### Séminaires de l’année 2012

# Séminaire de la Fédération PHYSTAT-SUD : Florent Krzakala

## Statistical physics approach to compressed sensing

## Florent KRZAKALA, Physico-Chimie Théorique UMR CNRS Gulliver ESPCI

Compressed sensing is triggering a major evolution in signal acquisition that changes completely the way we think about experiments and measurements. It indicates that most data, signals and images, that are usually compressible and have redundancy, can be reconstructed from much fewer measurements than what was usually considered necessary, resulting in a drastic gain of time, cost, and measurement precision. The idea consists in sampling a sparse signal using some random projections, and later using computational power for its exact reconstruction, so that only the necessary information is measured. This has been applied to many situations, from medical imagery and one-pixel-camera to confocal microscopy, acoustic holography or DNA micro-array analysis in biology.

In this talk, I will start by a general instruction to compressed sensing for physicists and discuss the state of the art reconstruction algorithms. Currently used reconstruction techniques are however limited to acquisition rates still higher than the true density of the signal. By using a mapping to a statistical physics problem, and motivated by the theory of crystal nucleation, I will introduce a new algorithm, and new measurement protocols, that achieves exact reconstruction of the signal even at measurement rates very close to the lowest possible ones.

References:

http://arxiv.org/abs/1109.4424

http://nuit-blanche.blogspot.com/p/teaching-compressed-sensing.html

http://nuit-blanche.blogspot.com/2011/09/stunning-development-in-breaking-donoho.html

# Séminaire du LPTMS : Serguei Brazovski

## Strong local and nonequilibrium events in electronic systems.

## Serguei Brazovskii (LPTMS)

This review seminar will report on resent joint experimental/theoretical studies of low-dimensional electronic system with symmetry broken states in general, mostly electronic crystals, notably charge density waves, with extensions to superconductors. The selected observations will be related to strong, usually topologically nontrivial, perturbations of the order parameter under an external impact. The pattern may be either static, induced by either electric field or doping or disorder, or dynamic, under the optical pumping – a major recent trend in solid state physics.

Problems in temporal evolution and remnants of symmetry breaking phase transitions span subjects from high energy and cosmology to condensed matter. Recent optical study [1] of a far-from-equilibrium electronic charge ordering recovered coherent aperiodic undulations of the order parameter, critical slowing down of the collective mode, and evolution of the particle-hole gap. Numerical modeling with no fitting parameters allowed interpreting the observations, particularly the spatio-temporal distortions arising from “earthquakes” - annihilation events of topological defects in depth of the sample.

Strong perturbations are also recovered at the microscopic scale accessed by the new STM [2]; there are the amplitude solitons playing a role of neutral spin carriers - spinons. Their aggregation into solitonic lattices gives rise to modulated phases in spin-polarized superconductors or Charge Density Waves. Other experiments on nano-junctions and their modeling recover the intrinsic reconstruction by creating arrays of electronic vortices – dislocations.

[1] In collaboration with D. Mihailovic group, Ljubljana, Slovenia. Yusupov, et al, “Coherent dynamics of macroscopic electronic order through a symmetry breaking transition”, Nature Physics, 2010

[2] In collaboration with C, Brun (Paris-Nano center), Z.Z. Wang (LPN, Marcoussis), P. Monceau (Inst. Neel, Grenoble). " Direct observation of spinons - the single-electron solitons - in an electronic solid " , PRL 2012, to appear.

# Soutenance de thèse : Elia Zarinelli

### Spin-glass models and interdisciplinary applications

The main subject of this thesis is the physics of spin glasses. After their introduction in the 70s in order to describe dilute magnetic alloys, spin-glass models have been considered prototype models to understand the behavior of supercooled liquids. Among the systems that can be described and analyzed using the language of disordered systems, there are problems of combinatorial optimization.

In the first part of the thesis, we consider spin-glass models with Kac interactions in order to investigate the supercooled phase of glass-forming liquids. Afterwards, we show how some features of spin-glass models can be described by ubiquitous results of Random Matrix Theory in connection with Extreme Value Statistics. Finally, from the interaction of spin-glass theory and computer science, we put forward a new algorithm of immediate application in Financial problems.

La soutenance sera suivie d'un pot en salle 201.

#### Auditorium Irène Joliot-Curie, bâtiment 100, Orsay

# Séminaire "fluides quantiques" : Guilia Ferrini

## Macroscopic superpositions in the presence of phase noise in a Bose Josephson junction

## Guilia Ferrini, LKB (CNRS - Université P. et M. Curie)

A Bose Josephson Junction is a system composed of bosons which can occupy two modes which can be coupled. This system models either an ultracold bosonic gas trapped in a double-well potential, either a gas of ultracold bosons in two different hyperfine states, trapped in the same harmonic potential. Both configurations have been experimentally realized, and found interesting applications, e.g. in high-precision interferometry [1]. If the system is initially prepared in a coherent state and evolves after suppressing the coupling of the two modes, at short time the state undergoes squeezing [2], and at larger time macroscopic superpositions of coherent states are formed [3]. One of the most relevant sources of noise in such a system, together with particle losses, is phase noise, resulting from stochastic fluctuations of the energies of the two modes. We address the question how the presence of phase noise affects the formation of squeezed states and macroscopic superpositions, showing in particular how these latter display an unexpected robustness against decoherence induced by the noise considered [4].

[1] M. Albiez et al, Phys. Rev. Lett. 95, 010402 (2005); J. Esteve et al, Nature 455, 1216 (2008).

[2] C. Gross et al, Nature 464, 1165 (2010). M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993).

[3] F. Piazza, L. Pezze and A. Smerzi, Phys. Rev. A 78, 051601 (2008); G. Ferrini, A. Minguzzi and F.W.J. Hekking, Phys. Rev. A 78, 023606 (2008).

[4] G. Ferrini et al, Phys. Rev. A 82, 033621 (2010); Phys. Rev. A 84, 043628 (2011).

# Séminaire du LPTMS: P. Ribeiro

## Thermal and quantum ﬂuctuations in superconducting nanostructures

## P. Ribeiro, MPI Dresden

I will report a study on the combined eﬀect of thermal and quantum ﬂuctuations in a zero dimensional superconductor.

Using path integral techniques, the expression for the partition function is obtained as well as the superconducting order parameter which include both types of ﬂuctuations.

These results are valid for any temperature and to leading order in $delta/Delta_0$ where $delta$ is the mean level spacing and $Delta_0$ is the bulk energy gap.

Divergences arising at low temperatures, previously reported in the literature, are avoided by identifying and treating non-perturbatively a low-energy collective mode.

In the low and high temperature limit our results agrees with those from the random phase (RPA) and the static path approximation (SPA) respectively.

# Séminaire du LPTMS: Y. Tourigny

## The Dyson-Schmidt approach to studying diffusion in a Levy environment

## Yves Tourigny, Université de Bristol

A diffusion may be thought of as a certain limit of a corresponding random walk. When the environment is random, this limit is convenient because of the variety of analytical tools that can brought to bear on its study. This talk will be concerned with the approach pioneered by Bouchaud, Comtet, Georges and Le Doussal in 1990, which maps the diffusion problem to a disordered supersymmetric quantum problem. I shall review the Dyson-Schmidt method for the calculation of the Lyapunov exponent and of the density of states when the disorder is modelled by a Levy process. The interpretation of these self-averaging quantities in the context of difusion will be discussed, and a number of new "solvable" cases will be presented.

