# Séminaire du LPTMS: Francis Corson

## A geometric approach to biological patterning

### Francis Corson, Institut Pasteur

Understanding how developmental patterns arise remains a central question in developmental biology. While genetic studies have revealed lists of genes and molecules involved in this process, it is often difficult to assemble them into predictive models. The theory of dynamical systems suggests a geometric approach that focuses on the qualitative structure of dynamics, yet allows quantitative predictions. We have applied this approach to the vulva of C. elegans, a simple organ that forms from a small number of cells. The model can be used to predict a “phase diagram” of the system, i.e. the outcome of development in different conditions, and these predictions largely recapitulate the experimentally observed outcomes. A similar approach naturally extends to the patterning of larger assemblies of cells, and I will discuss its application to the development of mechanosensory hair in Drosophila.

# Tri-sémianaire de Physique Statistique : Marc Potters

## A Random Matrix Bayesian framework for out-of-sample quadratic optimization

### Marc Potters, Capital Fund Management (CFM), Paris

Large empirical sample covariance matrices exhibit a distribution of eigenvalues well described by the work of Marcenko and Pastur. As a consequence, mean-variance optimization using the sample-covariance matrix gives disastrous out-of-sample results as the methods overweighs modes of spuriously low variance.  We propose here a Bayesian framework for the true covariance matrix whose conditional expectation should be used for mean-variance optimization. While the framework is quite general, we explore a few rotationally invariant priors, namely shifted-Wigner, Wishart and inverse-Wishart. While the latter is easily solved and leads to linear shrinkage the other two give rise to interesting matrix integrals. A naïve matrix saddle point gives an approximate solution, the zeroth order term in a systematic expansion in planar Feynman diagrams.  The first few terms of this expansion can be computed. The eigenvalue saddle point involves the orthogonal version of the Itzykson-Zuber integral that we solve exactly only in a very special case. We also discuss a numerical method that allows the computation of the conditional mean by Monte Carlo simulation. The methodology presented here has direct applications in finance (portfolio optimization) and should be applicable to other fields of “big data.”

# Séminaire du LPTMS: Jean-Marie Stephan

## Entropy and Mutual information in low-dimensional classical and quantum critical systems

### Jean-Marie Stephan, University of Virginia

In studies of new and exotic phases of quantum matter, the Renyi entanglement entropy has established itself as an important resource. For example it is universal at one-dimensional quantum critical points: the leading term can be used to extract the central charge c of the underlying conformal field theory, and thus identify the universality class.

In this talk I will show how an analogous quantity defined for classical systems, the Renyi Mutual Information (RMI), can be used to access universality classes in 2d. In particular for a rectangle cut into two rectangles, the shape dependence of the RMI can be computed exactly and is proportional to c. This makes it possible to extract c from (transfer-matrix) Monte Carlo simulations.
I will also discuss how this Mutual information is related to the entanglement entropy of certain Resonating valence bond states in 2d, as well as other basis-dependent entropies in 1d quantum systems.

Reference: arXiv:1312.3954

# Séminaire du LPTMS : Anna Minguzzi

## Anna Minguzzi (LPMMC Grenoble)

We study persistent currents for interacting bosons on a tight ring trap, subjected to an artificial gauge field induced by a rotating barrier potential. We show that at intermediate interactions the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings.

# Physics-Biology interface seminar: Alexis Gautreau

## Inhibitory signalling to the Arp2/3 complex steers cell migration

### Alexis Gautreau (LEBS - Gif-sur-Yvette)

Cell migration requires the generation of branched actin networks that power the protrusion of the plasma membrane in lamellipodia. The Arp2/3 complex is the molecular machine that nucleates these branched actin networks. This machine is activated at the leading edge of migrating cells by the WAVE complex. The WAVE complex is itself directly activated by the small GTPase Rac, which induces lamellipodia. However, how cells regulate the directionality of migration is poorly understood. Here we identify a novel protein that inhibits the Arp2/3 complex in vitro, Arpin, and show that Rac signalling recruits and activates Arpin at the lamellipodial tip, like WAVE. Consistently, upon depletion of the inhibitory Arpin, lamellipodia protrude faster and cells migrate faster. A major role of this inhibitory circuit, however, is to control directional persistence of migration. Indeed, Arpin depletion in both mammalian cells and Dictyostelium discoideum amoeba resulted in straighter trajectories, whereas Arpin microinjection in fish keratocytes, one of the most persistent systems of cell migration, induced these cells to turn. The coexistence of the Rac-Arpin-Arp2/3 inhibitory circuit with the Rac-WAVE-Arp2/3 activatory circuit can account for this conserved role of Arpin in steering cell migration. Loss of this inhibitory circuit promotes exploratory behaviors and might commit carcinoma cells to the invasive state.

# Séminaire du LPTMS: Julia Meyer

## Disordered topological metals

### Julia Meyer (CEA Grenoble)

Topological behavior can be masked when disorder is present. A topological insulator, either intrinsic or interaction induced, may turn gapless when sufficiently disordered. Nevertheless, the metallic phase that emerges once a topological gap closes retains several topological characteristics. By considering the self-consistent disorder-averaged Green function of a topological insulator, we derive the condition for gaplessness. We show that the edge states survive in the gapless phase as edge resonances and that, similar to a doped topological insulator, the disordered topological metal also has a finite, but non-quantized topological index. We then consider the disordered Mott topological insulator. We show that within mean-field theory, the disordered Mott topological insulator admits a phase where the symmetry-breaking order parameter remains non-zero but the gap is closed, in complete analogy to 'gapless superconductivity' due to magnetic disorder.

# Séminaire du LPTMS: Clément Sire

## Universal statistical properties of competitive systems: application to poker tournaments, sport championships (baseball, football), and tree games

### Clément Sire (LPT Toulouse)

We present a simple model of Texas hold'em poker tournaments, a toy realization of a (greedy!) human society, which retains the two main aspects of the game: a) the minimal bet grows exponentially with time, mimicking inflation; b) players have a finite probability to bet all their fortune (a risky but potentially rewarding investment). The distribution of the fortunes of players not yet eliminated is found to be universal and independent of time during most of the tournament, and reproduces very accurately data obtained from Internet tournaments and world championship events. The properties of the "chip leader" (the richest player at a given time) are also considered. This model makes the connection between poker and the persistence problem widely studied in physics (the probability for a temporal signal to remain above a given threshold), as well as some models of biological evolution (the number of "leaders" in a competition), and extreme value statistics. Finally, the modelization of other competitive systems (baseball and football championships; tree games, like tic-tac-toe or chess, and their link with a random polymer model and wavefront propagation...) will be briefly addressed.

Une page de vulgarisation sur ce thème avec d'autres liens utiles : http://www.lpt.ups-tlse.fr/spip.php?article239

# Physics-Biology interface seminar: Aurélien Roux

## Role of membrane elasticity in clathrin-mediated endocytosis

### Aurélien Roux (Université de Genève, Suisse)

In Clathrin-mediated endocytosis, Clathrin assembles into a soccerball-like structure at the plasma membrane that was proposed to deform the membrane by scaffolding. However, controversies in the community have appeared on the exact role of Clathrin: does its polymerization force is sufficient to curve the membrane, or deformation by other means (protein insertion) is required? We studied the formation of Clathrin buds from Giant Unilamellar Vesicles, and found that the pits can be flattened when membrane tension is increased. This suggested that the Clathrin polymerization force could be counteracted by membrane tension, which we further proved by directly measuring Clathrin polymerization force: by pulling a membrane tube out of a GUV aspirated in a micropipette, we can measure the force required to hold the tube through an optical tweezer system. When Clathrin is added, it polymerizes onto the GUV predominantly, and the force drops. From these measurements, we can deduce that the polymerization strength of Clathrin is in the range of a few hundred micronewtons per meter. This value confirms that clathrin polymerization can be counteracted efficiently by membrane tension. To finalize endocytosis, the clathrin-bud needs to be separated from the plasma membrane. Membrane fission requires the constriction and breakage of a transient neck, splitting one membrane compartment into two. The GTPase Dynamin forms a helical coat that constricts membrane necks of Clathrin-coated pits to promote their fission. Dynamin constriction is necessary but not sufficient, questioning the minimal requirements for fission. Here we show that fission occurs at the edge of the Dynamin coat, where it is connected to the uncoated membrane. At this location, the specific shape of the membrane increases locally its elastic energy, facilitating fission by reducing its energy barrier. We predict that fission kinetics should depend on tension, bending rigidity and the Dynamin constriction torque. We verify that fission times depend on membrane tension in controlled conditions in vitro and in Clathrin-mediated endocytosis in vivo. By numerically estimating the energy barrier from the increased elastic energy, and measuring the Dynamin torque, we show that: 1- Dynamin torque, ≈1nN.nm, is huge but necessary to achieve constriction, and 2- Dynamin work sufficiently reduces the energy barrier to promote spontaneous fission.

# Tri-séminaire de Physique Statistique : Martin Evans

## Speed selection in coupled Fisher waves

### Martin Evans, University of Edinburgh, Institute for Condensed Matter and Complex Systems, School of Physics

The Fisher equation describes the spread of a population or the spread of an advantageous gene through a population. It is well known as a simple nonlinear equation which exhibits travelling wave solutions. Within statistical physics It has played a major role in our understanding of phase ordering dynamics and random first order phase transitions. In this talk we review the selection mechanism for the speed of the travelling waves which was established some time ago. We go on to consider two coupled Fisher equations representing two populations e.g. sub-populations of bacteria which are susceptible or resistant to antibiotic. We show that a subtle coupling between two population waves gives rise to a novel speed selection mechanism.

# Séminaire du LPTMS: Zoran Ristivojevic

## Decay of excitations in interacting one-dimensional Bose gases

### Zoran Ristivojevic (CPhT, Ecole Polytechnique, Palaiseau)

Excitation spectrum in weakly-interacting systems of bosons have the Bogoliubov form. In three dimensions, those excitations are unstable due to residual weak interactions. The resulting process is known as Beliaev decay [1,2] and has been experimentally observed [3]. The related problem of decay of excitations in one-dimensional Bose gases is a fundamental long-standing problem. In this talk I will present its solution [4]. As a result of the conservation laws in one dimension, at zero temperature the leading mechanism of decay of a quasiparticle excitation is its disintegration into three others. We find that a phonon excitation has a decay rate proportional to the seventh power of momentum. In the integrable case of contact interaction between the bosons, the decay rate vanishes. Our theory is based on studying the anharmonic effects produced by the leading integrability breaking perturbations to the Lieb-Liniger model. It is not limited to the decay of lowest momentum phonon excitations and can describe full crossover as momentum increases and the excitation spectrum approaches its quadratic form.

[1] S. T. Beliaev, Sov. Phys. JETP 7, 299 (1958).
[2] L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 2 (Pergamon Press, Oxford, 1980).
[3]  N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, Phys. Rev. Lett. 89, 220401 (2002).
[4] Z. Ristivojevic and K. A. Matveev, arxiv:1312.5322 (2013).

# Séminaire du LPTMS : Lih-King Lim

## Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry

### Lih-King LIM (Institut d'Optique, Palaiseau)

The aim of the present work is to show that a Stückelberg interferometer made of two massive Dirac cones can reveal information on band eigenstates such as the chirality and mass sign of the cones. For a given spectrum featuring two gapped cones, we propose several low-energy Hamiltonians differing by their eigenstates properties. The corresponding inter-band transition probability is affected by such differences in its interference fringes being shifted by a new phase of geometrical origin. This phase can be a useful bulk probe for cold atoms in topological optical lattices.

