# Seminaires Phystat

**Renseignements :**

**Jeudi 2 février 2012 à 14h30**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Andreas Wagner**

(University of Zurich)

**The origins of evolutionary innovations**

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.

**Lundi 9 janvier 2012 à 14h30**

Salle Itzykson, IPhT Saclay

**Florent Krzakala**

(Physico-Chimie Théorique UMR CNRS Gulliver ESPCI)

## Statistical physics approach to compressed sensing

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

**Jeudi 1er décembre 2011 à 14h**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Jacqueline Bloch**

(Laboratoire de Photonique et de Nanostructures, LPN/CNRS, Route de Nozay, 91460 Marcoussis)

## Propagation and optical manipulation of Bose condensates in semiconductor microcavities

Cavity polaritons are mixed exciton-photon states arising from the strong coupling regime between excitons confined in quantum wells and photons confined in an optical microcavity. They are bosonic quasi-particules with a very small effective: they offer the possibility to investigate the physics of Bose condensates in a solid state system. Polariton condensates are out of equilibrium dynamical condensates, with weak interactions mediated by their excitonic part. They have a pseudo-spin which can be optically addressed. After a general introdution to cavity polaritons, I will describe recent experiments performed on one dimensional cavities. We have generated polariton condensates which can propagate over macroscopic distances while preserving their spatial coherence. We have shown that these condensates can be optically manipulated, coupled through a controlled tunnel barrier or trapped in a controlled way. Interactions play a key role in these experiments. I will also address scattering by disorder in this one dimensional propagation as well as condensation experiments in a periodic potential. All these results open the way toward the realization of new optical circuits based on the propagation and manipulation of polariton condensates.

References :

Spontaneous formation and optical manipulation of extended polariton condensates, E. Wertz, et al., Nature Physic 6, 860 (2010).

Interactions in Confined Polariton Condensates, L. Ferrier et al., Phys. Rev. Lett. 106, 126401 (2011)

Backscattering suppression in supersonic 1D polariton condensates, D. Tanese et al., arXiv:1110.0359 (2011)

Polariton condensation in photonic molecules, M. Galbiati et al., arXiv:1109.5583 (2011)

**Lundi 7 novembre 2011 à 14h**

Salle Itzykson, IPhT Saclay

**Thierry Lévy **

(Laboratoire de Probabilités et Modèles Aléatoires, UPMC, Paris 6)

## Two-dimensional Yang-Mills measure and diffusions on unitary groups

The two-dimensional Yang-Mills measure is one of the few examples of a functional integral issued from gauge theories which can be constructed in a mathematically rigorous manner. A. Migdal had rightly identified in 1975 that this construction should involve in an essential way the heat semigroup on the structure group. This naturally raised the interest of probabilists, who are particularly fond of this semigroup and the associated diffusion, the Brownian motion. In this talk, I will discuss two distinct threads which both lead from the two-dimensional Yang-Mills measure to combinatorial objects, namely random ramified coverings on surfaces. The first thread is a beautiful duality between the unitary groups and the symmetric groups, known as the Schur-Weyl duality, which in principle allows one to translate any computation on a unitary group into a computation on a symmetric group. In 1994, D. Gross and W. Taylor interpreted this duality as a duality between the two-dimensional Yang-Mills theory and a string theory, and they exhibited wonderful formulae for the expectation of Wilson loops, the simplest of which can be proved mathematically. The second thread is a reflection on the role of the semi-group property in the construction of the Yang-Mills measure, and an extension of this construction to diffusions on the structure group which are more general than the Brownian motion. This extension builds a correspondence between a class of random fields which share the essential properties of the Yang-Mills measure, in particular a two-dimensional version of the classical Markov property -- a class of diffusions on compact groups known as Lévy processes (Paul Lévy's 125th birthday was celebrated a few weeks ago)-- and a class of almost topological quantum field theories, which act as a kind of algebraic skeleton of the corresponding random fields.

**Jeudi 6 octobre 2011 à 14h**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Elie Raphaël**

(ESPCI-Paris Tech)

## Moving at the Air-Water Interface

It is generally believed that in order to generate waves, a small object (like an insect) moving at the air-water surface must exceed the minimum phase speed of capillary-gravity waves. We show that this result is only valid for a rectilinear uniform motion, an assumption often overlooked in the literature. In the case of a steady circular motion (a situation of particular importance for the study of whirligig beetles), we demonstrate that no such velocity threshold exists and that even at small velocities a finite wave drag is experienced by the object. This wave drag originates from the emission of a spiral-like wave pattern. These results should be important for a better understanding of the propulsion of water-walking insects. For example, it would be very interesting to know if whirligig beetles can take advantage of such spirals for echolocation purposes.