# Séminaire de la Fédération PHYSTAT-SUD : Andreas Wagner

## The origins of evolutionary innovations

## Andreas Wagner (University of Zurich)

Life can be viewed as a four billion year long history of innovations. These range from dramatic macroscopic innovations like the evolution of wings or eyes, to a myriad molecular changes that form the basis of macroscopic innovations. We know many examples of such innovations -- qualitatively new phenotypes that provide an advantage to their bearer --, but we have no systematic understanding of the principles that allow organisms to innovate. Most phenotypic innovations result from changes in three classes of systems: metabolic networks, regulatory circuits, and protein or RNA molecules. I will discuss evidence that these classes of systems share two important features that are essential for their ability to innovate

# Séminaire du LPTMS: B. Altshuler

## Dissipative coupling and weak lasing of exciton-polariton condensates

## B. Altshuler, Columbia University, New York

In spite of having finite life-time exciton-polaritons in microcavities are known to condense at strong enough pumping of the reservoir. I will discuss an analytical theory of such Bose-condensates on a set of localized one-particle states: condensation centers. To understand physics of these arrays one has to supplement the Josephson coupling by the dissipative coupling caused by the interference between the bosons emitted by different centers. Combination of these couplings with the one-site interaction between the bosons leads to a rich nonlinear dynamics. In particular, a new regime of radiation appears. This regime can be called weak lasing: the centers have macroscopic occupations and radiate coherently, but the coupling alone is sufficient for stabilization. The system can have several stable states and switch between them. Moreover, the time reversal symmetry in this regime is, as a rule, broken. A number of existing experimental puzzles find natural interpretation in the framework of this theory.

# Seminaire Fluides Quantiques : Chris Westbrook

## Acoustic analog of the dynamical Casimir effect in a BEC

#### Chris Westbrook, LCFIO, Palaiseau

Although we often picture the quantum vacuum as containing virtual quanta whose observable effects are only indirect, it is a remarkable prediction of quantum field theory that the vacuum can generate real particles when boundary conditions are suddenly changed. Thus the dynamical Casimir effect results in the spontaneous generation of photon pairs in an empty cavity whose boundaries are rapidly accelerating. A recent experiment has demonstrated this effect in the microwave regime using superconducting circuits. Acoustic analogs of this effect exist as well, and Bose Einstein condensates are attractive candidates in which to study such analogs because their low temperatures promise to reveal quantum effects. I will - describe our group's work to develop an acoustic analog to the dynamical Casimir effect by modulating the confinement of a Bose-Einstein - condensate. We are able to observe the generation of correlated pairs of excitations both in the phonon and particle-like regimes in a process which also formally resembles parametric down conversion..

# Séminaire commun LPT-LPTMS : Thierry Bodineau

## Corrélations à longue portée dans des systèmes hors équilibre

#### Thierry Bodineau, DMA, ENS

Les systèmes maintenus hors équilibre ont, en général, des corrélations à longue portée dans l’état stationnaire. Nous décrirons quelques exemples de dynamiques stochastiques où ce type de corrélations peut être calculé (exclusion symétrique avec batterie, modèle ABC) et discuterons les singularités de ces corrélations à l’approche de la transition de phase.

# Séminaire du LPTMS: Thierry Champel

## Quasi-local quantum mechanics for disordered 2D electron gases at high magnetic fields

*Thierry Champel, Université Joseph Fourier*

We have developed a semicoherent-state Green's function formalism which rigorously describes quantum mechanical motion of an electron in a perpendicular magnetic field and a 2D disordered potential landscape beyond the semi-classical guiding center picture. Our general technique is connected to the deformation (Weyl) quantization theory in phase space developed in mathematical physics. For generic 2D quadratic potentials, we exactly solve the limit of large cyclotron frequency (yet at finite magnetic length) where Landau level mixing becomes negligible, both for the ordinary two-dimensional electron gas and for graphene (relativistic dispersion). Furthermore, the coherent-state representation is shown to display a hierarchy of local energy scales ordered by powers of the magnetic length and successive spatial derivatives of the local potential, which allows one to devise controlled approximation schemes at finite temperature for arbitrary and possibly disordered potential landscapes. As an application, we derive general analytical expressions for the local density of states, which allow us to account for many puzzling features recently observed in high magnetic field scanning tunneling spectroscopies on semiconducting heterostructures and graphene. Our recent theoretical developments in relation with percolative transport at high magnetic fields will also be evoked.

Refs.:

T. Champel and S. Florens, PRB 80, 125322 (2009);

T. Champel and S. Florens, PRB 82, 045421 (2010);

M. Flöser, S. Florens, and T. Champel, PRL 107, 176806 (2011).

# Séminaire du LPTMS: A. Petkovic

## Fluctuations of the superconducting order parameter in two dimensions

## A. Petkovic, ENS Paris

Transport properties of 2D superconducting systems can be very different from those of bulk superconductors because thermal and quantum fluctuations of superconducting order parameter are more pronounced and play a crucial role. First we focus on influence of superconducting fluctuations on dynamics, while the system is in the normal state but close to the superconducting transition. In the fluctuational regime, we derive Ginzburg-Landau-type action under far-from equilibrium conditions. Then, utilizing it, we calculate fluctuation-induced density of states and Maki-Thomson- and Aslamazov-Larkin-type contributions to the in-plane electrical conductivity [1,2]. We propose experimental setup where our results can be tested: thin superconducting film sandwiched between a gate and a substrate, which have different temperatures and different electrochemical potentials.

Then, we concentrate on transport at lower temperatures in close-to-equilibrium conditions investigating influence of quantum fluctuations on unbinding of vortex-untivortex pairs. We determine the temperature below which quantum fluctuations dominate over thermal fluctuations and describe the transport in this quantum regime. The crossover from quantum to classical regime is discussed and the quantum correction to the classical current-voltage relation is determined [3].

[1] Phys. Rev. Lett. 105, 187003 (2010)

[2] Phys. Rev. B 84, 064510 (2011)

[3] Phys. Rev. B 80, 212504 (2009)

# Séminaire du LPTMS: M. Colangeli

## Fluctuation-dissipation relation for chaotic non-Hamiltonian systems

#### Matteo Colangeli, Politecnico di Torino

In dissipative dynamical systems phase space volumes contract, on average. Therefore, the invariant measure on the attractor is singular with respect to the Lebesgue measure. As noted by Ruelle, a generic perturbation pushes the state out of the attractor, hence the statistical features of the perturbation and, in particular, of the relaxation, cannot be understood solely in terms of the unperturbed dynamics on the attractor. This remark seems to seriously limit the applicability of the standard fluctuation dissipation procedure in the statistical mechanics of nonequilibrium (dissipative) systems. Yet, it will be shown that the singular character of the steady state does not constitute a serious limitation in the case of systems with many degrees of freedom. The reason is that one typically deals with projected dynamics, and these are associated with regular probability distributions in the corresponding lower dimensional spaces.

# Mini Symposium PALM-LUMAT

## Physics at the X-FEL

## Louis DiMauro, Jan Lüning, Patrick Audebert, Boris Vodungbo

# Séminaire commun LPT-LPTMS : Masaharu Isobe

## Higher Order Parameters for Establishing Transient Crystals

#### Masaharu Isobe, Nagoya Institute of Technology

The long slow decaying potential part of the stress autocorrelation function has been called the “molasses tail” to distinguish it from the hydrodynamic origin of the long time tail in the velocity autocorrelation functions and to emphasize its relation to highly viscous glassy state. We are investigating the molasses tail in dense hard core fluids by using extensive Event-Driven MD simulation through the orientational autocorrelation functions[1, 2]. Near the fluid-solid phase transition, there exist three regimes in the relaxation of the pair orientational autocorrelation function, namely the kinetic, molasses(stretched exponential), and diffusional power decay. The most striking observation through the bond orientatinal order parameter is the dramatic increase of the transient nuclei cluster size near the freezing density[2]. We are now improving the alternative general methods based on the autocorrelation functions of higher order parameters even for quadruplet contributions (i.e. 8 point-correlation) to establish the transient nuclei, which are composed of a few hundred hard particles in dense liquid system [3].

- [1] M. Isobe and B. J. Alder, Mol. Phys. 107, 609 (2009).
- [2] M. Isobe and B. J. Alder, Prog. Theor. Phys. Suppl. 184, 437 (2010).
- [3] M. Isobe and B. J. Alder, in preparation.

# Séminaire de la fédération PHYSTAT SUD : Jean-Philippe Bouchaud

## Financial applications of random matrix theory : a short review

## Jean-Philippe Bouchaud, CFM, Paris

We discuss the applications of random matrix theory in the context of Financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. We intended to briefly review various theoretical results, old ones (the Marcenko-Pastur spectrum and its various generalizations) and newer ones (random singular value decomposition, eigenvector dynamics) as well as some concrete applications to portfolio optimization and out-of-sample risk estimation.

