogonal polynomial approach which makes contact with instanton effects in the string theory literature. We use this framework to derive the distribution for large deviations in the case of multi-critical potentials.

# Physics-Biology interface seminar : Abdul Barakat

## Mechanotransduction in Vascular Endothelial Cells: Mechanisms and Implications

### Abdul Barakat (École Polytechnique)

The ability of arterial endothelial cells, the cells lining the inner surfaces of blood vessels, to respond to mechanical forces associated with blood flow is essential for normal vascular function. Abnormalities in endothelial cell mechanotransduction play a critical role in the development and progression of cardiovascular disease. The mechanisms governing how endothelial cells sense mechanical forces on their surfaces and how they subsequently transmit these forces within the intracellular space remain poorly understood. In this talk, I will present experimental and computational results in support of a central role for the cellular cytoskeleton in force transmission within endothelial cells. Because endothelial cells are often simultaneously exposed to multiple biophysical stimuli, I will show data that demonstrate that endothelial cells integrate biophysical stimuli derived from simultaneous apical cellular stimulation by flow and basal stimulation by nano-scale substrate patterning. Finally, I will discuss the role of proteins that link the cytoskeleton to the nucleus in modulating mechanotransduction in endothelial cells.

# Séminaire du LPTMS: M. Kardar

## Levitation by Casimir forces in and out of equilibrium

### Mehran Kardar, MIT

A generalization of Earnshaw's theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. In the off-equilibrium context, I shall discuss non-classical heat transfer, and some manifestations of the dynamical Casimir effect.

# Journal Club du LPTMS: Olivier Giraud

## Orbiting walkers

### Olivier Giraud (LPTMS)

"Trajectory eigenmodes of an orbiting wave source", E. Fort and Y. Couder, EPL 102, 16005 (2013)

"Level splitting at Macroscopic scale", A. Eddi, J. Moukhtar, S. Perrard, E. Fort and Y. Couder, PRL 108, 264503 (2012)

Des surfaces liquides soumises à une vibration verticale périodique peuvent soutenir le rebond de gouttelettes liquides pendant des temps longs. Ces gouttelettes peuvent être animées de mouvements horizontaux dus à leur interaction avec l'onde qu'elles génèrent à chaque rebond, se transformant ainsi en "marcheurs". Diverses analogies avec le comportement de particules quantiques ont été observées (quantification des orbites, effet tunnel).

Nous rappellerons les principes de base de ces expériences et présenterons des résultats récents sur le mouvement et les propriétés de marcheurs soumis à une force centrale.

# Séminaire du LPTMS : Anupam Kundu

## Exact distributions of the number of distinct and common sites visited by N independant random walkers

### Anupam Kundu (LPTMS)

# Physics-Biology interface seminar : Christoph Cremer

## Fluorescence Microscopy of Biostructures @ Molecular Optical Resolution

### Christoph Cremer (Institute of Molecular Biology (IMB), Mainz; Kirchhoff-Institute for Physics (KIP) and Institute for Pharmacy and Molecular Biotechnology (IPMB), University Heidelberg )

**SPECIAL DATE & TIME Seminar hosted by Olivier Acher & Guillaume Dupuis**

Conventional epifluorescence microscopy is limited in resolution (to about 200 nm laterally, 600 nm axially) by the shere nature of light (by diffraction), and is hence insufficient to study the nanostructure of subcellular components.

At IMB-Mainz and Heidelberg University we have established a variety of superresolution microscopy ("nanoscopy") methods, for example Structured Illumination SMI and Localisation microscopy SPDMphmyd with blinking dyes, like standard GFP. Our microscope systems can and have been applied to study the composition, function and metabolism of many biomolecular structures and small paticles like single viruses in high densities. Currently we reach a resolution down to 5 nm in 2D and 40 nm in 3D in the co-localization mode.

There are various applications in the fields of molecular biology, (clinical) medicine, diagnosis and pathology.

- Christoph Cremer, Barry R. Masters (2013) Resolution enhancement techniques in microscopy, The European Physical Journal H 38, 3, pp 281-344
- Kaufmann R, Muller P, Hausmann M and Cremer C (2011). Imaging label-free intracellular structures by localisation microscopy. Micron, 42, 348-352.
- Kaufmann R, Müller P, Hildenbrand G, Hausmann M and Cremer C (2011) Analysis of Her2/neu membrane protein clusters in different types of breast cancer cells using localization microscopy. Journal of Microscopy, 242, 46-54.
- Gunkel M, Erdel F, Rippe K, Lemmer P, Kaufmann R, Hoermann C, Amberger R and Cremer C (2009). Dual color localization microscopy of cellular nanostructures. Biotechnology Journal, 4, 927-938.

# Séminaire "Fluides quantiques" du LPTMS

## Dopon-spinon confinement in the t-J model

### Alvaro Ferraz (Department of Theoretical and Experimental Physics, Federal University of Rio Grande do Norte, Brasil)

# Séminaire exceptionnel du LPTMS : Adélaïde Raguin

## Traffic regulated by junctions: A statistical model motivated by cytoskeletal transport

### Adélaïde Raguin, Université Montpellier 2

Active intracellular transport of motor proteins along the cytoskeleton is an important mechanism essential to accomplish many biological functions in eukaryotic cells. For instance, motor protein transport is involved in cell migration, feeding of the cell, and cell contractions. Importantly, several neurodegenerative diseases are a consequence of the malfunctioning of motor protein transport.

Motor protein transport forms as well a challenge in statistical physics. It consists in the study of a non-equilibrium transport process along a complex and dynamic network. The totally asymmetric simple exclusion process (TASEP) can be considered as a minimal model to study motor protein transport. Along a single segment this model has been well studied, but how active particles organize along a complex networks has not been studied extensively. Motivated by recent experimental works based on tracer experiments of motor proteins moving along junctions of intersecting cytoskeletal filaments we formulate the TASEP along a junction. The first part of my talk will deal with how the microscopic traffic dynamics at a junction can modulate the transport on the whole network. In the second part of my talk I will introduce a more realistic model of motor protein transport at the junctions. Using the tools developed earlier I can characterize the various stationary states of motors moving along complex junctions as arising in living cells.