**Vendredi 10 juin 2011 à 14h**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Riccardo Zecchina**

(Politecnico di Torino)

## Statistical physics approach to dynamical and structural optimization over random networks

We discuss some recent advances in static and dynamical optimization problems over networks and compare the results of statistical physics approaches with state of the art techniques. In particular, we shall discuss the common aspects between structural optimization (identification of optimal sub-structures in a given network), stochastic optimization (matching problems under uncertainty) and dynamical optimization (optimal initial conditions to control irreversible dynamical processes). All these cases correspond to root optimization/inference problems over networks which often appear jointly. They can be approached analytically in the case of random networks.

**Lundi 2 mai 2011 à 14h**

Salle Itzykson, IPhT Saclay

**A.C. Maggs**

(ESPCI, Paris)

## Statistical Mechanics with Maxwell's equations

We show how to generate the long-ranged Coulomb interaction with the help of an auxiliary ?eld evolving with constrained but local dynamics. This allows one to simulate systems containing electric charges without ever calculating the Coulomb potential or solving Poisson’s equation. Our methods require the imposition of Gauss’s law as a dynamical constraint. The dynamical system samples a constrained partition function, which leads to a new formulation of Lifshitz/Casimir forces. We show how to evaluate such interactions in complex geometries.

**Jeudi 7 avril 2011 à 14h**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Amin Coja-Oghlan**

(University of Warwick, UK)

## On belief propagation guided decimation for random k-SAT

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-constructive arguments show that F is satisfiable for clause/variable ratios m/nc.r(k)/k, for a constant c>0 independent of k.

**Lundi 7 mars 2011 à 14h**

Salle Itzykson, IPhT Saclay

**Emmanuel Fort**

(Institut Langevin, ESPCI ParisTech - Université Paris Diderot)

## A macroscopic wave-particle duality: Quantum-like behaviors in a "classical world"

We have shown recently that a droplet bouncing on a vertically vibrated liquid interface can become dynamically coupled to the surface waves it excites. It thus becomes a self-propelled "walker", a symbiotic object formed by the droplet and its associated wave. Through several experiments we will address one central question. How can a continuous and spatially extended wave have a common dynamics with a localized and discrete droplet? We will show that in all cases (diffraction, interference, tunnelling, etc…) where the wave is split, a single droplet has an apparently random response but that a deterministic behaviour is statistically recovered when the experiment is repeated. The truncation of the wave is thus shown to generate an uncertainty in the drop’s motion. Finally, in another set of experiments analogous to Landau experiments, we demonstrate that when the walker has an orbiting motion, the possible radii of the orbit are discrete. We will show how these properties result from what we call the walker's "path-memory". The limits in which these results can be compared to those at quantum scale will be discussed.

**Jeudi 10 février 2011 à 14h**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Thierry de la Rue**

(Laboratoire de Mathématiques Raphaël Salem, Université de Rouen)

## Pavages aléatoires par touillage de dominos

Le but de cet exposé est la présentation d'une variation de l'algorithme de "touillage" de dominos (traduction de "domino shuffling algorithm") originellement proposé par James Propp pour construire des pavages aléatoires du diamant aztèque. Notre algorithme est spécialement étudié pour le cas où certaines position des dominos sont interdites, ce qui permet de générer des pavages aléatoires de nombreux graphes planaires en les plongeant dans un diamant aztèque assez grand. L'exposé est basé sur un travail en collaboration avec Élise Janvresse et Yvan Velenik (The Electronic Journal of Combinatorics 13, n° 1 (2006)), et une présentation presque "grand public" est disponible sur "Images des mathématiques" : http://images.math.cnrs.fr/Pavages-aleatoires-par-touillage.html

**Lundi 10 janvier 2011 à 14h**

Salle Itzykson, IPhT Saclay

**Giulio Biroli**

(IPhT, CEA Saclay)