# Séminaire du LPTMS: J. Bellissard

## Atomic Motion and Transverse Geometry of Tiling Spaces

#### J. Bellissard, Georgia Tech

Based on the example of the notion of flip-flops in quasicrystals, illustrated by the Fibonacci case, it is advocated that atomic transport can be described by a dissipative dynamics associated with the transverse Riemannian Geometry of a tiling space.

# Séminaire commun LPT-LPTMS : Gregory Berkolaiko

## Universality in chaotic quantum transport : the concordance between random matrix and semiclassical theories

#### Gregory Berkolaiko, Texas A&M University

Electronic transport through chaotic quantum dots exhibits universal, system independent properties which are consistent with random matrix theory. The observable quantities can be expressed, via the semiclassical approximation, as sums over the classical scattering trajectories. Correlations between such trajectories are organized diagrammatically and have been shown to yield universal answers for some observables.

We develop a general combinatorial treatment of the semiclassical diagrams by casting them as unicellular maps (graphs embedded on surfaces) and relating them to factorizations of permutations. The expansion of transport quantities in inverse channel number corresponds to a genus expansion of the combinatorial generating function. Taking previously calculated answers (Heusler et al, 2006) for the contribution of a given diagram, we prove agreement between the semiclassical and random matrix approaches to moments of the transmission amplitudes. The proof covers all orders, all moments (including nonlinear), and systems with or without time reversal symmetry. It explains the mathematics behind the applicability of random matrix theory to chaotic quantum transport. The streamlined calculation could also pave the way for inclusion of non-universal effects.

Based on joint work with Jack Kuipers (Regensburg)# Séminaire du LPTMS: C. Cammarota

## Exploration of glass transition by pinning particles

## Chiara Cammarota, IphT Saclay

Understanding the physical mechanism behind glass formation is a lasting problem in condensed matter physics. Interestingly from a theoretical point of view, there are reasons to think that the viscous slowing down of super-cooled liquids' dynamics, preluding glass formation, is due to a new kind of thermodynamic transition, the glass transition. This is conjectured to be an entropy vanishing critical point with many peculiarities, notably an exponential growth of relaxation time. I will first point out why assessing the mere existence of the glass transition in real systems is particularly difficult; indeed this issue is still largely questioned. Then I will present an idea, based on pinning particles at random from an equilibrium configuration, recently designed to solve this problem. Furthermore, I will show our predictions for the static and dynamical behaviors of glassy pinned systems, obtained through mean field computations and a non-perturbative Renormalization Group approach. I will finally discuss why the idea of pinning particles could be used to produce decisive tests for the existence of the glass transition in real systems.

# Séminaire exceptionnel du LPTMS: Y. Ikhlef

## Finite-size left-passage probability in percolation

## Yacine Ikhlef, Université de Genève

The main objects of study in 2D percolation are the percolation clusters and the lattice curves surrounding them (hulls). In the scaling limit, Conformal Field Theory (CFT) and SLE allow the determination of correlation functions of these hulls. It turns out that some of these functions can be computed in finite size, opening a way to rigorous proofs of conformal invariance and universality, and uncovering some less understood aspects of CFT. I will present how, using transfer-matrix methods (Yang-Baxter, qKZ), we obtained an exact expression of the probability for a percolation hull to touch the boundary, on a strip of finite width L. We also relate the left-passage probability in the Fortuin-Kasteleyn cluster model to the magnetisation profile in the open XXZ chain: this is a new geometrical application of Bethe-Ansatz techniques developed for spin chains.

# Séminaire du LPTMS: A. Kundu

## Energy conduction in lattice systems

## Anupam Kundu, ESPCI

The famous phenomenological law in the context of energy conduction is the Fourier’s law, which relates current density with local temperature gradient. Many computer simulation and analytical studies, starting from microscopic description, show that Fourier’s law is not satisfied in low dimensional systems. We will discuss the validity of this law in higher dimensional lattice system. We will also discuss about large deviation of the energy current in a mass-disordered harmonic chain. In the end we present a more general linear response theory in this context to obtain a Green-Kubo type formula for open system.

# Séminaire commun LPT-LPTMS : Olga Dimitrova

## Specific heat of the Gaussian random bond Ising model on a square lattice

## Olga Dimitrova

The free energy and the specific heat of the two-dimensional Gaussian random bond Ising model on a square lattice are found with high accuracy using graph expansion and analysis of continuation of the high-temperature series. At low temperatures the specific heat reveals a zero-temperature criticality described by the power law $Cpropto T^1+alpha$, with $alpha= 0.65(10)$, the result confirmed independently by counting many-body states in finite size samples. The interpretation of the free energy in terms of droplet excitations gives the density of the two-level states, that follows a novel power law $rho(epsilon)propto epsilon^alpha$ at low energies.

# Séminaire du LPTMS: F. Ricci-Tersenghi

## Adding loops to mean field approximation for disordered models

## Federico Ricci-Tersenghi, Université Sapienza, Rome

In disordered models, the extension of mean-field approximations in order to include the effects of short loops is a challenging task, still largely open. Recently we have developed an analytical approximation (Replica Cluster Variational Method) and some related algorithms, which are able to provide a much better description of finite-dimensional spin glass models, than what the Bethe approximation does. I will summarize these results.

# Séminaire de la Fédération PHSYTAT-SUD : X. Viennot

## The combinatorics of some exclusion model in physics

## Xavier Viennot, LaBRI, Université de Bordeaux

The PASEP (partially asymmetric exclusion process) is a toy model in the physics of dynamical processes far from equilibrium (particles moving in a strip) and has been extensively studied by physicists. They gave explicit expressions for the stationary probabilities of the associated Markov chain, in relation with some orthogonal polynomials and some quadratic algebras. More recently, combinatorists gave a combinatorial approach to this model. I will give an introduction to this hot and active subject, which is at the crossroad of physics, probability, algebra and combinatorics.

# Séminaire exceptionnel: B. Estienne

## D-Algebra Structure of Topological Insulators

## Benoit Estienne

In the quantum Hall effect, the density operators at different wave-vectors generally do not commute and give rise to the Girvin MacDonald Plazmann (GMP) algebra with important consequences such as ground-state center of mass degeneracy at fractional filling fraction, and W_{1 + infty} symmetry of the filled Landau levels. We show that the natural generalization of the GMP algebra to higher dimensional topological insulators involves the concept of a D-algebra formed by using the fully anti-symmetric tensor in D-dimensions. For insulators in even dimensional space, the D-algebra is isotropic and closes for the case of constant non-Abelian F(k) ^ F(k) ... ^ F(k) connection (D-Berry curvature), and its structure factors are proportional to the D/2-Chern number. In odd dimensions, the algebra is not isotropic, contains the weak topological insulator index (layers of the topological insulator in one less dimension) and does not contain the Chern-Simons theta form (F^A - 1/3 A^A^A in 3 dimensions). The possible relation to D-dimensional volume preserving diffeomorphisms and parallel transport of extended objects is also discussed.

# Séminaire du LPTMS: G. Montambaux

## Manipulation de points de Dirac, du graphène aux atomes froids

## Gilles Montambaux, LPS, Université Paris-Sud

Je considère plusieurs exemples de cristaux 2D où les propriétés électroniques de basse énergie peuvent être décrites par un hamiltonien 2 X 2 avec un spectre présentant plusieurs cônes de Dirac. Ces cônes sont caractérisés par une relation de dispersion linéaire et, tout aussi important, par une “charge” topologique reliée à une phase de Berry associée à la structure spinorielle de la fonction d’onde. Par exemple, le spectre du graphène présente une paire de cônes de Dirac avec des phases de Berry opposées. On étudie sous quelles conditions ces cônes peuvent être manipulés, créés ou supprimés par des modifications des paramètres de bande, sous la condition de conservation de la charge totale.