# Séminaire exceptionnel du LPTMS : Paolo Malgaretti

## Molecular motors: velocity speed-up, bidirectional motion and confinement-induced rectification

### Paolo Malgaretti (University of Barcelona)

The energy-consuming motion of molecular motors is responsible form many cellular tasks, ranging from cargo transport, cellular signalling and cellular division. The performances of single motors are strongly affected by the environment in which they work. Variation in ATP concentration, viscosity of the cytoplasm due to molecular crowding and motor-motor interactions can strongly affect the overall performances of molecular motors. Here I will focus on how the cytoplasm molecular motors move in affects single as well collective molecular motors dynamics. On one hand I will show that, due to their reduced sizes and velocities, molecular motors move in the low Reynolds regime where the large range of the hydrodynamic interaction lead to collective behaviour not captured by the rigid-coupling picture. Such interaction lead to large velocity speed-up that can be up to two order of magnitude as compared to the single motor case[1]. On the other hand hydrodynamic coupling can lead to spontaneous symmetry breaking when motors pulling on opposite direction act on the same cargo[2].

On the other hand the high concentration of suspended molecules and proteins in the cytoplasm as well as local geometrical confinement imposed by organelles or large vesicles in suspension can affect molecular motors dynamics.

I will show that the effective space motors can explore while moving along a filament lead to a local bias that, coupling to the motor intrinsic stepping mechanism, provides an alternative route to control molecular motors velocity[3].

[1] P. Malgaretti, I. Pagonabarraga, D. Frenkel ``Running faster together: Huge Speed up of Thermal Ratchets due to Hydrodynamic Coupling, Phys. Rev. Lett. 109, 168101 (2012)

[2] P.Malgaretti, I. Pagonabarraga, J-F. Joanny, in preparation

[3] P.Malgaretti, I. Pagonabarraga, J. M. Rubi, Confined Brownian ratchets, J. Chem. Phys. 138, 194906 (2013)

# Soutenance de thèse : Arthur Lavarélo

## Frustration and disorder in quantum spin chains and ladders

### Arthur Lavarélo

In quantum spins systems, frustration and low-dimensionality generate quantum fluctuations and give rise to exotic quantum phases. This thesis studies a spin ladder model with frustrating couplings along the legs, motivated by experiments on cuprate BiCu2PO6.

First, we present an original variational method to describe the low-energy excitations of a single frustrated chain. Then, the phase diagram of two coupled chains is computed with numerical methods. The model exhibits a quantum phase transition between a dimerized phase and resonating valence bound (RVB) phase. The physics of the RVB phase is studied numerically and by a mean-field treatment. In particular, the onset of incommensurability in the dispersion relation, structure factor and correlation functions is discussed in details.

Then, we study the effects of non-magnetic impurities on the magnetization curve and the Curie law at low temperature. A low-energy effective model is derived within the linear response theory and is used to explain the behaviors of the magnetization and Curie constant.

Eventually, we study the effect of bonds disorder, on a single frustrated chain. The variational method, introduced in the non-disordered case, gives a low disorder picture of the dimerized phase instability, which consists in the formation of Imry-Ma domains delimited by localized spinons.

# Séminaire du LPTMS: Giulia Foffano

## Stokes' law violation and negative drag in active fluids

### Giulia Foffano, University of Edinburgh

Active fluids are suspensions of particles that absorb energy from their surroundings or from an internal tank, in order to do work. Main examples can be found in biological contexts and are e.g. bacteria suspensions and the actomyosin solution, that constitutes the cytoskeleton. I will present simulations where a small constant force is applied to a spherical colloid embedded in an active liquid crystal. In the linear regime the dissipative force acting on the particle embedded in a simple fluid is described by Stokes' law. Here instead we find a strong non-linearity with respect to the size of the probe and, strikingly, a regime where the colloid reaches a steady state of negative drag.

# Physics-Biology interface seminar: Matthieu Caruel

## Muscle power-stroke as a collective mechanical phenomenon

### Matthieu Caruel (Inria and École Polytechnique)

The mechanism of muscle contraction, residing in nano-scale interaction between actin and myosin filaments, was intensely studied by using fast loading protocols. These experiments revealed the important mechanical role of the internal conformational change inside protruding myosin heads known as the power-stroke. It was realized that fast force recovery after abrupt loading, taking place at 1 ms time scale, is a purely mechanical phenomenon linked exclusively to the power-stroke and not limited by metabolic fuel delivery.

In this presentation, we explore previously unnoticed difference in fast force recovery taking place in hard and soft loading devices and propose a purely mechanical model that explains the origin of this unusual behavior. We link the inequivalence of soft and hard loading ensembles to the presence of long range interactions between the individual actin-myosin cross-links known as cross-bridges. Our fit of experimental data suggests that 'muscle material' is finely tuned to perform close to a critical point which explains large fluctuations observed at stall forces. The proposed mean field model clarifies the collective nature of the power-stroke and reveal new properties of the celebrated Huxley and Simmons 1971 model.

# Séminaire du LPTMS: Maxim Imakaev

## Three dimensional architecture of human chromosomes: from data analysis to polymer models

### Maxim Imakaev, MIT

The three-dimensional and physical organization of genomes within cells plays critical roles in regulating chromosomal processes, including gene regulation, DNA replication, and genome stability. A recently developed method, Hi-C, provides a comprehensive whole-genome information about physical contacts between genomic region. Analysis of these data has begun to reveal determinants of 3D genomic organization.