## The Glass Transition

When a liquid is super-cooled below the crystallisation transition, its relaxation time increases dramatically. A mere temperature decrease of one third of the crystallisation temperature makes the viscosity shoot up of fourteen, or more, orders of magnitude. The relaxation time increases so much, that eventually the liquid does not relax anymore on experimental time-scales and becomes an amorphous rigid material, called glass. This phenomenon the glass transition is common to many other systems: it emerges in soft matter and granular media at high enough density and it plays a very important role even in other branches of science, such as computer science and combinatorial optimization. The glass transition remains a conundrum yet to be fully explained and which does not seem to fit in well with the standard theory of phase transitions. Recently, there has been a lot of progress : growing dynamical correlations have been identified; it has been shown that amorphous order is developing approaching the glass transition; several new theoretical results have been obtained and new theoretical frameworks have been developed. In this talk, after an introduction to the glass transition and its multiple facets, I will present these new results.

**Jeudi 9 décembre 2010 à 15h**

Amphithéatre Jolie Curie, Bât. 100, Université Paris Sud Orsay

**Mark G. Raizen**

(Center for Nonlinear Dynamics and Department of Physics, The University of Texas, Austin, USA)

## Controlling Matter with Light

In 1871, James Clerk Maxwell proposed a thought experiment, and in 1907, Albert Einstein made a prediction. Both men concluded that the experimental realizations would be impossible. In this talk I will describe our recent work that relates to this history, and show how it has enabled new methods for controlling matter with light.

**Lundi 15 novembre 2010 à 14h**

Salle Itzykson, IPhT Saclay

**Ady Stern**

(Weizmann Institute)

## Proposed experimental probes of non-abelian anyons

I will describe the non-abelian quantum Hall effect, how its excitations become non-abelian anyons, and how they may be used for topological quantum computation. I will then focus on several proposed experiments that can serve as litmus tests for identifying non-abelian anyons. My talk will assume NO PRIOR KNOWLEDGE of any of these scary looking concepts.

**Jeudi 21 octobre 2010 à 14h**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Bernard Derrida**

(LPS -ENS Paris)

## Fluctuations de courant dans les systèmes hors d'équilibre

Cet exposé donnera une revue de résultats obtenus récemment sur les fluctuations de courant dans des systèmes diffusifs pour différentes géométries: état stationnaire hors d'équilibre maintenu par contact avec

deux réservoirs, système à l'équilibre dans une géométrie circulaire, système formé de deux sous systèmes à l'équilibre à des températures différentes et mis en contact au temps t=0. Quelques questions ouvertes

seront discutées, en particulier le comportement de systèmes mécaniques unidimensionnels.

**Lundi 6 septembre 2010 à 14h**

Salle Itzykson, IPhT Saclay

**John Cardy**

(University of Oxford)

## Entanglement Entropy in Extended Quantum Systems

Quantum critical points in extended systems, such as spin chains, are associated with singular behaviour of the quantum entanglement in the ground state between different spatial regions. One way to quantify this is through the entanglement entropy. We argue that these critical singularities have a universal form, which, in 1d, can be understood by conformal field theory and corner transfer matrix methods. These predict unusual corrections to scaling which have been observed in numerical data.

**Lundi 7 juin 2010 à 14h**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Jon Keating**

(University of Bristol, Department of Mathematics)

## Random Matrices and Number Theory

The Riemann zeta function encodes information about the primes through the positions of its zeros. These zeros are the subject of the Riemann Hypothesis. Remarkably, everything we know about them is consistent with their being distributed like the eigenvalues of random matrices. They thus exhibit the characteristics of the energy levels of complex quantum systems. This connection extends to generalizations of the zeta function and has shed new light on several long-standing problems in number theory. I shall review these ideas.

**Jeudi 20 mai 2010 à 14h**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Lev Ioffe **

(LPTMS, Rutgers University)

## Superconductor-Insulator transition driven by disorder.

I will begin by reviewing the experimental data on the superconductor-insulator transition in InO, TiN and similar films. I will argue that the transition in these materials is driven entirely by the competition of the disorder and attraction. I will discuss the solution of the simplest mathematical model that has these ingredients and show that the resulting quantum critical point has many anomalous and unexpected features. The most striking feature of the solution is that the phase formed in the vicinity of the quantum critical point becomes very non-uniform and that it is this non-uniformity that is responsible for most physical properties. I will present very recent data from STM measurements that confirm some of the predictions of the theory.