Nous avons trouvé deux scénarios: (1) La fusion de points de Dirac avec des “charges” opposées est une transition topologique entre une phase semi-métallique et un isolant, avec un spectre remarquable, “semi-Dirac” à la transition : il est linéaire dans une direction et massif dans l’autre ! (2) Une paire de points de Dirac avec la même charge peut aussi fusionner en un point unique avec une charge double, et un spectre quadratique sans gap. C’est le cas dans les bicouches de graphène. Pour les deux scénarios, on a obtenu un hamiltonien universel qui décrit continûment le couplage entre les vallées.

Récemment, une très belle expérience avec des atomes ultrafroids dans un réseau optique a permis la réalisation de « graphène artificiel », dans lequel il est possible de déplacer et fusionner les points de Dirac et d’étudier le scénario (1) prévu théoriquement. L’évolution du spectre et la transition topologique sont révélés par les oscillations de Bloch d’un gaz de Fermions (40K). On mesure la probabilité Landau-Zener de transition entre les deux bandes et on caractérise ainsi les points de Dirac qui relient les deux bandes. Nous avons calculé cette probabilité de transition en utilisant l’hamiltonien universel qui décrit la fusion des points de Dirac et j’expliquerai l’accord remarquable que nous avons obtenu avec les résultats expérimentaux.

Finalement je discuterai d’autres scénarios de fusion de points de Dirac, en particulier dans les bicouches de graphène sous contrainte ou dans des gaz ultrafroids en présence de champs de jauge artificiels.

# Séminaire Fluides Quantiques: D. Gangardt

## Quantum Grey Solitons in Confining Potentials - Trapped Lieb II mode

### Dimitry Gangardt, University of Birmingham

We define and study hole-like excitations (the Lieb II mode) in a weakly interacting Bose liquid subject to external confinement. These excitations are obtained by semiclassical quantization of grey solitons propagating on top of a Thomas-Fermi background similarly to the uniform case. Radiation of phonons by an accelerated gray soliton leads to a finite lifetime of these excitations. We calculate the life-time of grey solitons and show that, for a large number of trapped atoms, most of the Lieb II levels can be experimentally resolved.

D. C. Wadkin-Snaith and D. M. Gangardt, Phys. Rev. Lett. 108, 085301 (2012)

# Séminaire du LPTMS: M. Tamm

## Overlap of Brownian trajectories

### Mikhail Tamm, Physics Dept., Moscow State University

I will present our recent results on the mean number of common sites visited by several random walk trajectories of a given length starting at a given distance from each other. I will start with the formulation of the problem and show the general solution in the Laplace space which is viable for any Markovian random walks in any geometry; then proceed to consideration of the Brownian motion in two specific cases: that of several trajectories starting from a common center, and that of two trajectories starting at a given distance. For the first case, I will show the existence of three distinct regimes depending on the dimensionality of space and the number of trajectories, and construct the corresponding morphology diagram. For the second case, I will show that in 1D and 3D it is possible to do the reverse Laplace transform and get the explicit expressions for the scaling functions of interest, which turn out to be in perfect agreement with computer simulation results.

The work is done in collaboration with S. Majumdar (LPTMS), A. Ilyina (Moscow State University), and D. Grebenkov (Ecole Polytechnique).

# Séminaire du LPTMS: Iosif Bena

## Trous noirs dans la Théorie des Cordes

## Iosif Bena (IPhT Saclay)

String theory is a quantum theory of gravity, and has had several amazing successes in describing black holes. After discussing some paradoxes related to the physics of black holes, I will explain how to construct black holes in string theory, and how to count their entropy. I will then describe a new paradigm in the study of black holes that recent research appears to support: a black hole solution gives only a thermodynamic description of the physics, and the "microscopical" statistical description of the physics is given by a very large number of microstate geometries, that look the same as a black hole from far away, but do not have a horizon.

# Séminaire de la fédération phystat-sud: Neil O'Connell

## Titre: Exactly solvable random polymers and their continuum scaling limits

### Orateur: Neil O'Connell (Université de Warwick)

Résumé: I will describe some recent developments on random polymer models which have an underlying integrable structure which makes them exactly solvable.

The continuum scaling limits of these models are related to the KPZ equation and have some remarkable properties. Parts of this talk will be based on joint work with Ivan Corwin, Timo Seppalainen, Jon Warren and Nikos Zygouras.

# Séminaire du LPTMS: Maxime Richard

## One dimensional polariton condensate in semiconductor microstructure

### Maxime Richard, Institut Néel

In semiconductor nanostructures like microcavities, when the so-called exciton-photon strong coupling regime is reached, the proper eigenstates of the system are mixed exciton-photon states called exciton-polaritons. This last decade, 2-dimensional microcavity exciton-polaritons in the quantum degenerate regime have shown fascinating properties e.g. polariton lasing, Bose-Einstein condensation and superfluidity [1]. Recently, new systems and new geometries are being developed in order to study the polariton physics of dimensionality D

Recently, new systems in the strong coupling regime like ZnO microwires have been introduced [4]. We show that polaritons in these systems have unusual characteristics: they have only one spatial degree of freedom and they exhibit low thermal decoherence thanks to a large Rabi splitting. Furthermore, they are robust at large density and high temperature owing to the large exciton binding energy of ZnO. Striking differences exist also in the condensate phase. At cryogenic temperature and under strong pulsed optical excitation, a transient polariton condensate is formed by stimulated relaxation into a state with a 97% excitonic fraction, i.e. with a mass 15 times heavier than for polaritons usually encountered in planar microcavities. This feature is enabled by the combination of a large Rabi splitting (300 meV) and a very small inhomogeneous broadening of excitons (~1 meV).

[1] L.S. Dang et al. Phys. Rev. Lett. 81 3920 (1998) ; J. Kasprzak et al., Nature 443, 409 (2006) ; A. Amo et al., Nat. Phys. 5, 805 (2009).

[2] E. Wertz et al., Nat. Phys. 6, 840-864 (2010).

[3] G. Christmann et al. Appl. Phys. Lett. 93, 051102 (2008).

[4] L. Sun et al, Phys. Rev. Letters 100, 156403 (2008); A. Trichet et al., Phys. Rev. B 83, 041302R (2011)

# Séminaire du LPTMS: Mathias Albert

## Waiting times distribution of electrons flowing across mesoscopic conductors

### Mathias Albert (LPS, Orsay)

** ** Electronic transport through mesoscopic devices is known to be stochastic due to the quantum nature of the charge carriers. The noise power spectrum as well as the Full Counting Statistics (FCS) provide many important informations about the system under study as it has been shown during the past 20 years. However the distribution of waiting times (WTD) between the detection of several charge carriers has been recently investigated and shown to be very powerful to understand the short time physics and correlations between different elementary events [1-3] in the same spirit than the level spacing distribution in the spectral statistics of complex systems. In this talk we will use this quantity to discuss the short time correlations in a perfect one dimensional quantum channel with a quantum point contact. Although the system is extremely simple, the WTD reveals quite striking transport properties that can be explained using random matrix theory in a totally unexpected context. Some other quantum states, such as a train of Lorentzian pulses [4] will be also considered and the relation between the WTD and the FCS also discussed.

[1] T. Brandes, Ann. Phys. (Berlin) **17**, 477 (2008).

[2] M. Albert, C. Flindt and M. Buttiker, Phys. Rev. Lett. **107**, 086805 (2011).

[2] M. Albert, G. Haack, C. Flindt and M. Buttiker, Phys. Rev. Lett. **108**, 186806 (2012).

[3] J. Keeling, I. Klich, L. S. Levitov, Phys. Rev. Lett. **97**, 116403 (2006).

# Séminaire du LPTMS: Marc Rabaud

## Est-ce que le sillage des canards sur le lac du Mail est toujours à 19°?

### Marc Rabaud (FAST, Orsay)

Tout objet se déplaçant à l'interface de deux fluides peut générer des ondes de surface et subit alors un force de traînée. Kelvin (1887) a montré que les ondes de gravité sont confinées dans un triangle à l'arrière de l'obstacle qui a un angle constant quelle que soit la vitesse de l'obstacle. Nous montrerons en images issues de simulations et d'expériences en quoi la longueur capillaire mais aussi la taille finie de l'obstacle peuvent modifier ce résultat.