Chromosomes can be understood as long polymers. We use a combination of data analysis and polymer modelling to pinpoint main determinants of the 3D genomic organization in several studied organisms. We build polymer models based on the known or suggested principles of chromosomal organization and validate them against the Hi-C data. In particular, we have shown that yeast chromosomal organization can be well-described by a star-polymer model. The model we developed is consistent with the yeast Hi-C data, microscopy observations and diffusion measurements of yeast chromosomes.

We also study folding of the human chromosomes during metaphase, which is vital for completion of cell division. Here, polymer modelling allowed us to discriminated between the two long-studied models of metaphase chromosomes: "bottle-brush" model of loops emanating from a central scaffold, and an hierarchical folding principle.

# Séminaire du LPTMS: Antonio Prados

## A general class of dissipative models: fluctuating hydrodynamics and large deviations

### A. Prados, Universidad de Sevilla

We consider a general class of models, described at the mesoscopic level by a fluctuating balance equation for the local energy density. This balance equation has a diffusive term, with a current that fluctuates around its average behaviour given by Fourier's law, and a dissipation term which is a general function of the local energy density. The latter does not include a fluctuating term, as the dissipation fluctuations are enslaved to those of the density due to the (assumed) quasi-elasticity of the underlying microscopic dynamics. This quasi-elasticity of the microscopic dynamics is compatible with the existence of a finite dissipation over the diffusive time scale which is relevant at the mesoscopic level.

This general fluctuating hydrodynamic picture [1], together with an "additivity conjecture" [2], makes it possible to write the functional giving the probability of large deviations of the dissipated energy from the average behaviour. The functional has the same form as in the non-dissipative case, due to the subdominant role played by the dissipation noise. The above hydrodynamic description is shown to emerge from a general class of models, with stochastic dissipative dynamics at the microscopic level, in the large system size limit. Both the average macroscopic behaviour and the noise properties of the hydrodynamic fields are obtained from the microscopic dynamics. Finally, this general scheme is applied to the simplest dissipative version of the so-called KMP model [3] for heat transport. The theoretical predictions are compared to extensive numerical simulations, and an excellent agreement is found [4-6].

1. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Phys. Rev. Lett. **87**, 040601 (2001); Phys. Rev. Lett. **94**, 030601 (2005); J. Stat. Mech. P07014 (2007); J. Stat. Phys. **135**, 857 (2009).

2. T. Bodineau and B. Derrida, Phys. Rev. Lett. **92**, 180601 (2004).

3. C. Kipnis, C. Marchioro and E. Presutti, J. Stat. Phys. **27**, 65 (1982).

4. A. Prados, A. Lasanta and P. I. Hurtado, Phys. Rev. Lett. **107**, 140601 (2011).

5. A. Prados, A. Lasanta and P. I. Hurtado, Phys. Rev. E **86**, 031134 (2012).

6. P. I. Hurtado, A. Lasanta, and A. Prados, Phys. Rev. E **88**, 022110 (2013).

# Physics-Biology interface seminar: Marie Doumic-Jauffret

## Division Control in Escherichia coli is Based on a Size-sensing rather than Timing Mechanism

### Marie Doumic-Jauffret (INRIA Rocquencourt)

Models describing the growth of cell populations have been developed based on assumptions on the stochastic mechanisms underlying growth and division at the single cell level. In particular, two different models have been widely used for decades, assuming that cell division probability depends respectively on cell age (the renewal equation) or cell size (the size-structured or growth-fragmentation equation) - or both.

We confront these models with data on E. coli single cells growth, and develop a new estimation methodology, based on nonparametric functional testing within the PDE models, in order to test the hypothesis of an age-dependent versus size-dependent division rate. We conclude that in E. Coli, the division is controlled by a size-sensing rather than timing mechanism.

This is a joint work with L. Robert and M. Hoffmann.

# Séminaire du LPTMS: Tom Witten

## A colloidal dance: synchronizing motion of brownian particles

### Thomas A. Witten, University of Chicago

Watch a small flake of plastic gradually sink in a glass of water. The asymmetric flake pivots into a preferred orientation and then rotates steadily as it sinks. The reason for this rotational response to gravity is independent of length scale; thus it applies to microscopic colloidal objects as well. Analogous responses occur under other forces, eg from electric fields. The response is governed by a 3x3 matrix called the twist matrix that depends on the object's shape and its mass distribution. The twist matrix controls the motion in much the same way as the (symmetric) inertia tensor controls the free tumbling motion of a body. However, the twist matrix gives a richer response because it is not symmetric. In this talk we explore ways to use this rotational response to organize a sample of objects so that they all rotate in unison, with the same orientation. This complete orientation can be achieved without using interaction between the particles; instead we exploit the transient pivoting response before the object settles into a fixed rotational axis. We demonstrate two types of programmed, time-dependent forcing that bring a set of randomly oriented particles into a common orientation. The first is a simple alternating rocking motion. The second is a rotating force analogous to the rotating magnetic field in an NMR device. Once oriented, the objects must respond identically to further forcing; they translate and rotate in unison.

# Séminaire exceptionnel du LPTMS: Srikanth H. Sastry

## Dynamical transition and memory in cyclically deformed amorphous solids

### Srikanth H. Sastry (TIFR Centre for Interdisciplinary Sciences, Hyderabad)

# Soutenance de thèse : Pierre-Elie Larré

## Fluctuations quantiques et effets non-linéaires dans les condensats de Bose-Einstein : des ondes de choc dispersives au rayonnement de Hawking acoustique

### Pierre-Elie Larré

Cette thèse est dédiée à l'étude de l'analogue du rayonnement de Hawking dans les condensats de Bose-Einstein. Dans un premier temps, on présente de nouvelles configurations dans lesquelles l'écoulement d'un condensat atomique réalise l'équivalent acoustique d'un trou noir gravitationnel. Nous donnons dans chaque cas une description analytique du profil de l'écoulement, des fluctuations quantiques associées et du spectre du rayonnement de Hawking. L'analyse des corrélations à deux corps dans l'espace des positions et des impulsions fournit des signatures caractérisant l'occurrence du rayonnement de Hawking. Dans une deuxième partie, nous analysons les propriétés superfluides et/ou dissipatives de condensats de polaritons s'écoulant autour d'un obstacle. L'étude des ondes de polarisation dans ces systèmes nous permet enfin de proposer des signatures prometteuses pour l'observation de l'effet Hawking dans les gaz de polaritons et les condensats atomiques à deux composantes.