# Séminaire "Fluides Quantiques" : Natalia Matveeva

## Ultracold atoms with dipolar interaction: a quantum Monte Carlo perspective

### Natalia Matveeva (BEC Center, University of Trento, Italie)

Ultracold gases with dipolar interactions became a hot topic in the field of ultracold atoms due to the recent experimental progress towards the creation of polar molecules in the quantum degenerate regime.

In the strongly interacting regime the beyond mean-field effects can play an important role, therefore the use of numerical techniques, such as quantum Monte Carlo methods, becomes preferable. In my talk I present the results of the Fixed-Node Diffusion Monte Carlo study of dipolar fermions in two dimensions at zero temperature [1,2]. I discuss the liquid-crystal phase transition, the impurity problem and BCS-BEC crossover phenomenon.

[1] N. Matveeva and S. Giorgini, Phys. Rev. Lett. 109, 200401, 2012
[2] N. Matveeva and S. Giorgini, Phys. Rev. Lett. 111, 220405, 2013

# Journal-Club: Andriy Gudyma

## Journal-Club: A superheated Bose-condensed gas

### Andriy Gudyma, LPTMS

Paper: Alexander L. Gaunt, Richard J. Fletcher, Robert P. Smith & Zoran Hadzibabic, A superheated Bose-condensed gas, Nature Physics 9, 271–274 (2013).

Abstract :
Our understanding of various states of matter usually relies on the assumption of thermodynamic equilibrium. However, the transitions between different phases of matter can be strongly affected by non-equilibrium phenomena. Here we demonstrate and explain an example of non-equilibrium stalling of a continuous, second-order phase transition. We create a superheated atomic Bose gas, in which a Bose–Einstein condensate (BEC) persists above the equilibrium critical temperature, Tc, if its coupling to the surrounding thermal bath is reduced by tuning interatomic interactions. For vanishing interactions the BEC persists in the superheated regime for a minute. However, if strong interactions are suddenly turned on, it rapidly boils away. Our observations can be understood within a two-fluid picture, treating the condensed and thermal components of the gas as separate equilibrium systems with a tunable inter-component coupling. We experimentally reconstruct a non-equilibrium phase diagram of our gas, and theoretically reproduce its main features.

# Séminaire du LPTMS: Marine Thiébaud

## Some nonlinear effects in soft matter

### Marine Thiébaud, Université Joseph Fourier (Grenoble)

I am going to present my PhD Work about nonequilibrium properties of low surface tension interfaces. This analytical and numerical work is based on experimental study on colloidal fluid interfaces, made by Derks et al [1]. I will focus on the last part of my work about moderate and large shear rates. A numerical study shows similarites between Burgers phenomenology and the studied model which made the model a promising object of study. Then, I am going to introduce some results about the bidimensional rheological properties of vesicle suspension at fixed concentration, the object of my post-doc work. After a few words on the numerical method, I am going to show the relationship between vesicle organisation and apparent viscosity.

[1] Derks, Aarts, Bonn, Lekkerkerker, and Imhof, Suppression of Thermally Excited Capillary Waves by Shear Flow, Phys. Rev. Lett. 97, 038301 (2006)

# Physics-Biology interface seminar: Éric Raspaud

## Elasticity and wrinkled morphology of Bacillus subtilis pellicles

### Éric Raspaud (LPS Orsay)

Bacterial biofilms refer to communities of bacteria that self-assemble into an extracellular cohesive matrix on a surface. We are recently interested in floating biofilms formed by wild strains of Bacillus subtilis on liquid medium. Wrinkles appear during their maturation. We have studied the formation of wrinkles in relation to their mechanical property and have shown that they could be due to a buckling instability. In this talk I will present our experimental results and their theoretical interpretations.

[caption id="attachment_22671" align="aligncenter" width="300"] Top view of bacterial pellicles floating on liquid media. Two wild strains of Bacillus subtilis are shown in Figure A and B.[/caption]

Trejo M., C. Douarche, V. Bailleux, C. Poulard, S. Mariot, C. Regeard, E. Raspaud, Elasticity and wrinkled morphology of Bacillus subtilis pellicles. Proc Natl Acad Sci USA 110 (2013), 2011-2016.

# Séminaire du LPTMS: Liza Huijse

## Emergent supersymmetry at the Ising-Kosterlitz-Thouless multicritical point

### Liza Huijse, Stanford University

Supersymmetry is a powerful concept in high-energy physics, but is often thought to require too much fine-tuning to be relevant for condensed matter systems. However, in this talk, I will show that supersymmetry emerges in a large class of models with a Z2 and U(1) symmetry at the multicritical point where the Ising and Kosterlitz-Thouless transition coincide. To arrive at this result we performed a detailed renormalization group analysis of the multicritical theory including all perturbations allowed by symmetry. I will sketch this analysis and show how it reveals an intricate flow diagram with a marginally irrelevant direction that preserves part of the supersymmetry of the fixed point. The flow along this special line is very slow and we discuss the implications of this slow flow.

# Journal-Club : Martin Lenz

Paper: J. A. Hanna and C. D. Santangelo, "Slack Dynamics on an Unfurling String", Phys. Rev. Lett. 109, 134301 (2012)

Abstract: An arch will grow on a rapidly deployed thin string in contact with a rigid plane. We present a qualitative model for the growing structure involving the amplification, rectification, and advection of slack in the presence of a steady stress field, validate our assumptions with numerical experiments, and pose new questions about the spatially developing motions of thin objects.

# Séminaire du LPTMS: Roberto Bondesan

## Pure scaling operators at the integer quantum Hall plateau transition

### Roberto Bondesan, Universität Köln

Stationary wave functions at the transition between plateaus of the integer quantum Hall effect are known to exhibit multi-fractal statistics. In this talk I will discuss this critical behavior for the case of scattering states of the Chalker-Coddington model with point contacts. I will argue that moments formed from the wave amplitudes of critical scattering states decay as pure powers of the distance between the points of contact and observation. These moments in the continuum limit are proposed to be correlation functions of primary fields of an underlying conformal field theory. Characterizations of such a theory and extensions of our methods to other systems will be presented. This is joint work in collaboration with D. Wieczorek (Cologne) and M. Zirnbauer (Cologne).

# Séminaire exceptionnel du LPTMS: Abhi Sharma

## Nonlinear elasticity in filamentous networks: a critical phenomenon

### Abhi Sharma, Amsterdam University

Most biological materials exhibit highly nonlinear mechanics apparent as striking increase in the stiffness under application of strain. In non-thermal networks such as collagen, the nonlinear behavior arises from the collective non-affine deformations. I will show that stiffening in such networks can be regarded as a strain-driven phase transition with rich critical behavior analogous to the ferromagnetic phase transition. The critical exponents obtained are non mean-field and are independent of the detailed structure of the network. Moreover, the exponents are independent of the dimensionality of the system.

# Séminaire du LPTMS: Laura Foini

## Relaxation dynamics of a coherently split one-dimensional gas

### Laura Foini, LPT ENS

Non-equilibrium dynamics and relaxation processes in isolated quantum systems represent, at present, a vivid research direction both theoretically and experimentally. Such interest is sustained by the overwhelming progress in the field of cold atoms that allows to investigate the unitary dynamics of the system.

In this talk I will review an experiment that has considered the splitting of a one-dimensional Bose gas into two coherent gases, where, ultimately, the properties of the system are probed by matter-wave interference.

While previous works have focused on the independent dynamics of the two systems after the splitting, in our study we take into account the effect of a finite tunneling coupling between the two. Comparisons between the results obtained for such non-equilibrium problem and the thermal ones will be drawn.

# Journal club: François Landes

## Paper: A. Celani & M. Vergassola, "Bacterial strategies for chemotaxis response", Proc. Natl. Acad. Sci. U. S. A. 107, 1391–6 (2010).

### François Landes, PhD student LPTMS

Regular environmental conditions allow for the evolution of specifically adapted responses, whereas complex environments usually lead to conflicting requirements upon the organism’s response. A relevant instance of these issues is bacterial chemotaxis, where the evolutionary and functional reasons for the experimentally observed response to chemoattractants remain a riddle. Sensing and motility requirements are in fact optimized by different responses, which strongly depend on the chemoattractant environmental profiles. It is not clear then how those conflicting requirements quantitatively combine and compromise in shaping the chemotaxis response. Here we show that the experimental bacterial response corresponds to the maximin strategy that ensures the highest minimum uptake of chemoattractants for any profile of concentration. We show that the maximin response is the unique one that always outcompetes motile but nonchemotactic bacteria. The maximin strategy is adapted to the variable environments experienced by bacteria, and we explicitly show its emergence in simulations of bacterial populations in a chemostat. Finally, we recast the contrast of evolution in regular vs. complex environments in terms of minimax vs. maximin game-theoretical strategies. Our results are generally relevant to biological optimization principles and provide a systematic possibility to get around the need to know precisely the statistics

# Séminaire du LPTMS: Enrique Abad

## Fractional equation approaches to subdiffusion problems: a tale of tails

Anomalous transport (in the sense of a nonlinear growth of the mean square displacement) is ubiquitous in nature, notably in biological systems. A widely used model to mimic anomalous transport processes with a large dispersion of waiting times is the celebrated Continuous Time Random Walk (CTRW). The CTRW with a long-tailed waiting time distribution and a jump length distribution of finite variance (both decoupled from one another) is known to become equivalent to a fractional diffusion equation in the long-time limit. While the fractional diffusion equation is an integrodifferential equation, it is nevertheless amenable to exact solution via Laplace transform methods or a variable separation ansatz.

We consider a number of first-passage problems of interest involving the solution of the fractional diffusion equation with absorbing boundary conditions. The solutions are characterized by a very detailed memory of the initial condition persisting even in the long-time regime; the solutions are also peculiar from a mathematical viewpoint as a) the long-time decay modes can be used to construct new polynomial approximations for Bessel functions and b) for a proper choice of the system parameters divergent series are seen to emerge in the solution. Such series must be suitably regularized to recover the physically correct solutions.

Finally, we shall also give an overview on how to deal with problems where the absorption process is not constrained to a boundary, but is delocalized in space. In this case one must use highly non-intuitive reaction-subdiffusion equations which find a proper justification in the framework of a mesoscopic approach. We shall discuss the application of this type of equations to understand a key process in developmental biology, namely, the formation of morphogen concentration gradients by means of subdiffusive transport.

# Physics-Biology interface seminar: Jean-Marc Allain

## Etude multi-échelle des tissus riches en collagène

### Jean-Marc Allain (École Polytechnique)

Nous nous intéressons au lien entre l'organisation du collagène dans les tissus mous (comme la peau ou les tendons) et leurs propriétés mécaniques. Pour cela, nous avons mis au point avec le LOB de l'Ecole Polytechnique un montage original qui combine une machine de traction avec un microscope à Génération de Seconde Harmonique. Cette microscopie non-linéaire permet d'image les fibrilles de collagène en 3D et sans marquage dans un tissu, donnant accès à son organisation à l'échelle micrométrique. We avons validé ce dispositif sur le tendon, avant de l'utiliser sur d'autres tissus.