# Séminaire "Fluides Quantiques" du LPTMS : David Papoular

## Cooling by heating a superfluid

### David Papoular (BEC Center, Trento)

We consider a uniform superfluid confined in two compartments connected by a superleak and initially held at equal temperatures. If one of the two compartments is heated, a fraction of the superfluid will flow through the superleak. We show that, under certain thermodynamic conditions, the atoms flow from the hotter to the colder compartment, contrary to what happens in the fountain effect observed in superfluid Helium. This flow causes quantum degeneracy to increase in the colder compartment. In superfluid Helium, this novel thermomechanical effect takes place in the phonon regime of very low temperatures. In dilute quantum gases, it occurs at all temperatures below Tc. The increase in quantum degeneracy reachable through the adiabatic displacement of the wall separating the two compartments will also be discussed.

# Séminaire exceptionnel du LPTMS : Mikhail Zvonarev

## Relaxation of the mobile impurity injected into one-dimensional quantum liquid

### Mikhail Zvonarev (LPTMS)

I will discuss a time evolution of the mobile impurity injected with an arbitrary velocity into one-dimensional quantum liquid. I will demonstrate that the impurity holds a finite fraction of its initial momentum even after infinitely long waiting time and that the impurity momentum oscillates during the equilibration process. To obtain these results a combination of exact (Bethe Ansatz), variational, and numerical methods were used. I will finally overview the experiments in the ultracold atomic gases which are related to impurity dynamics.

# Séminaire du LPTMS: J. Reingruber

## Phototransduction in rod and cone photoreceptors

### Jürgen Reingruber, Ecole Normale Superieure

Vision is initiated with the absorption of light by rod and cone photoreceptors in the retina, which are highly specialized sensory cells. Rods sustain monochrome night vision, while cones maintain colorful day vision. Phototransduction is the process by which light is transformed into an electrical signal in photoreceptors, a topic that still moves at the forefront of signal transduction research.

In this talk I will first give an introduction to phototransduction in rod and cone photoreceptors. Despite of decades of intense research, an overall biophysical model that integrates and explains all the experimental data is still missing. For example, it was realized already 70 years ago that rods are so sensitive that they can reliably detect the absorption of a single photon. However, up to today it is still not fully understood what determines the high fidelity of a rod cell.

Based on novel experimental recordings of the background noise and single photon response in genetically modified mouse rods (collaboration with G. Fain (UCLA)), I will present recent results obtained from a combined effort between biophysical modeling, mathematical analysis and numerical simulations to understand the molecular mechanisms underlying the single photon response.

Finally, I will briefly discuss the importance of molecular modeling to improve new optogenetic treatments of retinal diseases caused by photoreceptor degeneration (collaboration with S. Picaud (Institut de la Vision, Paris)).

# Séminaire du LPTMS: Jon Harrison

## New forms of quantum statistics on graphs

### Jon Harrison, Baylor University

We consider the quantum statistics of indistinguishable particles on a graph. In three dimensions quantum states are symmetric or anti-symmetric under exchange of pairs of identical particles, corresponding to Bose-Einstein or Fermi-Dirac statistics respectively. Restricting the particles totwo dimensions topologically inequivalent exchange paths correspond to elements of the braid group instead of the symmetric group. This opens up the possibility of Anyon statistics on a surface, characterized by a single free choice of an exchange phase. We consider the case when the particles are further restricted to lie on a quasi-one-dimensional network; a graph. For sufficiently complex graphs new forms of statistics emerge. Quantum statistics of indistinguishable particles on graphs may be characterized by multiple independent free Anyon phases and discrete-valued phases. Possible applications of the new forms of quantum statistics include topological quantum computing, the fractional quantum Hall effect, superconductivity, topological insulators and molecular physics. This is work with JP Keating and JM Robbins at Bristol University. Proc. R. Soc. A doi:10.1098/rspa.2010.0254

# Séminaire de la Fédération PHSYSTAT-SUD : Matteo Marsili

## Collaboration in social networks

### Matteo Marsili ( The Abdus Salam International Center for Theoretical Physics, Trieste)

The very notion of social network implies that linked individuals interact repeatedly with each other. This notion allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated games shows that these circumstances are conducive to the emergence of collaboration in simple games of two players. We investigate the extension of this concept to the case where players are engaged in a local contribution game and show that rationality and credibility of threats identify a class of Nash equilibria—that we call “collaborative equilibria”—that have a precise interpretation in terms of subgraphs of the social network. For large network games, the number of such equilibria is exponentially large in the number of players. When incentives to defect are small, equilibria are supported by local structures whereas when incentives exceed a threshold they acquire a nonlocal nature, which requires a “critical mass” of more than a given fraction of the players to collaborate. Therefore, when incentives are high, an individual deviation typically causes the collapse of collaboration across the whole system. At the same time, higher incentives to defect typically support equilibria with a higher density of collaborators. The resulting picture conforms with several results in sociology and in the experimental literature on game theory, such as the prevalence of collaboration in denser groups and in the structural hubs of sparse networks.

# Séminaire du LPTMS: R. Santachiara

## Emerging integrable structures in Abelian and non-Abelian quantum Hall liquids

### Raoul Santachiara, LPTMS

I'll review the main properties of Laughlin incompressible quantum liquids. I will discuss in particular the low-energy edge excitations and their connection to the area-preserving transformations. The corresponding algebraic structures suggest that the integrable 1D quantum model Calogero-Sutherland plays a crucial role. Recently, by using conformal field theory techniquesm we have shown that a similar scenario is emerging in the case of the non-Abelian quantum Hall liquids. I will discuss the main results trying to focus only the general ideas behind this approach.

# Séminaire "Fluides quantiques" du LPTMS : Layla Hormozi

## Fractional Quantum Hall Effect of Lattice Bosons Near Commensurate Flux

### Layla Hormozi (National University of Ireland in Maynooth)

We study interacting bosons on a lattice in a magnetic field. When the number of flux quanta per plaquette is close to a rational fraction, the low energy physics is mapped to a multi-species continuum model: bosons in the lowest Landau level where each boson is given an internal degree of freedom, or pseudospin. We find that the interaction potential between the bosons involves terms that do not conserve pseudospin, corresponding to umklapp processes, which in some cases can also be seen as BCS-type pairing terms. We argue that in experimentally realistic regimes for bosonic atoms in optical lattices with synthetic magnetic fields, these terms are crucial for determining the nature of allowed ground states. In particular, we show numerically that certain paired wavefunctions related to the Moore-Read Pfaffian state are stabilized by these terms, whereas certain other wavefunctions can be destabilized when umklapp processes become strong.

(Online pre-print: http://arxiv.org/abs/1109.3434)

# Séminaire du LPTMS: Gabriel Téllez Acosta

## Expanded Vandermonde powers, Jack polynomials and the two-dimensional one-component plasma

### Gabriel Téllez, Departamento de Física, Universidad de Los Andes, Bogotá, Colombia

The two-dimensional one-component plasma (2dOCP) is a system of N mobile particles of the same charge q on a surface with a neutralising background. The Boltzmann factor of the 2dOCP at temperature T can be expressed as a Vandermonde determinant to the power Gamma = q^2/(k_B T). Recent advances in the theory of symmetric and anti-symmetric Jack polymonials provide an efficient way to expand this power of the Vandermonde in their monomial basis, allowing the computation of several thermodynamic and structural properties of the 2dOCP for N values up to 14 and Gamma equal to 4, 6 and 8. In this work, we present some applications of this formalism.

# Séminaire du LPTMS: Geoffroy Lerosey

## A broadband approach to sub-diffraction far field imaging and focusing with metamaterials

### Geoffroy Lerosey (Institut Langevin, ESPCI ParisTech & CNRS UMR 7587)

In this talk I will show how the use of time dependent and broadband wavefields, in conjunction with metamaterials, permits to beat the diffraction limit from the far field for imaging or focusing purposes. I will introduce the idea of resonant metalens, first demonstrated in the microwave domain, and explain its principles. In particular, I will show how the concept of time reversal can be utilized to focus in this metamaterial based lens and from the far field, onto focal spots much smaller than the diffraction limit. I will then prove the generality of the approach by demonstrating its transposition to the acoustic domain thanks to a very simple setup: an array of soda cans. Then I will present our latest theoretical and numerical results obtained using a resonant metalens made out of plasmonic nanorods in the visible part of the spectrum. I will show that this lens allows, using polychromatic light, to focus light using far field time reversal onto spots as small as 1/30th of the wavelength in the visible. Finally I will prove that our approach can also be used in order to image from the far field and with a subwavelength resolution and could lead to real time sub-diffraction imaging systems.