# Séminaire exceptionnel du LPTMS : Shimshon Bar-Ad

## Transonic flow of light, sonic horizons and analogue gravity

### Shimshon Bar-Ad, Tel Aviv University

In 1981 W.G. Unruh predicted that a thermal spectrum of sound waves would be emitted from the sonic horizon in transonic fluid flow, in analogy to black-hole evaporation. Based on this idea, extended to the realm of nonlinear optics, we explore an optical analog of the Laval nozzle, in which light propagation through a suitably shaped waveguide, filled with a self-defocusing nonlinear medium, mimics the transonic acceleration of a real fluid expanding through a propulsive exhaust nozzle. Experimental demonstrations of transonic flow in prototype optical nozzles will be presented, and the prospect of observing fluctuations that are classical analogs of Hawking radiation will be discussed.

# Séminaire du LPTMS: Oleg Borisov

## Poisson-Boltzmann theory of polyelectrolyte brushes

### Oleg Borisov, IPREM, Université de Pau

The polyelectrolyte brush results if long flexible ionic polymer chains are attached by one end onto an impermeable solid surface or onto the surface of a colloidal particle and immersed in a solvent.

Understanding of the structure-properties relation in polymer and polyelectrolyte brushes is important for their applications for surface modification, in particular, in the field of biomaterial engineering. Functional polymer brush-like structures are found in biological systems. Examples of natural biopolyelectrolyte brushes include extracellular polysaccharides on bacterial surfaces, neurofilaments and microtubules with associated proteins, aggrecan macromolecules in articular cartilage, casein micelles etc. The possibility to trigger conformational transitions in surface-attached polymeric layers by external physical (temperature, electrical voltage, etc.) or chemical (pH, salinity, solvent composition, etc.) fields opens a perspective for design of stimuli-responsive interfaces.

Theory of equilibrium structural properties of polyelectrolyte brushes is developed in the frame of self-consistent field Poisson-Boltzmann approximation. We analyze the influence of ionic strength and (in the case of weak polyacid or polybase brushes) pH in the solution on the chain conformations in the brush. The effect of the counterion localization in the polyelectrolyte brush is most essential and governing the brush properties. The repulsive forces acting between surfaces or colloidal particles with grafted polyelectrolytes are calculated. Furthermore, we discuss interaction of polyelectrolyte brushes with multivalent counterions and with globular proteins and the effect of their accumulation in the brushes.

# Physics-Biology interface seminar: Timo Betz

## The mechanics of active and passive cellular assemblies: How biomimetic reconstitution can help to understand living cell

### Timo Betz (Institut Curie - Paris)

Understanding the intriguing complexity of living systems is one of the main driving forces of science. To gain insight we use biomimetic systems that reconstitute well defined cellular assemblies and compare these to the living system. Our main interests are the mechanical properties and the generation of forces, both mediated by the cytoskeleton and its interaction with the plasma membrane. Recent advances allow to mimic structures such as the actin cortex, sparse actin networks and actin bundles, and we use optical tweezers to quantify the mechanical properties of these structures and to compare them to living cells. While sparse actin networks and polymerizing actin bundles show rather passive behavior, we apply the same measurement methods to living cells such as cell blebs and red blood cells which allow to study the out-of-equilibrium mechanics of these systems, and to determine the timescale at which the system's activity becomes evident.

# Physics-Biology interface seminar: Daniel Axelrod

## Molecule motion inside secretory granules before and during exocytosis

### Daniel Axelrod (University of Michigan)

**SPECIAL DATE & TIME**

Despite ~10% of the human genome being comprised of secretory proteins, little is known about the dynamics of proteins inside the secretory granule before and during fusion with the plasma membrane. This talk presents early results on measuring the diffusion coefficient of two proteins within that submicroscopic and closed space, and relates the results to secretion and local membrane deformation rates during the fusion event. The techniques used, TIR-FRAP, TIR-FCS, and pol-TIRF have general applicability, and the theory and practice of especially the first two is discussed.

# Séminaire du LPTMS: Denis Basko

## Weak chaos and Arnold diffusion in the strongly disordered nonlinear Schroedinger chain

### Denis Basko, LPMMC - Université Joseph Fourier

I will discuss the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators, which is one of the simplest models allowing to study the effect of a classical nonlinearity on the Anderson localization. The system has chaotic behavior, and it is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of relaxation at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids.

# Tri-Séminaire de Physique Statistique : Sergey Nazarenko

**Condensation & BKT transition in 2d defocusing nonlinear Schrödinger equation.**

**Sergey Nazarenko ***(Mathematics Institute, University of Warwick)*

I will consider a 2D nonlinear Schrödinger equation model in a periodic box and truncated in Fourier space and study condensation phenomenon, Berezinskii-Kousterlitz-Thouless transition, and their links with the Wave Turbulence theory.