# Séminaire du LPTMS: Luca Tagliacozzo

## Physics of the 1D long range Ising model in a transverse field

### Luca Tagliacozzo, ICFO Barcelone

Long range interacting systems can show different behaviour from their short range version. Recently experiments with trapped ions have started to investigate them. I will charaterize  the ground state and low energy excitations of the long range Ising model in a transverse field, the simplest interacting long range model in 1D. In particular I will focus on the complexity of the ground state wave function in terms of entanglement measure and more traditional spin correlations. I will also present some results about the violation of causality when the long range interactions decay slowly enough with the distance. I will also briefly review the experiments with trapped ions that have confirmed our predictions.

# Tri-séminaire de Physique Statistique : Thierry Giamarchi

## Quantum magnets as quantum simulators

### Thierry Giamarchi (Université de Genève)

The ability to control the properties of magnetic insulators by magnetic fields large enough to fully polarize the system has opened a host of possibilities. In addition to the intrinsic interest of such questions for magnetic systems, is has been shown that such systems could be efficiently used as quantum simulators to emulate problems pertaining to itinerant fermionic or bosonic systems. The magnetic field can then be viewed as similar to a gate voltage controlling the number of particles'' allowing an unprecedented level of control. In parallel with the experimental developments, progress on the theoretical front both on the numerical and the analytical side, have allowed a remarkable level of accuracy in obtaining the physical properties and in particular the correlation functions of these systems. A comparison between theoretical predictions without adjustable parameters or fudging with results from NMR, Neutrons or other probes such as ESR is thus now possible. This has allowed for example to test quantitatively the physics of Tomonaga-Luttinger liquids and also to tackle the effects of the interactions between spinons by comparing the physics of weak rung ladders with the one of strong rung ones.

I will review the recent results obtained in this domain with the different experimental compounds and will discuss the open questions and challenges. This concerns in particular the issues of finite temperatures, higher dimensional systems and effects of disorder.

# Séminaire exceptionnel : Maciej Nowak

## "Burgers dynamics  in hermitian and nonhermitian RMM".

### Maciej Nowak, Jagellonian University, Cracovie.

We obtain several classes of non-linear partial differential equations for various random matrix ensembles undergoing Brownian type of random walk. These equations for spectral flow of eigenvalues as a function of dynamical parameter ("time") are exact for any finite size N of the random matrix ensemble and resemble viscid Burgers-like equations known in the theory of turbulence. In the limit of infinite size of the matrix, these equations reduce complex inviscid Burgers equations, proposed originally by Voiculescu in the context of free processes. We identify spectral shock waves for these equations in the limit of the infinite size of the matrix, and then we solve exact, finite N nonlinear equations in the vicinity of the shocks, obtaining in this way universal, microscopic scalings equivalent to Airy, Bessel and cuspoid kernels. Finally, we show that similar but  hidden Burgers-like structures appear (surprisingly)  also in nonhermitian random matrix models, e.g. in the Ginibre-Girko ensemble, where they govern the concurent  evolution of both eigenvalues and eigenvectors.

# Séminaire du LPTMS: Chiara Cammarota

## Quantitative theory of the random pinning glass transition and cooperative length scales

### Chiara Cammarota, Sapienza, Rome

First direct observations of the ideal glass transition may be realized through the study of randomly-pinned systems, systems where a fraction of the particles are frozen in the position they have in an equilibrium configuration. As an initial guideline for experimental tests of the glass transition induced by this construction, aka Random Pinning Glass Transition (RPGT), I will show the results of first-principles computations by the Hypernetted chain approximation for Hard Sphere glasses which confirm the expected enhancement of glassy behaviour under the procedure of random pinning. I will present the phase diagram as a function of the concentration of pinned particles and of the global packing fraction, showing a line of RPGT and two spinodal lines for the competing liquid and glass phases. The other main results I will highlight are the first microscopic computation of cooperative length-scales characterizing amorphous order in glass-formers and quantitative information on a key thermodynamic quantity defined in proximity of the ideal glass transitions, the amorhpous surface tension.

# Séminaire "Fluides quantiques" du LPTMS : Peter Forgacs

## Plane waves as tractor beams

### Péter Forgacs (LMPT, Université de Tours, Wigner Center Budapest)

The subject of the talk is a simple but somewhat surprising effect, when an incident plane wave exerts a pulling force on the scatterer instead of the expected pushing.
This effect, which goes under the names of "tractor beam" or "negative radiation pressure", appears in a number of systems in 1 and 2 spatial dimensions. The underlying physical mechanism for the appearance of the pulling force is the sufficiently strong scattering of the incoming wave into another propagating mode in the forward direction carrying away more momentum than that contained in the incoming wave. In such a case a "surplus" of momentum is created behind the scatterer leading to the eeffect. Such a negative radiation pressure is found to appear in nonlinear field theoretical systems (kinks, vortices), also in optical (birefringent) systems, and it may also be relevant for more exotic objects like cosmic strings.

Talk based on P. Forgács, Á. Lukács, T. Romanczukiewicz, Plane waves as tractor beams, Phys. Rev. D88, 125007 (2013).

# Séminaire exceptionnel du LPTMS: Serena Bradde

## Emergence of global patterns in bacterial growth: from single cells to communities

### Serena Bradde, City University of New York

Understanding how phenomenological behaviors observed in biological systems emerge from molecular interactions of many individual units and how these interactions shape the response of living systems to a changing environment are  challenging questions which lie at the interface between multiple disciplines.

In this talk I will draw an example from the human gut microbiome, the full consortium of microbes living in association with the human gutRecent developments in DNA sequencing have made it possible to monitor how the compositions of microbial species change in time.

Analysis of healthy adults under antibiotic treatment showed that the gut microbiota could take several weeks to recover after treatment cessation. This suggests that the combination of inter-species and host-microbe interactions and external perturbations could lead to hysteresis phenomena.

We investigate this possibility and propose an out of equilibrium stochastic model able to explain this phenomenon in terms of a first-order phase transition scenario. Our study reveals the importance of noise-activated dynamics in the recovery from antibiotic-perturbed states.

# Physics-Biology interface seminar: Lukas Kapitein

## Navigating the cytoskeleton: novel tools to dissect and direct intracellular transport

### Lukas Kapitein (Universiteit Utrecht, The Netherlands)

Active transport is important for proper cellular organization and functioning. Such transport is driven by a large variety of molecular motor proteins that can walk over cytoskeletal biopolymers such as microtubules and F-actin. Whereas controlled biophysical experiments using purified components have revealed many of the basic properties of these fascinating machines, much less is known about their specific intracellular activity and about the interplay between cytoskeletal organization and transport. To address these questions, we have developed novel tools to control the activity of specific motors inside cells. These experiments have revealed different mechanisms by which the underlying organization of the microtubule network guides motor transport to specific destinations. In addition, these tools enabled us to remote-control intracellular transport and alter cellular behavior using light.

Lukas Kapitein is assistant professor at the Division of Cell Biology of Utrecht University, where his group develops novel approaches to understand how the cytoskeleton and their associated motor proteins contribute to cellular organization and morphology. The combined use of well-controlled, inducible intracellular transport assays and fluorescence nanoscopy of the cytoskeleton offers unique insights into the interplay between cytoskeletal organization and motor-driven transport.

# Séminaire du LPTMS: Raphaël Chétrite

## Grande Déviation et Hors d'Equilibre

### Raphaël Chétrite, Université de Nice

Ce séminaire contiendra deux parties. La première sera une ''scratch'' présentation de la théorie des Grandes Déviations. La deuxième partie portera sur des résultats récents, obtenus avec Hugo Touchette (PRL 111, 120601 (2013)) portant sur des processus de Markov conditionnés à des événements rares. Je démontrerai, à l'aide de la théorie des grandes déviations, qu'un tel processus conditionné peut être représenté par un processus markovien sans conditionnement, appelé processus équivalent, ayant les mêmes propriétés typiques que le processus conditionné.  La motivation physique pour l'étude de tels processus conditionnés découle de la question de l'équivalence et de la simulation d'ensembles microcanoniques et canoniques hors d'équilibre.

# Séminaire du LPTMS : Jasleen Lugani

## Transmission spectra of an optical cavity coupled with ultracold atoms in an optical  lattice.

### Jasleen Lugani (IIT Delhi, New Delhi, India)

We consider the transmission characteristics of an optical cavity loaded with ultracold atoms in an optical lattice at absolute zero temperature. In particular, I will talk about the situation when the many body quantum state of the ultra cold atoms is an insulating state with fixed number of atoms at each site, which can be either density wave (DW) or Mott insulator (MI) phase, each showing different type of discrete lattice translational symmetry. We will see how transmission spectra of the cavity can serve as a tool to distinguish between such insulating phases. Further, I will also discuss how the respective spectrum changes when these insulating phases make a crossover to the superfluid (SF) phase with the changing depth of the optical lattice potential.

# Séminaire du LPTMS: Ian McCulloch

## Topological insulating phase in the molecular compound $mathrm{Mo_3 S_7 (dmit)_3}$

### Ian McCulloch (University of Queensland, Australie)

Using the infinite-size density matrix renormalization group (iDMRG) approach, we show that a Hubbard-like model on a triangular cluster, representative of the compound $mathrm{Mo_3 S_7 (dmit)_3}$, is in the universally class of the symmetry-protected topological 1D Haldane insulator, despite the presence of itinerant fermions which would normally destroy the symmetry protection. I will also illustrate a new technique, to calculate cumulant expansions of order parameters using iDMRG, which gives detailed information on quantum phase transitions and has many potential uses, eg full-counting statistics through a quantum quench.

# Cours du LPTMS : Raoul Santachiara

## Cours du LPTMS

### Introduction to Conformal Field Theory

The conformal field theory (CFT) approach aims to find the solutions of the infinite set of equations imposed by conformal invariance. This approach has been successfully employed in diverse areas of physics and mathematics for almost thirty years. We will survey the basics ideas of the CFT approach trying to minimize as much as possible the many technicalities hidden behind. We will see some (recent) applications on these concepts on 1D(2D) quantum(statistical) systems and in quantum topological states .

# Tri-séminaire de Physique Statistique : Vincent Vargas

## Complex Gaussian multiplicative Chaos

### Vincent VARGAS (Dépt. de Mathématique (DMA), Ecole Normale Supérieure Paris)

The mathematical theory of Gaussian multiplicative chaos was founded by J. P. Kahane in 1985. This theory has numerous applications in mathematical physics: 2d Liouville quantum gravity in the conformal gauge (boundary and non boundary Liouville measure, KPZ equation), the Kolmogorov-Obukhov model of energy dissipation in 3d turbulence, the maximum of log-correlated fields, etc... In this talk, we will review the theory of Kahane and discuss numerous extensions that have been developed the past few years, in particular to the complex case. Special emphasis will be made on applications which motivate these extensions. This is based on joint works with B. Duplantier, H. Lacoin, T. Madaule, R. Rhodes, S. Sheffield.

# Physics-Biology interface seminar: Gijsje Koenderink

## Living soft matter

### Gijsje Koenderink (FOM Institute AMOLF)

One of the defining qualities of soft matter is that it is readily driven far from thermodynamic equilibrium by external stress. Driving forces such as those due to an electric field or shear can drive colloidal suspensions and polymer networks into fascinating non-equilibrium patterns, such as banded or ordered steady states. By contrast, living cells naturally exhibit a unique form of internal driving in the form of chemomechanical activity. A prominent example is the cytoskeleton, a meshwork of protein polymers and force-generating motor proteins that constitutes the scaffold of cells. The cytoskeleton is responsible for driving vital cellular functions such as growth, division, and movement. In this talk, I will present two examples of our research on active cytoskeletal polymer gels. The first example concerns active contractility of the actin cortex, which lies underneath the cell membrane and drives shape changes by means of myosin motors. By reconstituting a simple model system composed of purified proteins, we could show how myosin motors and actin filaments collectively self-organize into force-generating arrays. We discovered that motors contract actin networks only above a sharp threshold in crosslink density, corresponding to a connectivity percolation transition. Surprisingly, the motors tend to drive initially well-connected networks robustly to this critical point. The second example I will discuss concerns cell shape polarization directed by interactions of actin filaments with microtubules. I will show that active force generation by growing and shrinking microtubules leads to feedback between the organization of the actin filaments and microtubules, explaining earlier observations made in living cells.