# Séminaire du LPTMS: Anuradha Jagannathan

## Introduction aux quasi-cristaux et modèles quantiques sur pavages quasi-périodiques

### Anu Jagannathan, Laboratoire de Physique des Solides, Orsay

On commencera par une introduction aux quasi-cristaux, sujets du prix Nobel de chimie de 2011, et quelques-unes de leurs propriétés structurelles remarquables. Divers modèles ont été proposés pour décrire les propriétés physiques de ces matériaux. Un des problèmes fondamentaux concerne les propriétés d'un électron dans un potentiel quasi-périodique. On peut se demander quelle est la forme des fonctions d'onde typiques comparées à celles connues dans la matière condensée, allant des fonctions d'onde étendues dans les métaux aux fonctions complètement localisées dans les amorphes. Une autre catégorie de problèmes concerne les propriétés de spins dans une telle structure, la nature de l'état fondamental magnétique, et les corrélations. On introduira des modèles définis sur des pavages quasi-périodiques, notamment le pavage de Penrose, avec une discussion de quelques méthodes théoriques et des résultats qui ont été obtenus.

# Soutenance de thèse : Tianyou Yi

## Modeling of dynamical vortex states in charge density waves

### Tianyou Yi, LPTMS

Electronic Crystals is a common form of organization in conducting solids. They take forms of Wigner crystals at hetero-junctions and nano-wires, charge density waves (CDWs) in chain compounds, spin density waves in organic conductors, stripes in doped oxides and high-Tc superconductors. In the CDW ground state, the elementary units can be readjusted by absorbing or rejecting pairs of electrons. Such a phase-slip process should go via topologically nontrivial configurations: solitons and dislocations – the CDW vortices. An experimental access to those states came from studies of nano-fabricated mesa-junctions, from the STM visualizations and from the X-ray micro-diffraction.

Following these requests, we performed a program to model the stationary states and their transient dynamic for the CDW in restricted geometries under the applied field or the passing current. A particular care had to be taken to derive a gauge invariant and current conserving scheme for the interacting condensed and normal charge densities. The model takes into account multiple fields in mutual nonlinear interactions: the amplitude and the phase of the CDW complex order parameter, distributions of the electric field, the density and the current of normal carriers. We have found that vortices are formed stepwise in the junction when the voltage across, or the current through, exceed a threshold. The vortex core concentrates the voltage drop, working as a self-tuned microscopic tunnelling junction. The studied reconstruction in junctions of the CDW is a convenient playground for modern efforts of field-effect transformations in strongly correlated materials with spontaneous symmetry breakings

# Séminaire du LPTMS: A. Bouzdin

## Non-uniform (FFLO) states and quantum oscillations in superconductors and superfluid ultracold Fermi gases

### A. Buzdin, Université de Bordeaux

A long time ago, it was predicted by Larkin and Ovchinnikov and Fulde and Ferrell that the non-uniform superconducting state (FFLO state) must appear in the magnetic field acting on the electron spins. We start with the discussion of the distinctive features of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) non-uniform superconducting state and review recent experiments on the heavy fermion superconductor CeCoIn5 and layered organic superconductors providing strong evidences in favor of FFLO phase observation. It is demonstrated that in 2D ( or quasi 2D) superconductors the FFLO state leads to an appearance of a very special oscillatory – like dependence of the upper critical field versus the field orientation.

Interestingly, in the superconductor-ferromagnet heterostructures the FFLO-like state may result in the formation of the Josephson junction with a spontaneous phase difference.

The FFLO-type instability may be also expected in ultracold Fermi gases in magneto-optical traps. In these systems it is caused not by the Zeeman interaction but by the tuning of the population imbalance between two lowest hyperfine states of the atoms. We briefly discuss the properties of such FFLO state and analyze the role the trapping potential confining the condensate.

# Séminaire du LPTMS: Sanjib Sabhapandit

## Fluctuations and large deviations in nonequilibrium processes

### Sanjib Sabhapandit (Raman Research Institute, Bangalore)

I will start with fluctuation theorems and its connections to large deviations. I will then describe how the large deviation function can be evaluated for the heat flow across a harmonic chain. Finally, I will show application of the results to an recent experiment.

# Séminaire de la fédération PHSYTAT SUD : Marcos Marino

## Matrix models and string theory

### Marcos Marino (University of Geneva)

In this talk I will try to provide a pedagogical overview of the interplay between random matrices and string theory. I will start with the "old" matrix models of non-critical strings and their applications to statistical systems, and explain some more recent developments on the connection between matrix models, gravity, and superstrings.

# Journées d'étude du Laboratoire

## Domaine de Seillac, 41150 Seillac

# Journées d’étude du Laboratoire

## Domaine de Seillac, 41150 Seillac

# Journées d’étude du Laboratoire

## Domaine de Seillac, 41150 Seillac

# Séminaire du LPTMS: Nicolas Laflorencie

## The Best Enemies of Superfluid Bose Condensates

### Nicolas Laflorencie, LPT Toulouse

Looking back at Helium-4, it took some time to admit that superfluidity and Bose-Einstein condensation, while distinct phenomena, occur (and disappear) together. However, apart from the particular cases of T=0 in one dimension and the finite-T BKT regime for 2D superfluids, we may ask if such a fact is always true. In this seminar we will address this issue through the idea of the competitors or "enemies" of the superfluid / Bose condensate, namely: repulsive interactions, disorder, and frustration. Across 2 specific examples of hard-core bosonic models in 3D, I will discuss the possibility to achieve (i) a T=0 condensate-free superfluid state through a frustrated proximity effect, directly relevant for the frustrated antiferromagnet BaCuSi2O6, and (ii) a finite temperature sliding regime for randomly stacked superfluid layers, which might explain some anomalies in the transport properties of the layered superconductors LSCO.

# Séminaire commun LPT-LPTMS: Sara Jabbari

## Interplay of anisotropy and interactions in charged colloidal disks

### Sara JABBARI-FAROUJI, LPTMS

Charged plate-like colloidal suspensions such as gibbsite and some clays exhibit interesting and rich phase behavior including liquid-crystalline and arrested gel-like states. The anisotropic shape of such particles suggests that these materials could form liquid crystalline phases due to the competition between positional and orientational entropy. In some cases, however, isotropic-nematic transition is hindered by formation of a gel-like viscoelastic phase. The question that arises is how the electrostatic interactions influence the liquid crystal formation. Motivated by these experimental findings, we have investigated the structure and dynamics of charged disks by means of Monte-Carlo simulations. In this talk, I will clarify the the role of anisotropic nature of screened electrostatic interactions on the formation of liquid-crystalline phases and arrested states. Finally, I will compare the results of our simulations with experiments.

# Séminaire du LPTMS: Takahiro Sagawa

## Information Thermodynamics in Small Systems

### Takahiro Sagawa, Yukawa Institute for Theoretical Physics, Kyoto University

Ever since the proposal of "Maxwell's demon" in the nineteenth century, the relationship between thermodynamics and information has attracted numerous attentions concerning the foundation of the second law of thermodynamics [1,2]. The demon seems to be able to violate the second law by using the information about the microscopic degrees of freedom of thermodynamic systems. Due to the recent developments of the experimental technologies of manipulating small thermodynamic systems, the demon has become a topic of active researches both in terms of theory and experiment of nonequilibrium statistical physics. In this seminar, I'd like to talk about our theoretical and experimental results on the foundation of the relationship between thermodynamics and information [3-6]. Theoretically, I will focus on the generalizations of the second law of thermodynamics to information processing processes such as measurement and feedback, in which information contents and thermodynamic variables are treated on an equal footing. I'd also like to talk about our experimental result, which has experimentally realized a Maxwell's demon that uses the obtained information as a resource of the free energy and the work [7]. References: [1] "Maxwell's demon 2: Entropy, Classical and Quantum Information, Computing," H. S. Leff and A. F. Rex (eds.), (Princeton University Press, New Jersey, 2003). [2] T. Sagawa and M. Ueda, arXiv:1111.5769, to appear in R. Klages, W. Just, C. Jarzynski (Eds.), "Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond" (Wiley-VCH, Weinheim, 2012). [3] T. Sagawa and M. Ueda, Phys. Rev. Lett. 100, 080403 (2008). [4] T. Sagawa and M. Ueda, Phys. Rev. Lett. 102, 250602 (2009). [5] T. Sagawa and M. Ueda, Phys. Rev. Lett. 104, 198904 (2010). [6] T. Sagawa and M. Ueda, arXiv:1206.2479, to appear in PRL. [7] S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Nature Physics 6, 988-992 (2010).