# Séminaire du LPTMS: Yasar Atas et François Landes

## Distribution of the ratio of level spacings in random matrix ensembles.

### Yasar Atas, LPTMS

Initially introduced as a description of energy levels of heavy atomic nuclei by Wigner, Random Matrix Theory (RMT) is nowadays an active field of theoretical physics with ramification in various disciplines such as number theory, quantum chaos and finance to cite just a few. In RMT, the distribution of level spacings plays a very important role: it has been widely used since the inception of the theory and is considered as the "reference" measure of spectral statistics. Since different models may and do have different level densities, one has to perform a procedure on the spectrum called unfolding in order to obtain the spacing distribution. This procedure is not unique and the choice of the unfolding procedure is quite arbitrary. It seems then natural to search for another measure which is independent of the level density. This has been done quite recently by Oganesyan and Huse [1]: instead of looking at the spacing they prefer to look at the ratio of two consecutive level spacings. This quantity has the advantage that it does not require any unfolding.

In this talk, I will make few remarks on random matrix theory and the unfolding procedure. I will then derive simple expressions for the probability distribution of the ratio of two consecutive spacings for the classical ensembles of random matrices [2]. These expressions, which were lacking in the literature, will be compared to numerical data from a quantum many-body lattice model and from zeros of Riemann zeta function.

[1] V. Oganesyan and D. A. Huse, Phys. Rev. B 75, 155111 (2007).

[2] Y. Y. Atas, E. Bogomolny, O. Giraud, and G. Roux, Phys. Rev. Lett. 110, 084101 (2013)

## Avalanche statistics in disordered visco-elastic interfaces

### François Landes, LPTMS

Many complex systems respond to a continuous input of energy by an accumulation of stress over time, and sudden energy releases, called avalanches. Recently, it has been pointed out that several basic features of avalanche dynamics are induced at the microscopic level by relaxation processes, usually neglected by conventional models. I will present a minimal model with relaxation and its mean field treatment, and a quick snapshot of the finite dimension results. In mean-field, our model yields a periodic behavior (with a new, emerging time scale), with events that span the whole system. In finite dimension (2D), the mean-field system-sized events become local, and numerical simulations give qualitative and quantitative results similar to the earthquakes observed in reality.

# Physics-Biology interface seminar: Roberto Toro

## Role of mechanical constraints on the establishment of neocortical organisation

### Roberto Toro (Institut Pasteur)

The mammalian brain is astonishingly diverse. Not only its size varies several orders of magnitude – from the 3 grams of the mouse brain to the 6 kg of the blue whale brain – but also its geometry and function. There is indeed a striking, largely unexplained, relationship between the folding of the mammalian brain and its cellular, functional and connective organisation. Brain folding appears as much more than a mere mechanical epiphenomenon, and besides its major evolutionary relevance, many psychiatric disorders such as autism or schizophrenia, are related to changes in brain folding.

I will present a brief overview of the developmental processes leading to the folding of the brain, and show some examples of functional correlates of brain folding in humans and other mammalian species. Finally, I will discuss some of the current theories proposed to explain the mechanism underlying the relationship between brain geometry and brain organisation, including our ongoing project on computational modelling and analysis of the development of the ferret brain.

# Journal-Club : Vincent Michal

## Dynamics of a quantum phase transition: exact solution of the quantum Ising Model Jacek Dziarmaga, PRL 95, 245701 (2005)

### Vincent Michal (Post doc LPTMS)

It will be based on the paper "Dynamics of a quantum phase transition: exact solution of the quantum Ising Model", by Jacek Dziarmaga, PRL 95, 245701 (2005).

Abstract of the paper:

The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with a probability depending on the transition rate. The average density of defects excited in this way scales like a square root of the transition rate. This scaling is the same as the scaling obtained when the standard Kibble-Zurek mechanism of thermodynamic second order phase transitions is applied to the quantum phase transition in the Ising model.

# Soutenance de thèse : Olga Valba

*Statistical analysis of networks and biophysical systems of complex architecture*

*Statistical analysis of networks and biophysical systems of complex architecture*

### Olga Valba (LPTMS)

Complex organization is found in many biological systems. For example, biopolymers could possess hierarchic structure, which provides their functional peculiarity. Artificially constructed biological networks are other common objects of statistical physics with rich functional properties. The aim of this thesis is to develop some methods for studying statistical systems of complex architecture with essential biological significance.

The first part addresses to the statistical analysis of random biopolymers. Apart from the evolutionary context, our study covers more general problems of planar topology appeared in description of various systems, ranging from gauge theory to biophysics.

In the second part of this work we focus our investigation on statistical properties of artificial and real networks. The importance of obtained results in applied biophysics is discussed. Also, the formation of stable patters of motifs in random networks under selective evolution in context of creation of islands of "superfamilies" is considered.

# Physics-Biology interface seminar: Emmanuel Margeat

## Looking at transcription mechanisms with single molecule FRET

### Emmanuel Margeat (Centre de Biochimie Structurale, Montpellier)

**Exceptional seminar hosted by Karen Perronet
SPECIAL DATE, TIME AND LOCATION**

Förster Resonance Energy Transfer (FRET) allows measuring the distance between two spectrally distinct fluorophores, in the 20-100 Å range. When monitored at the single molecule level, smFRET is useful in resolving subpopulations, or observing conformational changes as a function of time within single macromolecular complexes in vitro. I will describe here the methodologies used to measure FRET accurately on single biomolecular complexes, freely diffusing in solution or immobilized on surfaces. I will then focus on our studies on the mechanism of prokaryotic transcription such as antitermination control by the antiterminator LicT, and Rho-induced transcription termination.