# Cours du LPTMS : Raoul Santachiara

## Cours du LPTMS

### Introduction to Conformal Field Theory

The conformal field theory (CFT) approach aims to find the solutions of the infinite set of equations imposed by conformal invariance. This approach has been successfully employed in diverse areas of physics and mathematics for almost thirty years. We will survey the basics ideas of the CFT approach trying to minimize as much as possible the many technicalities hidden behind. We will see some (recent) applications on these concepts on 1D(2D) quantum(statistical) systems and in quantum topological states .

# Séminaire du LPTMS: A. de Luca

## Anderson localization on a Bethe lattice: non-ergodicity of extended states

### Andrea De Luca, LPT ENS

Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any disorder. The spectrum of fractal dimensions f(α) remains positive for α noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization, i.e. the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.

# Cours du LPTMS : Raoul Santachiara

## Cours du LPTMS

### Introduction to Conformal Field Theory

The conformal field theory (CFT) approach aims to find the solutions of the infinite set of equations imposed by conformal invariance. This approach has been successfully employed in diverse areas of physics and mathematics for almost thirty years. We will survey the basics ideas of the CFT approach trying to minimize as much as possible the many technicalities hidden behind. We will see some (recent) applications on these concepts on 1D(2D) quantum(statistical) systems and in quantum topological states .

# Cours du LPTMS : Raoul Santachiara

## Cours du LPTMS

### Introduction to Conformal Field Theory

The conformal field theory (CFT) approach aims to find the solutions of the infinite set of equations imposed by conformal invariance. This approach has been successfully employed in diverse areas of physics and mathematics for almost thirty years. We will survey the basics ideas of the CFT approach trying to minimize as much as possible the many technicalities hidden behind. We will see some (recent) applications on these concepts on 1D(2D) quantum(statistical) systems and in quantum topological states .

# Séminaire du LPTMS : Sanjib Sabhapandit

## High-energy tail of the velocity distribution of driven inelastic Maxwell gases

### Sanjib Sabhapandit, Raman Research Institute, Bangalore

A model of homogeneously driven dissipative system, consisting of a collection of $N$ particles that are characterized by only their velocities, is considered. Adopting a discrete time dynamics, at each time step, a pair of velocities is randomly selected. They undergo inelastic collision with probability $p$. With probability $(1-p)$, energy of the system is changed by changing the velocities of both the particles independently according to $vrightarrow -r_w v +eta$, where $eta$ is a Gaussian noise drawn independently for each particle as well as at each time steps. For the case $r_w=- 1$, although the energy of the system seems to saturate (indicating a steady state) after time steps of $O(N)$, it grows linearly with time after time steps of $O(N^2)$, indicating the absence of a eventual steady state. For $-1 <r_w leq 1$, the system reaches a steady state, where the average energy per particle and the correlation of velocities are obtained exactly. In the thermodynamic limit of large $N$, an exact equation is obtained for the moment generating function. In the limit of nearly elastic collisions and weak energy injection, the velocity distribution is shown to be a Gaussian. Otherwise, for $|r_w| < 1$, the high-energy tail of the velocity distribution is Gaussian, with a different variance, while for $r_w=+1$ the velocity distribution has an exponential tail.

# Séminaire du LPTMS: Paul Zinn-Justin

## Discrete holomorphicity and quantized affine algebras

### Paul Zinn-Justin, LPTHE

This is joint work with I. Ikhlef, R. Weston and M. Wheeler. I will discuss the interplay between two properties of two-dimensional statistical models, namely integrability (or exact solvability) and discrete holomorphicity. After introducing these concepts, I will explain how the Bernard-Felder construction of nonlocal currents out of quantized affine algebras provides a link between them, relating the discrete holomorphicity equation with conservation of these nonlocal currents. I will discuss as an example the case of the Temperley--Lieb (dense) loop model.

# Séminaire du LPTMS : Oleksandr Gamayun

### Oleksandr Gamayun, Lancaster University

We investigate the time evolution of the momentum of an impurity atom injected into a degenerate Tonks-Girardeau gas. We establish that given an initial momentum p0 the impurity relaxes to a steady state with a non-vanishing momentum p∞. The nature of the steady state is found to be drastically different for integrable and non-integrable impurity models, which is due to multiple coherent scattering processes leading to a resonant interaction between the impurity and the host in the integrable case. The dependence of $p_infty$ on $p_0$ remains non-trivial even in the limit of vanishing interaction between the impurity and host particles. In this limit $p_infty(p_0)$ is found explicitly and the case of the external force applied to the impurity is analyzed as well.

# Journal club : Martin Trulsson

## Martin Trulsson , LPTMS

Supercooled liquids are characterized by their fragility: The slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure controls fragility remains a challenge. Surprisingly, experiments indicate that the linear elasticity of the glass—a purely local property of the free energy landscape—is a good predictor of fragility. In particular, materials presenting a large excess of soft elastic modes, the so-called boson peak, are strong. This is also the case for network liquids near the rigidity percolation, known to affect elasticity. Here we introduce a model of the glass transition based on the assumption that particles can organize locally into distinct configurations that are coupled spatially via elasticity. The model captures the mentioned observations connecting elasticity and fragility. We find that materials presenting an abundance of soft elastic modes have little elastic frustration: Energy is insensitive to most directions in phase space, leading to a small jump of specific heat. In this framework strong liquids turn out to lie the closest to a critical point associated with a rigidity or jamming transition, and their thermodynamic properties are related to the problem of number partitioning and to Hopfield nets in the limit of small memory.

# Tri-Séminaire de Physique Statistique : Merouane Debbah

## Random matrices for wireless communications : when Wigner meets Shannon

### Merouane Debbah, Alcatel-Lucent Chair on Flexible Radio, Supélec

The asymptotic behaviour of the eigenvalues of large random matrices has been extensively studied since the fifties. One of the first related result was the work of Eugène Wigner in 1955 who remarked that the eigenvalue distribution of a standard Gaussian hermitian matrix converges to a deterministic probability distribution called the semi-circular law when the dimensions of the matrix converge to infinity. Since that time, the study of the eigenvalue distribution of random matrices has triggered numerous works, in the theoretical physics as well as probability theory communities. However, as far as communications systems are concerned, until the mid 90’s, intensive simulations were thought to be the only technique to get some insight on how communications behave with many parameters. All this changed in 1997 when large system analysis based on random matrix theory was discovered as an appropriate tool to gain intuitive insight into communication systems. In particular, the self-averaging effect of random matrices was shown to be able to capture the parameters of interest of communication schemes. Since the year 2000, the results led to very active research in many fields such as MIMO systems currently used in 4G technologies. This talk is intended to give a comprehensive overview of random matrices and their application to the analysis and design of wireless communication systems (4G and 5G systems).

# Presentation

During more than 50 years since the discovery of Anderson localization of particles, the physics of disordered quantum systems underwent tremendous developments. At present, the localization of interacting particles remains one of the global problems in condensed matter physics. The key issues concern metal-insulator transitions in mesoscopic systems, electron-phonon interaction and transport in the insulating and metallic states, superconductor-insulator transitions, disordered Josephson arrays. In the last decade, localization of interacting particles became one of the key problems in ultracold atomic quantum gases, which have temperatures in the nanokelvin regime and eight orders of magnitude lower densities than liquid helium. After first successful experiments in Orsay and Florence, the domain of quantum gases in disorder is rapidly growing. The aim of the present workshop is to bring together leading experts in condensed matter and atomic physics and to discuss recent developments in the field of disordered quantum systems.

# Invited speakers:

• Alain Aspect (Institut d'Optique, Palaiseau)
• Giulio Biroli (CEA, Saclay)
• Hélène Bouchiat (LPS, Orsay)
• Vincent Bouchiat (Institut Néel, Grenoble)
• Dominique Delande (LKB ENS, Paris)
• Benoît Douçot (LPTHE, Paris)
• Sergey Flach (Massey University, Auckland, New Zealand)
• Antoine Georges (Collège de France, Paris)
• Thierry Giamarchi (University of Geneva, Switzerland)
• Igor Lerner (University of Birmingham, UK)
• Charly Marcus (University of Copenhagen, Denmark)
• Giovanni Modugno (LENS, Florence, Italy)
• Gilles Montambaux (LPS, Orsay)
• Hugues Pothier (CEA, Saclay)
• Benjamin Sacépé (Institut Néel, Grenoble)
• Laurent Sanchez-Palencia (Institut d'Optique, Palaiseau)
• Andrey Varlamov (Rome University Tor Vergata, Italy)
• Vladimir Yudson (RQC, Moscow, Russia)

# Contact

For more information :  Tel: +33 1 69 15 31 82  Fax: +33 1 69 15 65 25  vincent.michal@lptms.u-psud.fr

# Presentation

During more than 50 years since the discovery of Anderson localization of particles, the physics of disordered quantum systems underwent tremendous developments. At present, the localization of interacting particles remains one of the global problems in condensed matter physics. The key issues concern metal-insulator transitions in mesoscopic systems, electron-phonon interaction and transport in the insulating and metallic states, superconductor-insulator transitions, disordered Josephson arrays. In the last decade, localization of interacting particles became one of the key problems in ultracold atomic quantum gases, which have temperatures in the nanokelvin regime and eight orders of magnitude lower densities than liquid helium. After first successful experiments in Orsay and Florence, the domain of quantum gases in disorder is rapidly growing. The aim of the present workshop is to bring together leading experts in condensed matter and atomic physics and to discuss recent developments in the field of disordered quantum systems. Download Poster

# Invited speakers:

• Alain Aspect (Institut d'Optique, Palaiseau)
• Giulio Biroli (CEA, Saclay)
• Hélène Bouchiat (LPS, Orsay)
• Vincent Bouchiat (Institut Néel, Grenoble)
• Dominique Delande (LKB ENS, Paris)
• Benoît Douçot (LPTHE, Paris)
• Sergey Flach (Massey University, Auckland, New Zealand)
• Antoine Georges (Collège de France, Paris)
• Thierry Giamarchi (University of Geneva, Switzerland)
• Igor Lerner (University of Birmingham, UK)
• Charly Marcus (University of Copenhagen, Denmark)
• Giovanni Modugno (LENS, Florence, Italy)
• Gilles Montambaux (LPS, Orsay)
• Hugues Pothier (CEA, Saclay)
• Benjamin Sacépé (Institut Néel, Grenoble)
• Laurent Sanchez-Palencia (Institut d'Optique, Palaiseau)
• Andrey Varlamov (Rome University Tor Vergata, Italy)
• Vladimir Yudson (RQC, Moscow, Russia)

# Contact

For more information :  Tel: +33 1 69 15 31 82  Fax: +33 1 69 15 65 25  vincent.michal@lptms.u-psud.fr

# Presentation

During more than 50 years since the discovery of Anderson localization of particles, the physics of disordered quantum systems underwent tremendous developments. At present, the localization of interacting particles remains one of the global problems in condensed matter physics. The key issues concern metal-insulator transitions in mesoscopic systems, electron-phonon interaction and transport in the insulating and metallic states, superconductor-insulator transitions, disordered Josephson arrays. In the last decade, localization of interacting particles became one of the key problems in ultracold atomic quantum gases, which have temperatures in the nanokelvin regime and eight orders of magnitude lower densities than liquid helium. After first successful experiments in Orsay and Florence, the domain of quantum gases in disorder is rapidly growing. The aim of the present workshop is to bring together leading experts in condensed matter and atomic physics and to discuss recent developments in the field of disordered quantum systems.