# Séminaire du LPTMS: Hiroki Ohta

## Lane formation in a lattice model for oppositely driven binary particles

### Hiroki Ohta, LPTMS

I will introduce a two-dimensional lattice model for oppositely driven binary particles with purely repulsive interactions where some classes of steady states have been constructed in systematic ways. Using such constructions, I will discuss nonequilibrium phase transitions in this lattice model [1]. Also, I would like to discuss those relevance to lane formations in colloidal suspensions [2] [3]. Reference: [1] H. Ohta, Europhys. Lett. 99, 40006 (2012). [2] J. Dzubiella, G. P. Hoffmann, H. Löwen, Phys. Rev. E 65, 021402 (2002). [3] T. Vissers, A. Wysocki, M. Rex, H. Löwen, C. P. Royall, A. Imhof, A. van Blaaderen, Soft Matter 7, 2352 (2011).

# Cours du LPTMS : Pierpaolo Vivo

"Introduction to Random Matrix Theory"

- Invariant vs. non invariant ensembles

- Edwards-Jones formula for density of states

- The Gaussian ensemble: semicircle law, method of orthogonal polynomials, resolvent equations

- The Coulomb gas method and linear statistics

- Largest eigenvalue: Tracy-Widom law and applications

# Cours du LPTMS : Pierpaolo Vivo

"Introduction to Random Matrix theory"

- Invariant vs. non invariant ensembles

- Edwards-Jones formula for density of states

- The Gaussian ensemble: semicircle law, method of orthogonal polynomials, resolvent equations

- The Coulomb gas method and linear statistics

- Largest eigenvalue: Tracy-Widom law and applications

# Séminaire du LPTMS: Jacopo Viti

## Field theory approach to percolation and phase separation in two dimensions

### Jacopo Viti, LPTENS

In 1+1 dimensions it exists a special class of Quantum Field Theories, the so-called Integrable QFT, for which an exact S-matrix can be written and correlation functions computed with a great accuracy. I will discuss some recent applications of Integrable QFT to the study of the percolation phase transition in two dimensions. Particular emphasis will be given to the results that have been tested numerically. In the final part of the talk I will describe how the same formalism can be applied to analyze the structure of the interfaces between two pure phases.

# Physics-Biology interface seminar: Nir Gov

**Non-equilibrium physics inspired by biology: from fluctuating membranes to active gels**

**Nir Gov, **(Weizmann Institute of Science)

The most ubiquitous and accessible non-equilibrium systems around us are in the form of living organisms. Motivated by pattern formation and random motion that are driven by active (out-of-equilibrium) processes in cells we investigate the similarities and differences between such motion and thermal random motion. A simple theoretical model of a kicked particle is used to extract analytic and numerical results which we then compare to observations of membrane fluctuations in cells, and fluctuations in active gels reconstituted in-vitro.

# Cours du LPTMS : Pierpaolo Vivo

"Introduction to Random Matrix Theory"

- Invariant vs. non invariant ensembles

- Edwards-Jones formula for density of states

- The Gaussian ensemble: semicircle law, method of orthogonal polynomials, resolvent equations

- The Coulomb gas method and linear statistics

- Largest eigenvalue: Tracy-Widom law and applications

# Séminaire du LPTMS: Jérôme Dubail

## Trial states for quantum Hall fluids and related sytems: an entanglement point of view

### Jérôme Dubail, Yale University

A celebrated theoretical approach to the Fractional Quantum Hall Effect consists in cooking up trial wavefunctions for various filling fractions. Some specific trial states (the ones given by field theory correlators) have particularly nice properties. Physically, they describe exotic phases of matter, for instance with non-abelian excitations. On the technical side, they bear some striking resemblance with Tensor Product States. The purpose of this talk is to explain how the edge excitations and the entanglement spectrum of these states both arise naturally in that framework.

# Cours du LPTMS : Pierpaolo Vivo

"Introduction to Random Matrix Theory"

- Invariant vs. non invariant ensembles

- Edwards-Jones formula for density of states

- The Gaussian ensemble: semicircle law, method of orthogonal polynomials, resolvent equations

- The Coulomb gas method and linear statistics

- Largest eigenvalue: Tracy-Widom law and applications

# Soutenance de thèse : Matthieu Barbier

## De l'impermanence des formes dans les fluides granulaires : croissance et relaxation dans les mélanges

### Matthieu Barbier, LPTMS

Ce travail porte sur la dynamique de la matière granulaire dans l'état fluide, et sa réponse à une excitation localisée dans deux limites : une faible perturbation suite à laquelle le système relaxe rapidement vers un état homogène, ou une agitation intense qui engendre une onde de choc semblable à un souffle d'explosion. Cette réponse est affectée par deux caractéristiques des fluides granulaires : les particules macroscopiques qui les composent sont d'une part inélastiques, de sorte que leur dynamique est dissipative et ne possède pas d'état d'équilibre, et d'autre part polydisperses, c'est-à-dire hétérogènes en taille et en masse. Nous isolons d'abord un effet dynamique de la polydispersité en montrant qu'il existe un mélange optimal qui minimise le temps de relaxation du fluide vers son état asymptotique. Nous nous intéressons ensuite au cas où une seule des espèces est perturbée par l'application d'un champ extérieur, et étudions l'état stationnaire hors d'équilibre ainsi établi, dans la limite du traceur où les autres espèces constituent un bain stationnaire. Enfin, nous modélisons la croissance de formes auto-similaires dans ce bain suite à une intense libération ponctuelle d'énergie, que nous comparons au souffle d'une explosion dans un gaz moléculaire.

---------

This work focuses on the dynamics of the fluid state of granular matter, and its response to a localized perturbation in two limiting cases : relaxation toward a homogeneous state or growth of a blast wave. This response is shaped by two distinctive features of granular media: their macroscopic constituent particles are both inelastic, entailing intrinsically non-equilibrium dynamics, and polydisperse or heterogeneous in their material properties. First, we isolate the effects of polydispersity in the return of a gas to its homogeneous asymptotic state, and evidence the existence of an optimal mixture for which the relaxation time is minimal. We then restrict the perturbation to accelerating a single species with an external field in order to study the induced non-equilibrium stationary state in the tracer limit, where other species are undisturbed by this process. Finally, we model the self-similar shock wave generated in such a dissipative bath by an intense yet localized release of energy, and contrast it with blast waves in molecular gases.

# Séminaire du LPTMS: Ezequiel Ferrero

## Non-steady relaxation and critical exponents at the depinning transition via large scale GPU simulations

### Ezequiel Ferrero, Centro Atómico Bariloche - CONICET

We study the non-steady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units (GPUs). We compute the time-dependent velocity and roughness as the interface relaxes from a given initial configuration at the thermodynamic critical force. We extract critical exponents from the Short Time Dynamics behavior of the system. Above the first, non-universal microscopic time-regime, we find a non-trivial long crossover towards the non-steady macroscopic critical regime, where it is accurate to fit. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent $beta$) found in the literature.

In addition, if time permits, I would like to briefly mention other implementations we have been developing for simulations in GPUs, including Monte Carlo dynamics of classical spin systems and Langevin dynamics for a $Phi^4$ model.