# Séminaire exceptionnel du LPTMS : Eugene Sukhorukov

## Fermi Edge Singularity in Quantum Hall Systems far from Equilibrium

### Eugene Sukhorukov (Geneva University)

We study non-equilibrium one dimensional physics on an example of a minimal setup inspired by the recent experiment based around a Mach-Zender interferometer composed of quantum Hall edge channels at integer filling factor, one of which is in Coulomb interaction with an artificial impurity. The fluctuations of the impurity charge due to the tunneling transitions lead to resonant suppression of coherence on the channel and of the visibility of the interference pattern. We consider the regime where the transitions are induced by the non-equilibrium partitioning noise created in the interferometer itself by the beam splitter, and describe the strong effects of both the orthogonality catastrophe and the non-equilibrium noise, that are revealed in the shape of the transition rates, in the asymmetry of the visibility dip and in the non-trivial dependence of the dip position on the transparency

# Journal-Club : Pierre Ronceray

## Improving the Density of Jammed Disordered Packings Using Ellipsoids

A. Donev, I. Cisse, D. Sachs, E. A. Variano, F. H. Stillinger, R. Connelly, S. Torquato, and P. M. Chaikin, Science, 303, pp 990-993 (2004).

Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction f=Pi/sqrt(18) ~ 0.74. It is also well known that certain random (amorphous) jammed packings have f~0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely— up to f~0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M’s Candies—and even approach f~ 0.74 for ellipsoids with other aspect ratios. We suggest that the higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle contacts required to mechanically stabilize the packing. We measured the number of contacts per particle Z~10 for our spheroids, as compared to Z~ 6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular media and ceramics, glass formation, and discrete geometry.

# Séminaire du LPTMS: Fabio Deelan Cunden

## Polarized ensembles of random pure states

### Fabio Deelan Cunden, Dipartimento di Matematica, Università di Bari

In the last years many researchers have been investigating the typical properties of random pure states, i.e. unit vectors drawn at ``random'' from the Hilbert space associated to a quantum system. This subject has attracted the attention in several directions, and some important results have been achieved. The standard ensemble which has been intensively investigated is that of random pure states with measure induced by the Haar measure on the unitary group. This ensemble, being the maximally symmetric one, implements in a natural way the case of minimal knowledge on a quantum state.

We recently presented a new family of polarized ensembles of random pure quantum states. Our idea is to move beyond the unbiased ensemble by using a natural operation at hand in the Hilbert space, namely superposition of vector states. These ensembles are quite manageable and manifestly show that the unitarily invariant measures interact nicely with the operation of linear superposition of states. Our approach has been oriented to the study of typical bipartite entanglement between subsystems, as measured by the local purity. This strategy yields an efficient and simple sampling of random pure states with fixed value of purity, and paves the way to further explorations and a deeper characterization of the geometry of isopurity manifolds.

Cunden F D, Facchi P, Florio G (2013) J. Phys. A: Math. Theor. **46**, 315306.

# Séminaire du LPTMS: Anders Carlsson

## Self-Organizing Waves and Patterns of Proteins in Biological Cells

### Anders Carlsson (Washington University)

Self-organized patterns, such as traveling waves and symmetry-breaking distributions of chemical species, demonstrate how simple laws of motion can lead to complex behaviors in physical systems. Such patterns result from a combination of positive and negative feedback effects with different time scales. The talk will discuss the example of waves of the protein actin in biological cells. Actin, the most abundant intracellular protein in mammals, occurs either as an isolated protein in solution, or in the form of filaments which have mechanical rigidity and are crosslinked into a gel. Recent experiments have shown that filamentous actin forms spontaneous waves that cause protrusion of the cell membrane. Such waves may serve as a “clock” that helps a cell explore its environment. A theoretical model of actin waves will be presented, based on the three-dimensional structure of the gel formed by actin filaments, interacting reciprocally with proteins in the cell membrane. Implementation of this model shows that positive feedback is inherent in the growth process of the actin gel, while negative feedback arises from the actin-membrane interaction. As the concentration of key proteins in the cell is varied, the model predicts phase transitions between different phases including traveling waves or patches, and static symmetry-breaking polarization of the cell.

# Physics-Biology interface seminar: Aurélien Bancaud

## Conformation and dynamics of DNA in confined environments: cross-talk between chromosomes in the nucleus and polymers in nanochannels

### Aurélien Bancaud (Laboratoire d'analyse et d'architecture des systèmes, Toulouse)

Genome structure and dynamics attacts considerable attention in the biology community to eludicate genome regulation principles, but also for biological physicists who aim to develop models of DNA in vivo. The challenges of this research is conceptual but also economical because of expected impact of DNA sequencing or DNA microarrays technologies in personalized diagnostics.

Our research is carried out at the nexus of technology and biology and aims to provide a physical description of the genome structural properties. We will first overview our results on chromosome dynamics in living yeast, showing the unexpected flexibility of these structures in vivo. We will then focus on new methods for chromosome analysis in vitro based on micro- and nano-fluidics, and we will finally emphasize that that these two topics are not so unrelated, given that the physics of DNA confined environment can be used as a common research framework.

# Séminaire du LPTMS: Claire Lemarchand

## Molecular composition and mechanical properties of bitumen : a molecular dynamic study

## Claire Lemarchand, Université de Roskilde

Bitumen is one of the essential components of roads. Its mechanical properties need to be controlled in order to reduce the rolling resistance developed between the tyre and the road as a vehicle is travelling on the road.

In this presentation, I will speak about the link between the molecular composition and the mechanical properties of "Cooee" bitumen. This model bitumen is composed of four realistic molecule types: saturated hydrocarbon, resinous oil, resin, and asphaltene. It is studied with molecular dynamic (MD) simulations. Asphaltene molecules are large and flat aromatic molecules.

The molecular dynamic simulations are able to reproduce the aggregation of asphaltene molecules into nanoaggregates. The size of the nanoaggregates was estimated in the simulations and shown to be comparable to experimental results. The dynamics of the nanoaggregates was precisely quantified in MD, giving new insights about their formation. Finally, the influence of these nanoaggregates on the bitumen mechanical properties and overall dynamics was investigated. This last part of the work enables us to set some rules about bitumen chemical composition to lower its viscosity.