# Invited speakers:

• Alain Aspect (Institut d'Optique, Palaiseau)
• Giulio Biroli (CEA, Saclay)
• Hélène Bouchiat (LPS, Orsay)
• Vincent Bouchiat (Institut Néel, Grenoble)
• Dominique Delande (LKB ENS, Paris)
• Benoît Douçot (LPTHE, Paris)
• Sergey Flach (Massey University, Auckland, New Zealand)
• Antoine Georges (Collège de France, Paris)
• Thierry Giamarchi (University of Geneva, Switzerland)
• Igor Lerner (University of Birmingham, UK)
• Charly Marcus (University of Copenhagen, Denmark)
• Giovanni Modugno (LENS, Florence, Italy)
• Gilles Montambaux (LPS, Orsay)
• Hugues Pothier (CEA, Saclay)
• Benjamin Sacépé (Institut Néel, Grenoble)
• Laurent Sanchez-Palencia (Institut d'Optique, Palaiseau)
• Andrey Varlamov (Rome University Tor Vergata, Italy)
• Vladimir Yudson (RQC, Moscow, Russia)

# Contact

Tel: +33 1 69 15 31 82
Fax: +33 1 69 15 65 25
vincent.michal@lptms.u-psud.fr

# Physics-Biology interface seminar: Marie-Pierre Valignat

## Leukocyte sensing of flow direction

### Marie-Pierre Valignat (Laboratoire Adhésion Cellulaire et Inflammation, Marseille)

As they leave the blood stream and travel to lymph nodes or sites of inflammation, leukocytes are captured by the endothelium and migrate along the vascular wall to permissive sites of transmigration. These processes are supposedly orchestrated by chemical signals and take place under the influence of a strong hemodynamic shear stress. The role of flow on leukocyte crawling and extravasation remains generally an unsolved question, however crawling T lymphocytes were recently reported in vivo and in vitro to orient against the direction of flow and to move upstream like salmons in a river. This non-intuitive behavior is manifestly not a passive drift of cells pushed by the flow, and we sought here to clarify the origin, role and mechanism of this upstream flow mechanotaxis behavior.

# Séminaire du LPTMS: Remy Dubertrand

## Two scenarios of multifractality breakdown

### Remy Dubertrand, LPT Toulouse

Multifractality is a powerful tool to describe non trivial fluctuations of a field. One seminal example is provided by the Anderson transition due to disorder in 3D: at the critical point the eigenstates of the Hamiltonian display multifractality, leading i.e. to anomalous diffusion. We have been interested in the effect of a perturbation on the multifractality in a quantum system. Considering two generic models I will show that multifractality disappears following two well identified scenarios. I will describe these scenarios in details and discuss their consequences in order to achieve a better understanding of multifractality in quantum mechanics.

# Séminaire du LPTMS : Ennio Gozzi

## On the geometry of geometric quantization

### Ennio Gozzi, University of Trieste

In this talk we will pedagogically review the Hilbert space approach to Classical Mechanics pioneered by Koopman and von Neumann. Next we will build its associated Classical Path Integral and study geometrically the many extra variables which make their appearance beside the phase-space ones. Quantization turns then out to be nothing else than a proper dimensional reduction and to be at the same time the functional counterpart of Geometric Quantization.

# Tri-séminaire de Physique Statistique: Nalini Anantharaman

## Quantum ergodicity

### Nalini Anantharaman, Département de Mathématiques d'Orsay, Université Paris-Sud

Quantum ergodicity deals with the (de)localization of eigenfunctions of Schrödinger operators, for classically chaotic systems. In this talk I will review the rigourous results on the subject. I will also talk about my recent work with Etienne Le Masson, where we studied the delocalization of eigenfunctions on large regular (discrete) graphs.

# Séminaire du LPTMS: Jean-Marc Luck (Attention, horaire inhabituel)

## On the frequencies of patterns of rises and falls

### Jean-Marc Luck, IPhT Saclay

We investigate the probability of observing a given pattern of rises and falls in a random stationary data series. The data can be modelled as a sequence of independent and identically distributed random numbers or, equivalently, as a uniform random permutation. The probability of observing a long pattern decays exponentially with its length in general. The associated decay rate is interpreted as the embedding entropy of the pattern. This rate is evaluated exactly for all periodic patterns, generalizing thus the pioneering work by André on alternating permutations. In the most general case, it is expressed in terms of a determinant of generalized hyperbolic or trigonometric functions. The probabilities of uniformly chosen random patterns are observed to obey multifractal statistics. The typical value of the rate, corresponding to the endpoint of the multifractal spectrum, plays the role of a Lyapunov exponent. A wide range of examples of patterns, either deterministic or random, is also investigated (Physica A 407 (2014) 252-275).

# Séminaire du LPTMS: Andrey Lokhov

## Dynamic message-passing equations and applications to epidemic and information spreading on networks

### Andrey Lokhov, LPTMS

Understanding and quantifying the out-of-equilibrium dynamics is one of the major tasks of today's science. Using dynamic cavity method on time trajectories, we show how to derive dynamic message-passing (DMP) equations for a large class of models with irreversible dynamics - the key point that makes the problem solvable. These equations are asymptotically exact for locally tree-like graphs and generally provide a good approximation for real-world networks. We illustrate the approach by applying the DMP equations for susceptible-infected-recovered (SIR) and ignorant-spreader-stifler models (ISS) models to the problems of inference of epidemic origin and optimal information spreading with awareness.

# Séminaire du LPTMS: Edouard Boulat

## Exact results on the out-of-equilibrium Kondo model

### Edouard Boulat, Université Paris Diderot

Transport in nanoscale quantum devices can be described in many situations by quantum impurity models in which the low energy regime is a strong coupling (SC) regime, an archetypical example being the Kondo model. Equilibrium properties in this regime are non perturbative but nevertheless fully accessible using integrability.

After discussing why the exact solution *at equilibrium* cannot be in general extended to describe the out-of-equilibrium situations, I will describe a recently developed framework for integrable quantum impurity models [1], in which we can exactly tackle various out-of-equilibrium situations in their SC regime, using their equilibrium integrability properties. It allows to compute directly the expansion of the universal scaling functions for physical quantities (like the electrical current), in principle to arbitrarily high order in the driving out-of-equilibrium, be it voltage, frequency... In particular, we show how to apply this to the Kondo model : our approach successfully goes beyond known results for the electrical current and noise.

[1] L.Freton and E.Boulat, PRL 112, 216802 (2014).

# Physics-Biology interface seminar: Francesco Piazza

## Diffusion-controlled reactions in complex media

### Francesco Piazza (Université d'Orléans)

In all biochemical reactions occurring in living tissues, reactants have to form an encounter complex before the specific chemical step. Invariably, in order to reach their binding partners, biomolecules have to diffuse in complex environments, both very crowded with all sorts of other biomolecules and organelles and confining, due to the presence of different membranes and cytoskeletal structures that strongly compartimentalize the available space.

Under such conditions, the standard Smoluchowski theory for biomolecular encounters valid in ideal solutions is no longer applicable and the need emerges for more sophisticated theoretical paradigms accounting explcitly for crowding and confinement in the computation of encounter rates.

In this talk, I will illustrate a general theoretical paradigm that we are developing in our group to solve this problem. Using addition theorems for spherical harmonics, we compute the diffusion rate to a sink in the presence of crowding agents that we model as spheres of arbitrary radius and endowed with arbitrary reactivity, from fully reflecting (purely excluded volume) to fully absorbing (competitive binding partners). We consider both diffusion in an unbounbded domain and diffusion occurring within a spherical domain, as an attempt to model encounters occurring within a cell. Different applications will be discussed, such as diffusion to a binding pocket in a coarse-grained model of protein and reactions occurring in vesicles and other kinds of nanoreactors.

# Séminaire du LPTMS: Alberto Parola

## A microscopic implementation of non Functional Renormalization Group in classical and quantum models

### Alberto Parola, Universita' dell'Insubria, Como, Italy

A general framework for implementing the Renormalization Group ideas to microscopic models in classical and quantum statistical physics is presented. The method, referred to as HRT, is devised so to retain information on non universal properties throughout the renormalization process by avoiding any coarse-graining procedure and the mapping onto effective models. Different implementations of HRT are briefly reviewed pointing out the close relationship with non-perturbative renormalization group methods. The critical properties of HRT for a O(n) order parameter are summarized, together with the behavior of the theory at first-order phase transitions. Applications to simple microscopic models in classical and quantum statistical physics, both on and off lattice, are discussed.

# Physics-Biology interface seminar: Manuel Théry

## Relaxation in Cell Cytoskeleton

### Manuel Théry (Hôpital Saint-Louis, Paris)

Using combinations of in vivo and in vitro approaches we try to unravel the mechanisms regulating actin bundle and microtubule mechanical properties in response to geometrical and/or mechanical stimulations.

# Séminaire du LPTMS: Gabriel Tellez

## Screening in 1D Coulomb systems

### Gabriel Tellez, Universidad de los Andes

We study a system of two like-charges screened by N counter-ions, living on a line and interacting through the 1D Coulomb potential. We obtain explicit analytic expressions for the canonical partition function and the effective force between the like-charges. It is shown that this force can be attractive depending on the distance between the charges and the parity of the number of counter-ions N.

# Séminaire exceptionnel du LPTMS: Pierpaolo Vivo

## Phase transitions in the condition number distribution of Gaussian random matrices

### Pierpaolo Vivo, LPTMS

We study the statistics of the condition number k (the ratio between largest and smallest squared singular values) of NxM Gaussian random matrices. Using a Coulomb fluid technique, we derive analytically and for large N its cumulative P(k<x) and tail-cumulative P(k>x) distributions. We find the decay of these distribution. The left and right rate functions are calculated exactly for any choice of the rectangularity parameter M/N-1. Interestingly, they show a weak non-analytic behavior at their minimum <k> (corresponding to the average condition number), a direct consequence of a phase transition in the associated Coulomb fluid problem.  Matching the behavior of the rate functions around <k>, we determine exactly the scale of typical fluctuations and the tails of the limiting distribution of  k. The analytical results are in excellent agreement with numerical simulations.

# Séminaire du LPTMS: Anna Bodrova

## Aggregation and fragmentation in granular mixtures

### Anna Bodrova, Moscow State University

Granular materials, such as gravel sand or different types of powders, are ubiquitous in nature and widely used in industry. Rarified granular systems, where the volume of a solid phase is small as compared to the total volume, are termed as granular gases. In the Earth conditions these may be obtained by placing granular matter into a container with vibrating or rotating walls, applying electrostatic or magnetic forces etc. Extraterrestrial granular gases are also common. Many astrophysical objects, like protoplanetary discs, Planetary Rings and interstellar dust clouds contain granular gases as one of the important component.

Granular materials represent a polydisperse mixture of grains of different mass and size. We investigate size and kinetic energy distribution in granular mixtures, arising due to interplay of aggregation and fragmentation of granular particles. We also discuss application of our theory to dense planetary rings and compare our results with data, available from the observations.