# Séminaire commun LPT-LPTMS: Hiroki Ohta

## Lane formation in a lattice model for oppositely driven binary particles

### Hiroki Ohta, LPTMS

I will introduce a two-dimensional lattice model for oppositely driven binary particles with purely repulsive interactions where some classes of steady states have been constructed in systematic ways. Using such constructions, I will discuss nonequilibrium phase transitions in this lattice model [1]. Also, I would like to discuss those relevance to lane formations in colloidal suspensions [2] [3].

Reference:

[1] H. Ohta, Europhys. Lett. 99, 40006 (2012).

[2] J. Dzubiella, G. P. Hoffmann, H. Löwen, Phys. Rev. E 65, 021402 (2002).

[3] T. Vissers, A. Wysocki, M. Rex, H. Löwen, C. P. Royall, A. Imhof, A. van Blaaderen, Soft Matter 7, 2352 (2011).

# Physics-Biology interface seminar : Emmanuel Beaurepaire

## Nonlinear microscopy of developing tissues and embryos

### Emmanuel Beaurepaire (Lab. for Optics and Biosciences, École Polytechnique/CNRS/INSERM)

Understanding the dynamics at play during embryonic and tissue development requires tissue-scale measurements with subcellular resolution. Nonlinear microscopy is attractive for live studies because it provides tissue 3D imaging and provides several contrast mechanisms. Intrinsic coherent signals such as second- and third-harmonic generation (SHG, THG) provide structural information and can be used in conjunction with fluorescence (2PEF) imaging. SHG signals are specifically obtained from dense organized structures, whereas THG signals are obtained from optical heterogeneities and provide images of the tissue morphology. We will discuss these principles and applications such as imaging the microstructure of intact unstained corneas, and reconstructing the early development of zebrafish embryos. Finally, we will discuss ongoing efforts to improve the capabilities of nonlinear microscopy for imaging developing tissues at advanced stages, such as wavefront control for aberration correction, and simultaneous excitation of multiple fluorescent proteins.

- References:
- Supatto et al, Curr. Opin. Gen. Dev. 21 538 (2011).
- Aptel et al, Invest. Ophtalmol. Vis. Sci. 51, 2459 (2010).
- Olivier et al, Science 339, 967 (2010).
- Zeng et al, Biomed. Opt. Express 3, 1898 (2012).
- Mahou et al, Nat. Methods 9 815 (2012).

# Cours du LPTMS : Pierpaolo Vivo

"Introduction to Random Matrix Theory"

- Invariant vs. non invariant ensembles

- Edwards-Jones formula for density of states

- The Gaussian ensemble: semicircle law, method of orthogonal polynomials, resolvent equations

- The Coulomb gas method and linear statistics

- Largest eigenvalue: Tracy-Widom law and applications

# Séminaire du LPTMS: Masud Haque

## Composite object dynamics in interacting 1D lattice systems: propagation, locking, and scattering

### Masud Haque, MPIPKS, Dresden

In one-dimensional lattice systems, I will present results on the dynamics of composite objects such as repulsively bound pairs, triplets and clusters. Highlights are: [A] a dramatic series of dynamics-suppression effects near edges or geometric features, associated with fractal structures in the energy spectrum; [B] dynamical `scattering' protocols which display visually obvious differences between integrable and non-integrable systems.

Versions of these phenomena appear in (1) the Bose-Hubbard model; (2) the spinless fermion model with nearest neighbor repulsion; (3) the XXZ spin chain; (4) the fermionic Hubbard chain.

# Cours du LPTMS : Pierpaolo Vivo

"Introduction to Random Matrix Theory"

- Edwards-Jones formula for density of states

- The Gaussian ensemble: semicircle law, method of orthogonal polynomials, resolvent equations

- The Coulomb gas method and linear statistics

- Largest eigenvalue: Tracy-Widom law and applications

# Séminaire de la fédération PHYSTAT-SUD : Jean-François Joanny

## Growth and instabilities of healthy and cancerous tissues

### Jean-François Joanny, Institut Curie, Paris

During development or during tumor growth, cells organize collectively by cell division and apoptosis in a tissue. The aim of our work is to build up theoretical tools based on non-equilibrium statistical mechanics and continuum mechanics to describe the mechanical properties of tissues and to apply them to various biologically relevant situations. We first show that because of the coupling between cell division and the local stress, a tissue can be considered as a visco-elastic liquid at time scales larger than the cell division time. We then show recent model experiments on cell aggregates showing the effect of mechanical stress on tissue growth. Finally, we use the hydrodynamic description to discuss the steady state structure of villis which are the protrusions of the surface of the intestine. We describe the formation of villis as a buckling instability of a polar cell monolayer. Similar instabilities occur as well for tube-like cellular structures such as arteries.

# Séminaire du LPTMS: Thomas Salez

## Polymers in Flatland: Self-Similarity and Nanorheology

### Thomas Salez, ENS/ESPCI

The study of ultra-thin polymer nanofilms is a rich and productive field for applied mathematics, fundamental physics, physiology and engineering. It has been enlightened by the recent results on dewetting, nanoindentation, electrostatic instabilities and micro-bubbles. We report here on a novel and simple technique based on capillary leveling of a thin polystyrene stepped film far above the glass transition temperature [1]. We present as well the analytical [2] and numerical [3] tools that allow one to precisely understand the experimental profiles in various conditions. In particular, we study the self-similar intermediate asymptotics of the solutions and we describe how they provide a direct and accurate viscosity probe for polymer materials and viscous flows in general. Finally, we show how those solutions can give quantitative insights on fundamental questions such as : the effect of confinement on the macromolecular mobility, the slip condition at the substrate in hydrodynamics, the spreading of a droplet onto a precursor film [4], or the evolution of the superficial mobility through the glass transition.

[1] McGraw, Salez, Baumchen, Raphael, Dalnoki-Veress, PRL 109 128303 (2012)

[2] Salez, McGraw, Baumchen, Dalnoki-Veress, Raphael, PoF in press (2012)

[3] Salez, McGraw, Cormier, Baumchen, Dalnoki-Veress, Raphael, EPJE in press (2012)

[4] Cormier, McGraw, Salez, Baumchen, Raphael, Dalnoki-Veress, PRL 109 154501 (2012)

# Séminaire exceptionnel du LPTMS: Uzy Smilansky

## Spectral Statistics of Permutation Matrices

### Uzy Smilansky, Weizmann Institute of Science, Rehovot

I shall present some new results obtained with Idan Oren on the spectral statistics of permutation matrices of large order. They show curious features which can be explained using classical number theory, modified slightly to be useful for the present application. Our result are consistent with the known leading order asymptotic expressions, and add to them the next to leading order corrections.

# Physics-Biology interface seminar : Massimo Vergassola

**Fluctuations and response in biological sensory systems**

**Massimo Vergassola **(Institut Pasteur)

The statistics of fluctuations in biological pathways and its relation to the response to environmental stimuli will be discussed. We shall specifically focus on bacterial chemotaxis, where detailed experiments and reliable models are available. A novel non-invasive experimental method to measure the chemotaxis response will first be presented. By using fluctuation relations, we then relate appropriate steady-state correlations to the response of the system to step and ramp stimuli of arbitrary amplitudes. That provides a systematic explanation for the observed relation between fluctuations and response and it also reconciles the out-of-equilibrium nature of the dynamics with the apparently standard form of the fluctuation-dissipation relation.

# Séminaire du LPTMS: Jean-Michel Raimond

## Mesure et contrôle quantique avec des atomes et des cavités

### Jean-Michel Raimond, LKB ENS

Nous piégeons quelques photons micro-onde dans une cavité supraconductrice et nous les sondons avec des atomes de Rydberg circulaires. Nous réalisons ainsi une mesure quantique idéale du nombre de photons, nous les voyons apparaître et disparaître un par un. Cette mesure « sans démolition quantique » est au cœur d'une méthode de reconstruction de l'état du champ, qui nous permet de suivre la décohérence rapide d'une superposition quantique mésoscopique (un état « chat de Schrödinger »), et d'explorer ainsi la frontière entre le quantique et le classique. Enfin, en détectant les sauts quantiques, nous pouvons contrecarrer leurs effets et maintenir constant le nombre de photons dans la cavité dans ce qui est la première réalisation d'une rétroaction quantique.