# Séminaire "Fluides quantiques" : Matteo Zaccanti

## Ultracold 6Li-40K Fermi mixtures with resonant interactions

### Matteo Zaccanti (LENS, Florence)

# Tri-Séminaire de Physique Statistique : David Holcman

## Analysis of superresolution data using Langevin equation. Brownian receptortrafficking on neuronal cells

### David Holcman (Institut de Biologie, Ecole Normale Supérieure - IBENS)

What is the basis of learning and memory in the brain? Neurons are the main players and synapses that are micro-contact between them play a critical role. How synapses are organized at a molecular level and what defines their synaptic strength at a molecular level remains unclear, although it is due to the combine effect of many molecules together. Thus the number of receptors and molecules must be well regulated. I will present here an integrative modeling approach of synaptic transmission that accounts for receptor dynamics and a novel method to extract local biophysical properties from thousands of individual trajectories obtained from superresolution microscopy data. This talk summarizes our long lasting effort in integrating key parameters involved in regulating synaptic transmission and plasticity.

# Séminaire "Fluides quantiques" : Dmytro Fil

## Superfluidity of electron-hole pairs in bilayers

### Dmytro Fil (Institute for Single Crystals, NASU, Kharkov)

# Journal-Club : Hao Lee

## Multi-orbital and density-induced tunneling of boson in optical lattices

### Hao Lee (doctorant au LPTMS)

Article de Dirk-Soren Luhmann, Ole Jurgensen and Klaus Sengstock, New Journal of Physics 14 ( 2012) 033021

We show that multi-orbital and density-induced tunneling have a significant impact on the phase diagram of bosonic atoms in opticallattices. Off-site interactions lead to density-induced hopping, the so-called bond-charge interactions, which can be identified with an effective tunneling potential and can reach the same order of magnitude as conventional tunneling. In addition, interaction-induced higher-band processes also give rise to strongly modified tunneling, on-site and bond-charge interactions.We derive an extended occupation-dependent Hubbard model with multiorbitallyrenormalized processes and compute the corresponding phase diagram.It substantially deviates from the single-band Bose–Hubbard model andpredicts strong changes of the superfluid-to-Mott-insulator transition. In general,the presented beyond-Hubbard physics plays an essential role in bosoniclattice systems and has an observable influence on experiments with tunableinteractions.

# Séminaire du LPTMS: Thomas Barthel

## Algebraic versus exponential decoherence in dissipative many-particle systems

### Thomas Barthel, LPTMS

Ultimately, every quantum system of interest is coupled to some form of environment which leads to decoherence. Until our recent study, it was assumed that, as long as the environment is memory-less (i.e. Markovian), the temporal coherence decay is always exponential -- to a degree that this behavior was synonymously associated with decoherence.

However, the situation can change if the system itself is a many-body system. In this case, the interplay between dissipation and internal interactions gives rise to a wealth of novel phenomena. In particular, the coherence decay can change to a power law.

After recapitulating the mathematical framework and basic notions of decoherence, I will discuss an open XXZ chain for which the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence. The results are based on quasi-exact simulations using the time-dependent density matrix renormalization group (tDMRG) and explained on the basis of perturbative treatments.

Reference: Z. Cai and T. Barthel, PRL 111, 150403 (2013)

# Séminaire du LPTMS : Giovanni Acquaviva

## Semi-classical and quantum effects in curved metrics

### Giovanni Acquaviva, University of Trento

Since the work by Hartle and Hawking, black hole spacetimes constituted an excellent playground for the study of quantum effects in curved metrics: in this context a great deal of theoretical tools have been employed in order to unveil the connections between general relativity and the quantum realm. In the seminar I will present two approaches that allow to highlight this aspect: i) the semi-classical tunneling method and ii) the quantum field-theoretical modeling of Unruh-DeWitt detectors. One of the open questions in this field regards the everpresent role of thermodynamics: does it just constitutes a parallel arising from a fundamentally statistical treatment? Or is there some more profound link?

# Physics-Biology interface seminar: Pascal Martin

## The hair-cell bundle as a mechanosensor and amplifier for hearing

### Pascal Martin (Institut Curie - Paris)

The ear works as a remarkable sound detector. Hearing can indeed operate over six orders of magnitudes of sound-pressure levels, with exquisite sensitivity and sharp frequency selectivity to weak sound stimuli. Curiously, the ear does not work as a high-fidelity sound receiver, introducing in the auditory percept “phantom” tones that are not present in the sound input. In this talk, I will present micromechanical experiments at the level of the cellular microphone of the inner ear – the hair cell – whose function is to transduce sound-evoked vibrations into electrical nervous signals. In particular, I will show that hair cells can power spontaneous oscillations of their mechanoreceptive hair bundles, a tuft of cylindrical protrusions that protrudes from the apical surface of each cell. The oscillatory instability is thought to result from a dynamical interplay between ion channels, elastic proteinous linkages and active molecular motors. We find that oscillations of the hair bundle allow the hair cell to actively resonate with its mechanical input at the expense of distortions with properties that are characteristic of hearing. I will conclude by arguing that our results promote a general principle of sound detection that is based on nonlinear amplification by self-sustained “critical” oscillators in the inner ear, i.e. active dynamical systems that operate on the brink of a Hopf bifurcation.

# Séminaire du LPTMS: Jon Keating

## Random Matrix Theory and quantum spin chains

### Jon Keating (Bristol University)

I will discuss a random matrix model for understanding statistical features of the spectrum and excited states of certain families of quantum spin chains. In the case of the states, this provides information about entanglement properties.