# Soutenance de thèse : François Landes

## Viscoelastic interfaces Driven in Disordered Media & Application to Friction

### François Landes, LPTMS

Many complex systems respond to a continuous input of energy by an accumulation of stress over time, interrupted by 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, which are neglected by most models. During my thesis, I studied two well-known models of avalanche dynamics, modified minimally by the inclusion of some forms of relaxation.

The first system is that of a viscoelastic interface driven in a disordered medium. In mean-field, we prove that the interface has a periodic behaviour (with a new, emerging time scale), with avalanche events that span the whole system. We compute semi-analytically the friction force acting on this surface, and find that it is compatible with classical friction experiments. In finite dimensions (2D), the mean-field system-sized events become local, and numerical simulations give qualitative and quantitative results in good agreement with several important features of real earthquakes.

The second system including a minimal form of relaxation consists in a toy model of avalanches: the Directed Percolation process. In our study of a non-Markovian variant of Directed Percolation, we observed that the universality class was modified but not completely. In particular, in the non-Markov case an exponent changes of value while several scaling relations still hold. This picture of an extended universality class obtained by the addition of a non-Markovian perturbation to the dynamics provides promising prospects for our first system.

# Séminaire du LPTMS : Kin'ya Takahashi

## Competition between instanton and non-instanton tunneling in multidimensional systems

### Kin'ya Takahashi, Kyushu Institute of Technology

There are two types of tunneling mechanisms working for mutli-dimensional barrier tunneling. One is well known instanton which induces barrier penetration. The other is non-instanton tunneling, in which tunneling particles go over a barrier top. It is explained by multiphoton assisted tunneling, while from the semiclassical view point it is interpreted by ’Stable-unstable manifold guided tunneling, say SUMGT as an abbreviation.In this talk, we investigate instanton type tunneling and non-instanton tunneling from the view points of quantum and semiclassical dynamics.Taking periodically perturbed step potential and barriers as models, we give the interpretation between quantum and semiclassical explanations of non-instanton tunneling and we discuss the problem: How do the transitions between instanton and non-instanton tunneling occur with change of the perturbation frequency? Further taking a periodically perturbed resonance potential, we consider the problem: How does the resonance affect the properties of instant type tunneling and non-instanton tunneling?

# Tri-séminaire de Physique Statistique : Steven H. Simon

## Topological matter and why you should be interested

### Steven H. Simon, Oxford University

In two dimensional topological phases of matter, processes depend on gross topology rather than detailed geometry. Thinking in 2+1 dimensions, particle world lines can be interpreted as knots or links, and the amplitude for certain processes becomes a topological invariant of that link. While sounding rather exotic, we believe that such phases of matter not only exist, but have actually been observed in quantum Hall experiments, and could provide a uniquely practical route to building a quantum computer.   Possibilities have also been proposed for creating similar physics in systems ranging from superfluid helium to strontium ruthenate to semiconductor-superconductor junctions to quantum wires to spin systems to cold atoms.

# Soutenance de thèse : Paul Soulé

## Edges of Fractional Quantum Hall Phases in a Cylindrical Geometry

### Paul Soulé, LPTMS

Fractional Quantum Hall (FQH) phases are exotic incompressible fluids which support gapless chiral edge excitations. I will present a microscopic study of those edges states in a cylindrical geometry where quasiparticles are able to tunnel between edges.

We first study the principal FQH phase at the filling fraction 1/3 whose ground state is well described by the Laughlin wave function. For an energy scale lower than the bulk gap, the effective theory is given by a very special one dimensional electron fluid localized at the edge: a chiral Luttinger liquid. Using numerical exact diagonalizations, we study the spectrum of edge modes formed by the two counter-propagating edges on each side of the cylinder. We show that the two edges combine to form a non-chiral finite-size Luttinger liquid, where the current term reflects the transfer of quasiparticles between edges. Then, we estimate numerically the Luttinger parameter for a small number of particles and find it coherent with the one predicted by X. G. Wen theory.

We then analyse edge modes of the FQH phase at filling fraction 5/2. From a Conformal Field Theory (CFT) based construction, Moore and Read (Nucl. Phys. B, 1991) proposed that this phase is well described by a P-wave paired state of composite fermions. A striking property of this state is that emergent excitations braid with non-abelian statistics. When localized along the edge, those excitations are described through a chiral boson and a Majorana fermion. In the cylinder geometry, we show that the spectrum of edge excitations is composed of all conformal towers of the IsingXU(1) model. Interestingly, the non-abelian tower is naturally observed as opposed to the usual disk geometry. In addition, with a Monte Carlo method, we estimate the various scaling dimensions for large systems (about 50 electrons), and find them consistent with the CFT predictions.

# Séminaire du LPTMS: Peter Schlagheck

## Coherent backscattering in the Fock space of a disordered Bose-Hubbard system

### Peter Schlagheck, Université de Liège

Coherent backscattering in disordered or chaotic systems is an ubiquitous wave phenomenon that arises in a number of physical contexts involving classical (e.g. electromagnetic) or quantum (matter) waves. It essentially refers to the coherent enhancement of the backscattering intensity in the direction that is opposite to the propagation of the incident wave. From a semiclassical point of view, this enhancement is caused by the constructive interference of backscattered classical paths with their time-reversed counterparts.

In my talk I shall discuss the generalization of this wave interference phenomenon to the many-body dynamics that takes place within an interacting Bose-Hubbard system. In this particular context, the "classical" paths are given by solutions of a discrete nonlinear Gross-Pitaevskii equation and their "quantum" interference arises within the Fock space of the Bose-Hubbard system. As a consequence, an initially prepared Fock state is, in the course of time evolution (and after averaging over random on-site energies), twice as often encountered as other Fock states of the system with comparable total energy. This semiclassical prediction represents a significant departure from the principle of quantum ergodicity in finite systems and is indeed confirmed by numerical simulations. We argue that an experimental detection of many-body coherent backscattering using ultracold bosonic atoms in optical lattices is within reach.

Ref.: T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, and J. D. Urbina, Phys. Rev. Lett. 112, 140403 (2014)

# Soutenance de thèse : Yasar Atas

## Some aspects of quantum chaos in many body interacting systems. Quantum spin chain and random matrices.

### Yasar Atas, LPTMS

My thesis is devoted to the study of some aspects of many body quantum interacting systems. In particular we focus on quantum spin chains. I addressed especially questions related to the structure of eigenfunctions, the level densities and the spectral properties of spin chain Hamiltonians.

It is known that the level densities of most integrable models tend to the Gaussian in the thermodynamic limit. However, it appears that in certain limits of coupling of the spin chain to the magnetic field and for finite number of spins on the chain, one observes peaks in the level density.  I show that the knowledge of the first two moments of the Hamiltonian in the degenerate subspace associated with each peak gives a good approximation to the level density both in the case of integrable and non integrable models.

Next, I study the statistical properties of the eigenvalues of spin chain Hamiltonians. One of the main achievements in the study of the spectral statistics of quantum complex systems concerns the universal behaviour of the fluctuation of measure such as the distribution of spacing between two consecutive eigenvalues. By following the Wigner surmise for the computation of the level spacing distribution, I obtained approximation for the distribution of the ratio of consecutive level spacings in the three canonical ensembles of random matrices. The prediction are compared with numerical results obtained by exact diagonalization of spin Hamiltonians and with zeros of the Riemann zeta function showing excellent agreement.

Finally, I investigate eigenfunction statistics of some canonical spin-chain Hamiltonians. Eigenfunctions together with the energy spectrum are the fundamental objects of quantum systems: their structure is quite complicated and not well understood. Due to the exponential growth of the size of the Hilbert space, the study of eigenfunctions is a very difficult task from both analytical and numerical points of view. I demonstrate that the groundstate eigenfunctions of all canonical models of spin chain are multifractal, by computing numerically the Rényi entropy and extrapolating it to obtain the multifractal dimensions.

Key words: Quantum spin chains, quantum Ising model, spectral statistics, level density, quantum chaos, random matrices, Wigner surmise, spacing distribution, multifractality, Rényi entropy.

# Physics-Biology interface seminar: Huan-Cheng Chang

## Bioimaging and quantum sensing with ion-irradiated nanodiamonds

### Huan-Cheng Chang (Academia Sinica, Taiwan)

Seminar co-hosted by François Treussart SPECIAL TIME AND LOCATION

As a wide band-gap material, diamond can contain a variety of atomic defects or impurities as color centers. Some of the color centers are highly luminescent, while others are luminescent with a very low quantum yield. For nanoscale diamonds (NDs) containing a high-density ensemble of vacancy-related defect centers, they are useful as nanoprobes for bioimaging and quantum sensing both in vitro and in vivo. In this seminar, we will show how ion-irradiated NDs can be routinely produced in our laboratory. Three examples of the applications by utilizing nitrogen-vacancy (NV−) centers and neutral vacancy (V0 or GR1) centers in NDs are discussed. First, we will present our results of using fluorescence lifetime imaging microscopy to achieve background-free real-time imaging of fluorescent NDs (denoted as FNDs) in living organisms such as C. elegans. With 100-nm FNDs conjugated with yolk lipoprotein complexes, we demonstrate that the nanoparticles serve well as a biomolecular nanocarrier without significantly altering the functionality of the cargos for intercellular transport, cell-specific targeting, and long-term imaging applications in vivo. Second, we report our recent work on the development of highly ion-irradiated NDs (denoted as INDs) as a photoacoustic contrast agent for deep-tissue imaging. The particles are so extensively damaged that graphitization occurs concurrently with the generation of the GR1 centers. Although the IND of ~40 nm in diameter has a much smaller absorption coefficient than gold nanorods (GNRs) of similar dimensions at 1064 nm, it shows a better performance due to higher thermal stability and a lower nanobubble formation threshold of the carbon-based nanomaterial. Finally, we apply the NV− centers in 100-nm FNDs for nanoscale temperature sensing by optically detected magnetic resonance. We conjugate FNDs with GNRs and employ them as both a nanoheater and a nanothermometer in solution and cells. The integration of heating and temperature sensing functions on the same particles opens an opportunity for active and high-precision control of temperature at the nanoscale by pure optical means.

# Séminaire exceptionnel du LPTMS: Joyjit Kundu

## Phase transitions in hard core lattice gas models of anisotropic particles

### Joyjit Kundu, Institute of Mathematical Sciences, Chennai

Hard core lattice gas models of particles interacting only through excluded volume interaction continue to be of interest in Statistical Physics. They are minimal models to study entropy driven phase transitions, have direct realizations in adsorption of gas particles on metal surfaces and are closely related to the freezing transition. In this talk, I will discuss the system of hard rectangles of size m x m k on a two dimensional lattice, where k is the aspect ratio. The phase diagram of this model for arbitrary m and k is determined using Monte-Carlo simulations, entropic arguments, and analytical calculations based on the Bethe approximation. In particular, it will be shown that, with increasing density,  the system undergoes three entropy driven phase transitions for large enough k.