**Jeudi 8 avril 2010 à 14h**

Salle 201, Bât. 100, Université Paris Sud Orsay

**Pierre Le Doussal**

(LPTENS, Ecole Normale Supérieure Paris)

## Shocks and avalanches in disordered elastic systems

I will review the theory of functional renormalization group of disordered elastic systems, present the more recent results on static and dynamic avalanches, and discuss relevant experiments on magnetic domains and wetting.

**Jeudi 7 janvier 2010 à 14h**

Salle des conseils de l'IPN

Bât. 100, Université Paris Sud Orsay

**Philippe Flajolet**

**(**INRIA-Rocquencourt)

## Machines et Nombres de Buffon

Une expérience bien connue due à Buffon produit un procédé probabiliste continu, une sorte de "calculateur analogique", dont la probabilité de succès met en jeu le fameux nombre Pi. Est-il possible de composer des procédés probabilistes simples et discrets, fondés uniquement sur des tirages à pile ou face, pour atteindre le même résultat? Une des motivations est la réalisation de simulateurs de Boltzmann pour de grands modèles combinatoires discrets. Nous examinerons des constructions qui permettent d'atteindre des constantes telles que pi, exp(-1), log2, sqrt{3}, cos(1/4), zeta(5) et réaliser une grande variété de fonctions (exponentielles, trigonométriques, algébriques, logarithmiques, hypergéométriques, etc). On en déduira notamment des générateurs purement discrets de la loi de Poisson et de la loi logarithmique. L'un des générateurs associés au nombre Pi nécessite moins de sept tirages de pièces en moyenne et l'expérience peut être facilement réalisée par un humain. (Ce travail est joint avec Maryse Pelletier et Michèle Soria, LIP6, Paris).

** Jeudi 17 septembre 2009 à 14h**

Salle des conseils de l'IPN

Bât. 100 Université Paris sud Orsay

**Gilles GODEFROY**

(Institut de Mathématiques de Jussieu (IMJ), Paris VI)

## Les polynômes de Robinson-Matijavesic

Soit P un polynôme à coefficients entiers. A-t-il une racine entière? Si P n'a qu'une seule variable, il est facile de répondre à cette question. S'il en a plusieurs, ça l'est moins. En fait, c'est si difficile que cela peut se révéler indécidable. Nous verrons quelques-unes des idées qui ont conduit à ce théorème montré en 1970 par Julie Robinson et Yuri Matijasevic, qui pose une limite surprenante au pouvoir de décision des mathématiques, et oriente vers le concret le théorème d'incomplétude de Gödel.

**Jeudi 2 juillet 2009 à 14h **

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud Orsay

**Alexios POLYCHRONAKOS**

(City College, University of New York)

## Integrable one dimensional systems and transparent particles

Many-body one-dimensional integrable systems with exchange interactions generalizing the Calogero family have been introduced a while ago and served as the basis for obtaining extended classes of solvable spin-chain models with long-range interactions. A remarkable property of these systems is that particles entirely go through each other in scattering events without reflection. We point out that there is a large class of systems that have this property, and therefore trivially satisfy the Yang-Baxter equation. Although this does not necessarily guarantee integrability, it makes them amenable to a statistical treatment through the TBA method.

**Jeudi 7 mai 2009 à 14h**

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud Orsay

**Alain RIAZUELO**

(Institut d'Astrophysique de Paris)

## Voyage autour (et à l'intérieur) d'un trou noir

À quoi ressemblent les distorsions gravitationnelles au voisinage immédiat d'un trou noir ? Le passage de l'horizon d'un trou noir se traduit-il par un effet observable ? Quelle est la dernière image qu'il soit donné de voir à un observateur atteignant une singularité ? À quoi ressemblent un trou blanc, une singularité nue ou le passage par un trou de ver ?

Si la structure géométrique des espaces-temps contenant un trou noir a été abondamment étudiée et que leurs géodésiques ont été classifiées depuis longtemps, relativement peu de travaux se sont focalisés sur la traduction visuelle de toute la panoplie des effets relativistes produits par les trous noirs, que les moyens informatiques modernes rendent pourtant relativement aisés à simuler. Dans ce séminaire à vocation pédagogique, je présenterai quelques résultats obtenus récemment sur ce sujet, avec de nombreuses illustrations sous la forme d'animations dont l'objectif est d'allier réalisme du point de vue scientifique à un certain soucis esthétique.