# Tri-séminaire de Physique Statistique : Denis Bernard

## Real Time Imaging of Quantum and Thermal Fluctuations : a Detour into Quantum Noise

### Denis Bernard, LPTENS

In the last decade progresses have been achieved in realising and manipulating stable and controllable quantum systems, and these made possible to experimentally study fundamental questions posed in the early days of quantum mechanics. We shall theoretically discuss recent cavity QED experiments on non-demolition quantum measurements. While they nicely illustrate the possibility to implement efficient quantum state manipulations, these experiments pose a few questions such as: What does it mean to observe a progressive wave function collapse in real time? How to describe it? What do we learn from them? Their analysis will allow us on the one hand to link these experiments to basics notions of probability or information theory, and on the other hand to touch upon notions of quantum noise.

As an illustration, we shall also look at quantum systems in contact with a heat bath and we shall describe the main physical features of thermally activated quantum jumps.

# Comité AERES

# Comité AERES

# Physics-Biology interface seminar: François Nédélec

## Optimal Design of Elongating Yeast Spindles

### François Nédélec (EMBL Heidelberg)

**Joint seminar with LEBS Gif-sur-Yvette
SPECIAL TIME AND LOCATION**

Bundles of filaments are universal elements that belong to the intracellular skeleton of eukaryotic cells. The anaphase spindle from fission yeast is an excellent example of such bundle that assembles repeatedly in the same manner at every cell division. It is also an excellent experimental system since yeast cells can easily be perturbed genetically, and their spindle is visualized using electron or light microscopy. The spindle is under compression at anaphase and based on electron tomographic reconstructions of its constituent microtubules, we calculated that the length and organization of microtubules within the fission yeast spindle are optimized to achieve maximal strength while minimizing the use of material. A combination of simulations and live cell imaging further indicated which of the properties of the microtubule cross-linkers are likely to be responsible for such a precise regulation of spindle morphology, and the synergy that exists between the cross-linkers in fission yeast.

# Journal Club : Clélia de Mulatier

*B. Houchmandzadeh, Phys*. *Rev*. *E* 80, 051920 (*2009*): Theory of neutral *clustering* for growing populations

### Clélia de Mulatier (PhD student LPTMS)

The spatial distribution of most species in nature is nonuniform. We have shown recently [ B. Houchmandzadeh Phys. Rev. Lett. **101** 078103 (2008)] on an experimental ecological community of amoeba that the most basic facts of life—birth and death—are enough to cause considerable aggregation which cannot be smoothened by random movements of the organisms. This clustering, termed neutral and always present, is independent of external causes and social interaction. We develop here the theoretical groundwork of this phenomenon by explicitly computing the pair-correlation function and the variance to mean ratio of the above neutral model and its comparison to numerical simulations.

W. R. Young, A. J. Roberts & G. Stuhne^{, }*Nature* **412**, 328-331 (19 July 2001)

# Séminaire du LPTMS: Haggai LANDA

## Solitons and nonlinearity with trapped ions

### Haggai Landa, LPTMS

Solitons are ubiquitous in many areas of physics and the natural sciences. Quantum dynamics of solitons, however, has proven experimentally challenging to measure. A system in which state-of-the-art quantum control over individual degrees of freedom has been demonstrated is the ion trap, where, due to the time-dependent trapping fields and the Coulomb interaction, trapped ions manifest rich nonlinear dynamics. I will present some theoretical work and collaboration with experimental groups from recent years, focusing in particular on the study of discrete solitons with trapped ions, and more generally, other nonlinear phenomena, both classical and quantum mechanical.

# Séminaire du LPTMS: Eduardo Sanz

## Crystallization in molecular and colloidal systems by means of computer simulations

### Eduardo Sanz, Universidad Complutense de Madrid

Crystallization is often used in separation and purification industrial processes. Most drugs, for instance, are stored and delivered in a crystalline form. Moreover, climate change is strongly influenced by the crystallization of water in tropospheric clouds. It is therefore important to deeply understand the kinetics of this phase transition, and computer simulations is a very suitable tool for this purpose. The reason is that crystallization starts by a nucleation step that consists in the emergence of a small embryo of the crystal phase in the bulk of the parent fluid phase. In molecular systems, such embryo is rather small (contains of the order of 10^2-10^3 molecules) and short-lived (lasts for ~10^-9 seconds) and it can not therefore be directly visualized experimentally. In this talk I will discuss several numerical studies of crystallization. First, I will discuss a case study in which several crystal phases (polymorphs) compete to nucleate in a metastable fluid of oppositely charged colloids. Then, I will present a computational study of homogeneous ice nucleation at low supercoolings. Finally, I will present a study of the mechanism by which a colloidal glass becomes crystalline.

# Physics-Biology interface seminar: Yang Si

## Fluorescent Nano-objects For Bioimaging Applications

### Yang Si (ENS Cachan)

**Special seminar: poster prize from the NOMBA workshop**

Bacteria are the most abundant organisms in the world. Studying models of bacterial chromosome dynamics in the cytoplasm is very important to understand how bacteria adapt to different growth environments and in response to stimuli. Optical labeling is one of the most common methodologies used for bioanalytical purposes. The fundamental issues for any fluorescent material are the same: brightness and stability. In the quest for very bright and stable labels, novel polymer-based, self-stabilized, fluorescent nanoparticles (FNPs) and fluorescent polymer chains (FPCs) have been developed in the PPSM laboratory. They are brighter, more stable, photobleach slowly and are more easily functionalized compared with other fluorescent labels like GFP and QDs. A methodology to insert these FNPs (60nm) into E.coli bacteria was developed. To control if the FNP are indeed internalized, we developed a protocol based upon FNP luminescence quenching by methylene blue. Biotin conjugated FNPs could be used to study specific membrane proteins. By using a strepdavidin-biotin link, we made a “Sandwich” to build a bridge between particles, specific antibodies and bacteria. Negatively charged FPCs can easily enter into E.coli bacteria. It is found that FPCs can label the cytoplasm but not the DNA, which appears to be more compact. These unique properties will allow the study of DNA and cytoplasm viscosity changes during bacterial growth.