# Tri-séminaire de Physique Statistique : Francesco Zamponi

## Exact computation of the critical exponents of the jamming transition

### Francesco Zamponi, LPTENS

The jamming transition marks the emergence of rigidity in a system of amorphous and athermal grains. It is characterized by a divergent correlation length of the force-force correlation and non-trivial critical exponents that are independent of spatial dimension, suggesting that a mean field theory can correctly predict their values. I will discuss a mean field approach to the problem based on the exact solution of the hard sphere model in infinite dimension. An unexpected analogy with the Sherrington-Kirkpatrick spin glass model emerges in the solution: as in the SK model, the glassy states turn out to be marginally stable, and are described by a Parisi equation. Marginal stability has a deep impact on the critical properties of the jamming transition and allows one to obtain analytic predictions for the critical exponents. The predictions are consistent with a recently developed scaling theory of the jamming transition, and with numerical simulations. Finally, I will briefly discuss some possible extensions of this approach to other open issues in the theory of glasses.

# Séminaire du LPTMS: Tridib Sadhu

## Large deviation in single-file diffusion

Single-file diffusion is referred to the motion of many particles in narrow channel where particles can not pass each other. As a consequence of the forbidden mutual passage the motion of individual particles is sub-diffusive. I shall apply the macroscopic fluctuation theory to analyse the probability distribution of position of a tracer particle in a large class of single-file systems. For Brownian point particles with hard-core repulsion this macroscopic approach leads to a parametric expression of the large deviation function of tracer position. I shall compare the results with that obtained in our exact microscopic analysis. I shall emphasise the unusual dependence of the statistics of the tracer position on the initial state.

à l'IHP Paris

à l'IHP Paris

# Séminaire du LPTMS: Giacomo Gradenigo

## Glassy properties of a XOR-SAT model in finite dimensions

Two competing scenarios have been proposed since a long time as alternative to explain the critical slowing down of glass-forming materials:  the dynamic facilitation scenario, well represented by kinetically constrained models (KCM), where glassiness arise just as a dynamical phenomenon, and the thermodynamic scenario of the Random First-Order Transition (RFOT) theory, according to which the slowing down of dynamics is the signature of a true thermodynamic transition, the glass transition.
In this talk I will review and discuss some properties of a finite dimensional XOR-SAT model, the triangular plaquette model, which is a typical example of kinetically constrained model. In particular I will explain the mechanism by which the addition of an arbitrarily small  perturbation in the Hamiltonian of this system may induce a finite temperature glass transition. I discuss therefore how the model studied, just by tuning a parameter, can be either representative of the dynamic facilitation scenario or of the thermodynamic one: this result suggest that the two scenarios should be regarded not as alternative but just as two complementary ways to explain the same kind of phenomenology.

# Séminaire du LPTMS: Kabir Ramola

## Correlated Extreme Values in Branching Brownian Motion

### Kabir Ramola, LPTMS

We investigate one dimensional branching Brownian motion in which at each time step particles either diffuse (with diffusion constant D), die (with rate d), or split into two particles (with rate b). When the birth rate exceeds the death rate (b > d), there is an exponential proliferation of particles and the process is explosive. When b < d, the process eventually dies. At the critical point (b = d) this system is characterized by a fluctuating number of particles with a constant average. Quite remarkably, although the individual positions of these particles have a non-trivial finite time behaviour, the average distances between successive particles (the gaps) become stationary at large times, implying strong correlations between them. We compute the probability distribution functions (PDFs) of these gaps, by conditioning the system to have a fixed number of particles at a given time t. At large times we show that these PDFs are characterized by a power law tail ~1/g^3 (for large gaps g) at the critical point and ~exp(- g/c) otherwise, with a correlation length c~sqrt(D/|b - d|). We discuss the emergence of these two length scales, the dominant overall length scale of the individual positions, and the sub-dominant gap length scale in this system. Direct Monte Carlo simulations confirm our predictions.

# Journal Club : Haggai Landa

## Nanofriction in cold ion traps, A. Benassi, A. Vanoss & E. Tosatti, Nature Communications 2, 236 (2011)

### Haggai Landa (post doc LPTMS)

Sliding friction between crystal lattices and the physics of cold ion traps are so far non-overlapping fields. Two sliding lattices may either stick and show static friction or slip with dynamic friction; cold ions are known to form static chains, helices or clusters, depending on the trapping conditions. Here we show, based on simulations, that much could be learnt about friction by sliding, through, for example, an electric field, the trapped ion chains over a corrugated potential. Unlike infinite chains, in which the theoretically predicted Aubry transition to free sliding may take place, trapped chains are always pinned. Yet, a properly defined static friction still vanishes Aubry-like at a symmetric–asymmetric structural transition, found for decreasing corrugation in both straight and zig-zag trapped chains. Dynamic friction is also accessible in ringdown oscillations of the ion trap. Long theorized static and dynamic one-dimensional friction phenomena could thus become accessible in future cold ion tribology.

# Physics-Biology interface seminar: Guillaume Tresset

## Understanding the self-assembly of simple icosahedral viruses

### Guillaume Tresset (Université Paris-Sud)

Viruses are ubiquitous pathogens in all kingdoms of life and are major public health issues as well as economic and veterinary concerns worldwide. Despite a huge body of work dedicated to the molecular biology of viral life cycles, there are currently no physical models accounting reliably for the mechanisms by which the hundreds of molecular building blocks making up a virus fit into the final structure with a pinpoint accuracy. I will first present the self-assembly pathway of empty icosahedral capsids derived from a bovine virus. A kinetic model constructed from time-resolved X-ray scattering data reveals a cooperative mechanism involving an unexpected long-lived intermediate species. Then, I will give some insights into the packaging of polyelectrolytes by capsid proteins derived from a plant virus. Accurate measurements of the mass of packaged polyelectrolyte demonstrate a nonspecific selectivity that may play a crucial role for genome packaging in host cells. Quite generally, physics provides a useful framework to describe viral self-assembly and should eventually support the development of novel therapeutic strategies.

# Séminaire du LPTMS: Sam Safran

## Non-linearities and interactions of cells with their mechanical environment

### Sam Safran Dept. Materials and Interfaces, Weizmann Institute of Science, Rehovot, Israel

Many experiments have shown that the elastic substrates upon which cells are placed or the extracellular matrix (ECM) in which cells reside in 3D can regulate cellular structure and function. From fate “decision making” of stem cells to rigidity-driven motion, cells actively sense and transduce elastic signals, which in turn depends on the elastic properties of the substrate or ECM. We review experimental evidence to demonstrate that cell structure and function is regulated by its mechanical environment (the presence of other cells, external stretch, matrix rigidity) and present a generic, theoretical model for cell response that combines mechanics and cell activity. We predict that even symmetric cells on or in isotropic substrates interact elastically, in contrast to the vanishing interactions for the case of “dead inclusions” under these situations.  The theory is extended to the biologically relevant case of “strain stiffening”, non-linear , elastic substrates where the local cell deformations are amplified far from their origin. Finally, we show how cell deformations can orient the surrounding medium which in turn, can provide guidance cues for cell motility.

# Soutenance HDR Guillaume Roux et mini-workshop

10h Habilitation à diriger les recherches – Salle des conseils RDC bât 100 Some numerical investigations on strongly-correlated systems: from quantum quenches to disordered models. Guillaume Roux 12h Buffet – Salle Bohigas au LPTMS, 2ème étage bât 100 13h10 LPTMS Workshop – Salle des conseils RDC bât 100 Chairman: Thierry Jolicoeur 13h15 - Competition between the Haldane insulator, superfluid and supersolid phases in the one-dimensional Bosonic Hubbard Model. George Batrouni 13h45 - The 2d Bose Hubbard model: Phase diagrams and new applications. Heiko Rieger 14h15 - Pause café 14h30 - On cold atom quasicrystals and their curious quantum behavior. Anu Jagannathan 15h00 - Skew scattering and the spin Hall effect in correlated materials. Tim Ziman 15h30 - Spin Meissner Effect, Mott Physics and Artificial Gauge Fields. Karyn Le Hur 16h00 - Fin

# Tri-séminaire de Physique Statistique : Viktor Eisler

## Free-fermion entanglement and random matrices

### Viktor Eisler, Institute for Theoretical Physics, Eötvös University, Budapest

Entanglement properties of quantum many-body systems have attracted considerable attention in the last decade. A particularly well studied case is a chain of free fermions where one has a very good analytical understanding of then entanglement structure in the ground state. The studies can also be extended to simple out-of-equilibrium situations such as quantum quenches or the time-evolution from a step-initial condition. Interestingly, in the course of these investigations several connections to random matrix theory appeared. The purpose of this talk is to give an overview about these relations and to point out how certain aspects of RMT can give useful input to the studies of free-fermion entanglement.

# Soutenance de thèse : Andrey Lokhov

## Dynamic cavity method and problems on graphs

### Andrey Lohhov, LPTMS

A large number of optimization, inverse, combinatorial and out-of-equilibrium problems, arising in the statistical physics of complex systems, allow for a convenient representation in terms of disordered interacting variables defined on a certain network. Although a universal recipe for dealing with these problems does not exist, the recent years have seen a serious progress in understanding and quantifying an important number of hard problems on graphs. A particular role has been played by the concepts borrowed from the physics of spin glasses and field theory, that appeared to be extremely successful in the description of the statistical properties of complex systems and in the development of efficient algorithms for concrete problems.

In the first part of the thesis, we study the out-of-equilibrium spreading problems on networks. Using dynamic cavity method on time trajectories, we show how to derive dynamic message-passing equations for a large class of models with unidirectional dynamics -- the key property that makes the problem solvable. These equations are asymptotically exact for locally tree-like graphs and generally provide a good approximation for real-world networks. We illustrate the approach by applying the dynamic message-passing equations for susceptible-infected-recovered model to the inverse problem of inference of epidemic origin.

In the second part of the manuscript, we address the optimization problem of finding optimal planar matching configurations on a line. Making use of field-theory techniques and combinatorial arguments, we characterize a topological phase transition that occurs in the simple Bernoulli model of disordered matching. As an application to the physics of the RNA secondary structures, we discuss the relation of the perfect-imperfect matching transition to the known molten-glass transition at low temperatures, and suggest generalized models that incorporate a one-to-one correspondence between the contact matrix and the nucleotide sequence, thus giving sense to the notion of effective non-integer alphabets.

# Physics-Biology interface seminar: Julien Heuvingh

## Mechanics and growth of the actin cytoskeleton probed by magnetic micro-objects

### Julien Heuvingh (PMMH, ESPCI)

The ability of cells to perform essential processes such as migration or deformation relies on their cytoskeleton, and especially on the structures and networks formed by the actin polymer and its associated proteins. Understanding the dynamics and the mechanics of the actin filaments and its multiple partner is a major goal at the frontier of biology and physics. Our team developed a new experimental setup to study the mechanics of in vitro reconstituted actin networks, with an unprecedented throughput. This technique is based on self-organized chains of micron-size magnetic beads or cylinders where the controlled attractive dipolar force between the colloids deforms the actin networks. We characterized for the first time the mechanics of actin networks reconstituted with different concentrations of purified proteins, leading to networks of different architectures, and drew conclusions on the origin of the elasticity on these networks (Pujol et al PNAS 2012). We are now measuring mechanical properties of networks reconstituted from yeast extract which allows comparison between a wild type containing hundred different actin binding proteins to mutants lacking some of them. Our experimental setup was decisively improved by the fabrication of magnetic micro-objects of cylindrical or cubic shape (Tavacoli et al. Soft Matter 2013) allowing the deformation of actin networks between two flat surfaces. In this way, we can access properties of dense branched networks such as non-linear elasticity and Poisson modulus, which are required to test theoretical models of fiber networks (Mikado). We are currently studying the growth velocity of the actin gel as a function of an applied mechanical stress and the architecture of the networks. I will also present other applications of our magnetic methods to probe the mechanics of whole cells.