**Jeudi 15 janvier 2009 à 14h**

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud ORSAY

**Paul Wiegmann**

(James Frank Institute and Enrico Fermi Institute, Department of Physics, University of Chicago)

## Critical Curves in 2D Critical Phenomena

**Jeudi 13 novembre 2008 à 14h**

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud ORSAY

**Christian Krattenthaler**

(Fakultät für Mathematik, Universität Wien)

## Exact and asymptotic enumeration of watermelons with a wall interaction

** Jeudi 18 septembre 2008 à 14h**

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud ORSAY

**Carlo Beenakker**

(Instituut-Lorentz, Leiden University)

## Shot noise in graphene

Recent measurements [1,2] of the low-temperature electrical noise in graphene have found a shot noise power which is three times smaller than the value expected for a Poisson process of independent current pulses. Two theoretical explanations are discussed, the first [3] in terms of the shot noise of evanescent modes, the second in terms of the shot noise of fractal diffusion [4].

[1] L. DiCarlo et al. Phys.Rev.Lett. 100, 156801 (2008).

[2] R. Danneau et al. Phys.Rev.Lett. 100, 196802 (2008).

[3] J. Tworzydlo et al. Phys.Rev.Lett. 96, 246802 (2006).

[4] C.W. Groth et al. Phys.Rev.Lett. 100, 176804 (2008)

**Jeudi 3 juillet 2008 à 14h**

Amphi Irène Joliot-Curie de l'IPN

Bât. 100 Université Paris Sud ORSAY

**Sriram Ramaswamy**

( Centre for Condensed-Matter Theory, Department of Physics, Indian Institute of Science Bangalore)

## Active Matter

Active particles contain internal degrees of freedom which take up energy from their surroundings and, in dissipating it, execute systematic movement. This definition obviously includes motile organisms, whether macroscopic or microscopic, cytoskeletal filaments with motors and ATP, and pumps in the cell membrane; monolayers of agitated granular rods are a less obvious example. My talk will survey our recent work on order, fluctuations and flow instabilities in this strange kind of matter.

**Jeudi 8 novembre 2007 à 14h**Salle des conseils de l'IPN Bât. 100 Université Paris Sud ORSAY

**Paul Fendley**(Theoretical Physics, University of Oxford)

## Strongly correlated fermions as frustrated magnets

I discuss a model of spinless fermions hopping on the square lattice where the repulsive interactions are tuned to give the model a supersymmetry. As a result, there is an extensive ground-state entropy (i.e. flat directions on the Fermi surface). I present substantial evidence that counting certain types of rhombus tilings yields the exact number of ground states. This behavior is akin to that of frustrated magnets, but the exact degeneracy persists in the quantum system.

**Jeudi 3 mai 2007 à 14h **

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud ORSAY

**Jean-Sébastien Caux **

(Institute for Theoretical Physics, University of Amsterdam)

## New results on the dynamics of spin chains and 1D Bose gases

Heisenberg quantum spin chains and interacting Bose gases in one dimension are two fundamental exactly solvable models of strongly- correlated physics with direct experimental relevance. Recent progresses in the theory of integrable models have opened the door to extremely accurate computations of their dynamical correlation functions, which are experimentally accessible via either inelastic neutron scattering (for spin systems) or Bragg spectroscopy (for quantum gases in optical lattices). We review these developments and their application in the description of experimental data on representative systems.

**Jeudi 1er mars 2007 à 14h**

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud ORSAY

**Konstantin Efetov**

(Ruhr-Universitat Bochum)

## Supersymmetry and low energy theory for interacting clean Fermi gas in arbitrary dimension.

We discuss a recent bosonization method developed to study clean Fermi gases with a repulsion in any dimensions. The method enables one to consider both density and spin excitations. It is demonstrated that due to a non-abelian structure of the effective supersymmetric theory, the spin excitations interact with each other, which leads to new logarithmic in temperature corrections to physical quantities. Using a renormalization group scheme constructed for the effective low energy field theory these logarithms are summed up in all orders. Temperature dependent corrections to the specific heat and spin susceptibility are obtained for all dimensions, d=1,2,3.

**Jeudi 11 mai 2006**

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud ORSAY

Première partie à 14h

**Gabriel Kotliar**

(CPHT-X, SPHT CEA Saclay, Center for Materials Theory Rutgers University)

## Strongly Correlated Electron Materials : A Dynamical Mean Field Perspective.

Strongly correlated electron materials display a remarkable set of properties, such as metal to insulator transitions in transition metal oxides and in organic materials as well as high temperature superconductivity in materials containing copper oxides layers to name a few. These interesting materials cannot be described within the standard model of solid state physics and require a new theoretical framework for describing its physical properties.