[caption id="attachment_26491" align="aligncenter" width="502"] Actin networks (green) growing from the side of magnetic cylinders. Superimposition of bright field image (gray) and fluorescent image (green). Cylinder length is ~12µm.[/caption]

# Séminaire du LPTMS: Lisa Manning

## Dynamical arrest of cell motion in tissues: a constant-density rigidity transition

### Lisa Manning, Syracuse University

For important biological functions such as wound healing, embryonic development, and cancer tumorogenesis, cells must initially rearrange and move over relatively large distances, like a liquid. Subsequently, these same tissues must undergo buckling and support shear stresses, like a solid. Our work suggests that biological tissues can accommodate these disparate requirements because the tissues are close to glass or jamming transition. While recent self propelled particle models generically predict a glass/jamming transition that is driven by packing density φ and happens at some critical φc < 1, many confluent biological tissues appear to undergo a jamming transition at a constant density (φ = 1). I will discuss a new theoretical framework for predicting energy barriers and rates of cell migration in 2D tissue monolayers, and show that this model predicts a novel type of rigidity transition, which takes place at constant φ = 1 and depends only on single cell properties such as cell-cell adhesion, cortical tension and cell elasticity. I will discuss the implications of these ideas for understanding cancer tumor boundaries and metastasis and pattern formation during development.

# Journal Club : Silvio Franz et Raoul Santachiara

## Solving the 3D Ising Model with the Conformal Bootstrap

### Silvio Franz, Raoul Santachiara

arXiv:1203.6064 Sheer El-Showk, Miguel F. Paulos, David Poland, Slava Rychkov, David Simmons-Duffin, Alessandro Vichi

# Séminaire exceptionnel : Jesper Levinsen

## Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential

### Jesper Levinsen (Aarhus Institute of Advanced Studies, Aarhus University)

The one-dimensional (1D) Fermi gas with repulsive short-range interactions provides an important model of strong correlations and is often amenable to exact methods. However, in the presence of confinement, no exact solution is known for an arbitrary number of strongly interacting fermions. Here, we propose a novel ansatz for generating the lowest-energy wavefunctions of the repulsive 1D Fermi gas in a harmonic potential near the Tonks-Girardeau limit of infinite interactions. We specialize to the case of a single $down$ particle interacting with $N_up$ particles, where we may derive analytic forms of the approximate wavefunctions. Comparing with exact numerics, we show that the overlap between the wavefunctions from our ansatz and the exact ones in the ground-state manifold exceeds $0.9997$ for $N_upleq8$. Moreover, the overlap for the ground-state wavefunction at strong repulsion extrapolates to $sim0.9999$ as $N_uptoinfty$. Thus, our ansatz is essentially indistinguishable from numerically exact results in both the few- and many-body limits. Reference: J. Levinsen, P. Massignan, G. M. Bruun, and M. M. Parish, arxiv:1408.7096

# Séminaire du LPTMS: Mikhail Tamm

## Genome packing and fractal globules: some new developments

### Mikhail Tamm (Physics department, Moscow State University)

The idea that genome packing in a cell nucleus is to a large extent governed by topological constraints has been around for many years: the corresponding topologically controlled state, known as a fractal globule, was first predicted in the late 1980s. Recently with the development of the new experimental techniques, especially the so-called Hi-C contact maps, a lot of new evidence appeared concerning the statistics of the genome spatial structure. This new data seems to support the fractal globule model, and therefore it caused a significant renewed interest in the physics of the fractal globule state in the recent years. In my talk, I will overview the ideas behind the fractal globule model and the current state of art in the theory of genome packing. After that, I will discuss two more narrow questions we have been trying to develop recently. In particular, first, I will talk about the fine structure of the Hi-C contact maps and possible ways to explain it by combining the hierarchical folding intrinsic to the fractal globule idea and the assumption about quenched block-copolymer structure of the genome. Second, I will discuss the dynamic of self-diffusion in the fractal globule and develop a scaling theory predicting it to be a subdiffusion with a scaling index 0.4. I will also discuss the implications of this result for the search processes in the fractal globule.

# Séminaire exceptionnel du LPTMS: Vladimir Kravtsov

## Multifractality of random eigenfunctions and generalization of Jarzynski equality

### V. E. Kravtsov, Abdus Salam ICTP, Trieste

Systems driven out of equilibrium experience large fluctuations of the dissipated work. The same is true for wave function amplitudes in disordered systems close to the Anderson localization transition. In both cases the probability distribution function (PDF) is given by the large deviation ansatz. We exploit the analogy between the PDF of work dissipated in a driven single-electron box (SEB) and that of random multifractal wave function amplitudes and uncover new relations which generalize the Jarzynski equality. We checked the new relations experimentally by measuring the dissipated work in a driven SEB and found a remarkable correspondence. The results represent an important universal feature of the work statistics in systems out of equilibrium and help to understand the nature of the symmetry of multifractal exponents in the theory of Anderson localization.

# Journal-club : Haggai Landa

## Nanofriction in cold ion traps, A. Benassi, A. Vanossi, E. Tosatti, Nature Communications 2, 236 (2011)

### Haggai Landa

Sliding friction between crystal lattices and the physics of cold ion traps are so far non-overlapping fields. Two sliding lattices may either stick and show static friction or slip with dynamic friction; cold ions are known to form static chains, helices or clusters, depending on the trapping conditions. Here we show, based on simulations, that much could be learnt about friction by sliding, through, for example, an electric field, the trapped ion chains over a corrugated potential. Unlike infinite chains, in which the theoretically predicted Aubry transition to free sliding may take place, trapped chains are always pinned. Yet, a properly defined static friction still vanishes Aubry-like at a symmetric–asymmetric structural transition, found for decreasing corrugation in both straight and zig-zag trapped chains. Dynamic friction is also accessible in ringdown oscillations of the ion trap. Long theorized static and dynamic one-dimensional friction phenomena could thus become accessible in future cold ion tribology.

# Physics-Biology interface seminar: Nikta Fakhri

## Hitching a ride at the nanometer scale: transport in passive and active complex media

### Nikta Fakhri (Georg-August-Universität Göttingen)

Transport in crowded and complex media is a ubiquitous phenomenon in nature, which poses fundamental questions in statistical and soft matter physics. In particular, transport in the bustling interior of living cells is fascinating and far from understood. On a molecular scale, transport can be diffusive or driven, either externally or by local force generators. In this talk, I will introduce single-walled carbon nanotubes (SWNTs) as highly versatile multi-scale probes to investigate different modes of transport in media of increasing complexity: from the confined dynamics of semiflexible polymers in crowded environments to random stirring generated by non-equilibrium dynamics of the cell cytoskeleton.

# Séminaire du LPTMS: Marcello Porta

## Mean-Field Evolution of Fermionic Systems

### Marcello Porta, Université de Zurich

In this talk I will discuss the dynamics of interacting fermionic systems in the mean-field regime. Compared to the bosonic case, fermionic mean-field scaling is naturally coupled with a semiclassical scaling, making the analysis more involved. From a physical point of view, as the number of particles grows one expects the quantum evolution of the system to be effectively described by Hartree-Fock theory. The next degree of approximation is provided by a classical effective dynamics, corresponding to the Vlasov equation.

I will consider initial data which are close to quasi-free states, both at zero and at positive temperature, with an appropriate semiclassical structure. Under some regularity assumptions on the interaction potential I will show that the time evolution of such initial data stays close to a quasi-free state, with reduced one-particle density matrix given by the solution of the time-dependent Hartree-Fock equation. The result holds for all (semiclassical) times, and gives effective bounds on the rate of convergence towards the Hartree-Fock dynamics as the number of particles goes to infinity.

# Tri-séminaire de Physique statistique : Christian Van den Broeck

## The unlikely Carnot efficiency

### Christian Van den Broeck, Université Hasselt, Belgique

The efficiency of a heat engine is traditionally defined as the ratio of its average output work over its average input heat. Its highest possible value was discovered by Carnot in 1824 and is a cornerstone concept in thermodynamics. It led to the discovery of the second law and to the definition of the Kelvin temperature scale. Small-scale engines operate in the presence of highly fluctuating input and output energy fluxes. They are therefore much better characterized by fluctuating efficiencies. In this study, using the fluctuation theorem, we identify universal features of efficiency fluctuations. While the standard thermodynamic efficiency is, as expected, the most likely value, we find that the Carnot efficiency is, surprisingly, the least likely in the long time limit in the case of a symmetric driving protocol. More generally, the long-time probability for observing a reversible efficiency in a given engine is identical to that for the same engine working under the time-reversed driving. Furthermore, the probability distribution for the efficiency assumes a universal scaling form when operating close-to-equilibrium. We illustrate our results analytically and numerically on several model systems, including the work-to-work conversion via a Brownian particle, effusion as a thermal engine, and an asymmetrically driven quantum dot.

# Séminaire du LPTMS: Mario Collura

## Interaction quenches in 1D Bose gas

### Mario Collura, SISSA Trieste

We study the non-equilibrium quench dynamics from free to hard-core one-dimensional bosons, in which the relation between modes is nonlinear, and consequently Wick’s theorem does not hold. We provide exact analytical results for the time evolution of the dynamical density-density correlation function. We prove that its stationary value is described by a Generalized Gibbs Ensemble (GGE). We analyze the entanglement properties of the the asymptotic steady state after the quench providing exact analytical results for both the leading extensive parts and the subleading terms for the entropies as well as for the cumulants of the particle number fluctuations. Finally, we extended the quench protocol in the presence of a hard-wall confining potential. We characterize the density profile and the two-point fermionic correlation function in the stationary state as well as their full time evolution.

# Journal-Club : Pierre Ronceray

## Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States

Phys. Rev. Lett. *86*, 2050 - Published 5 March 2001 Fugao Wang and D. P. Landau

We present a new Monte Carlo algorithm that produces results of high  accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of   energy, and the resultant density of states is modified continuously to produce locally flat histograms. This method permits us to directly access the free energy and entropy, is independent of temperature, and is  efficient for the study of both 1st order and 2nd order phase transitions.  It should also be useful for the study of complex systems with a rough energy landscape.

# Physics-Biology interface seminar: Gilles Charvin

## Single cell analysis of entry into replicative senescence in budding yeast

### Gilles Charvin (IGBMC Strasbourg)

Budding yeast cells have an asymmetrical division pattern. Each mother cell produces a limited number of smaller daughter cells before entering senescence and eventually dying. The detailed mechanisms that govern entry into senescence in mothers and daughter cell rejuvenation are still poorly understood. In this context, we have developed a microfluidic system that lets one monitor the successive divisions of single yeast cells in real-time under the microscope. Using this device, we have revisited classical paradigms associated with the age-dependent control of cell proliferation in this unicellular organism. Our results indicate that cells undergo a sharp transition to senescence, which is not related to the the loss of mitochondrial membrane potential, as previously proposed. Other applications of our methodology to the study of senescence induced by telomeres attrition and in other cellular biology contexts will be presented during the talk.

# Seminaire du LPTMS: Oleg Lisovyy

## Isomonodromic tau functions from Liouville conformal blocks

### Oleg Lisovyy, LMPT Université de Tours

I will show that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,C)-valued monodromy on n-punctured Riemann sphere can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at c=1. This implies a similar representation for the isomonodromic tau function. In the case n=4 we will thereby express the general solution of Painlevé VI equation in terms of 4-point conformal blocks. Time permitting, I will discuss how the c=1 fusion kernel can be calculated explicitly using this Painlevé/CFT relation.