Over the last fifteen years, a new approach to the strong correlation problem, the Dynamical Mean Field Theory (DMFT) has emerged. Inspired by techniques in statistical mechanics it stresses the use of local impurity problems as reference system to describe extended strongly correlated systems.

In this talk, we will introduce the ideas of dynamical mean field theory and its cluster extensions and will illustrate them with an application to the Mott transition problem in the organics and in the copper oxides high temperature superconductors.

Après une pause café de 30 minutes

**Fabien Alet**

(LPT Toulouse)

## Interacting bosons on a lattice

In addition to the connection to the physics of Cooper pairs in high-Tc superconductors, the interest in lattice models of interacting bosons has been rejuvenated due to several recent experimental achievements, e.g. in cold atomic gases trapped on optical lattices and in solid 4He. In this talk, I will make a review of the various phases and (quantum) phase transitions we can expect for models of interacting bosons on a lattice. I will present highly-accurate numerical results obtained on such systems, and when possible discuss the relevance to experimental findings. Recent developments in the field, including supersolids on the triangular lattice and the possible existence of exotic quantum phase transitions, will also be reviewed.

**Jeudi 9 mars 2006**

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud ORSAY

Première partie à 14h

**Bernard Nienhuis**

(Institute for Theoretical Physics, Amsterdam)

## Fractal force chains in static sand piles.

Sand is only the prototypical example of a form of matter called granular. The defining distinction of granular matter from molecular matter is that it consists of grains, macroscopic particles. Each of these grains has a large number of degrees of freedom. As a result kinetic energy of the moving and interacting grains can dissipate and modestly heat the grains. Thereafter, this energy is no longer available to set grains in motion, it is lost forever, or at least for as long as we wish to keep looking. This brings us to a second defining property to distinguish granular matter from colloidal suspensions, brownian particles and aerosols. Also in the latter case, the particles are macroscopic, but thermal energy is large enough to displace the particles or even set them in motion. Or, in other words, the internal degrees of freedom of the particles are in equilibrium with their kinetics.

Within these two defining notions (macroscopic particles in athermal condition) there are still many kinds of granular matter, sand, pebbles, loose rocks, rice, sugar, fruit, candy, pills, powders etc. Also it can be viewed in many different circumstances. In fact the familiar notions of solid liquid and gas seem to apply superficially to a sand hill, a land slide and a sand storm respectively. In this lecture we will focus on solid, i.e. static, granular matter.

The density of 'solid' sand is not as uniform as a regular solid, but density fluctuations are limited. The contact forces, however, fluctuate wildly. Since the forces on each grain balance, the contact forces tend to form spatial structures known as force chains. We have discovered in simulations of two dimensional sand piles that in a well defined sense the size distribution of these force chains is scale invariant, i.e. the frequency of occurrence of a force chain varies with the number of participating grains (or forces) as a power law. The associated exponents appear to be universal: We have varied physical properties of the sandpile, such as the size distribution of the grains, the elastic nature of the material, the pressure, the regularity of the packing, the friction, and it has no effect on the value of the exponents.

Deuxième partie à 15h30

**Martin van Hecke**

(Leiden)

## Frictional Packings near Jamming

When the external pressure on packings of deformable particles is lowered towards zero, the system looses the ability to withstand additional stresses and unjams. A lot a recent work has been devoted to studying the (un)jamming of frictionless spherical particles - here the transition exhibits features akin to a 2nd order phase transition (i.e. powerlaw scaling, diverging length & time scales). We have recently explored the situation for more realistic frictional particles. In this talk I will describe the nature of the vibrational/deformation modes of such packings near the jamming point and show that only for infinite friction, criticality is restored at the jamming transition. Moreover, I will present some intruiging findings on the local contact properties for packings with either very small or very large friction.

**Lundi 6 novembre 2006 à 14h**

Salle des conseils de l'IPN

Bât. 100 Université Paris Sud ORSAY

**Fabian Essler**

(Oxford)

## Applications of integrable QFT to (quasi) one dimensional systems with spectral gaps

I discuss applications of methods of integrable quantum field theory to the calculation of zero-temperature dynamical correlation functions in (quasi) one dimensional Mott insulators and two-leg ladder systems. I then describe difficulties encountered when trying to extend these results to finite temperatures.