Séminaires de l’année 2011

14 décembre à 14h Nicolas Dupuis (LPTMC)
Séminaire "Fluides quantiques" du LPTMS Quanutum criticality of a Bose gas near the Mott transition
  We discuss the quantum criticality of a Bose gas near the Mott transition using a non-perturbative renormalization-group approach to the Bose-Hubbard model (bosons hopping on a lattice with an onsite repulsion). This approach reproduces the phase diagram of the model (in very good quantitative agreement with the numerically exact Quantum Monte Carlo result) and captures the two universality classes of the Mott transition. We show how the universal character of the density-driven Mott transition manifests itself in the pressure P(mu,T), a quantity which can now be measured in cold atomic gases in an optical lattice. Finally, we compare our theoretical results with recent experiments on the thermodynamics of a two-dimensional Bose gas, with or without an optical lattice.
13 décembre à 11h Vahagn Poghosyan (Université Catholique de Louvain)
  The Discrete Laplacian in the Theory of Exactly Solvable Stochastic Lattice Models
  Following the recent proposal made by [J. Bouttier et al., Phys. Rev. E 76, 041140,(2007)], we study analytically the mobility properties of a single vacancy in the close-packed dimer model on the square lattice. Using the spanning web representation, we find determinantal expressions for various observable quantities. In the limiting case of large lattices, they can be reduced to the calculation of Toeplitz determinants and minors thereof. The probability for the vacancy to be strictly jammed and other diffusion characteristics are computed exactly. Single site height probabilities in the Abelian sandpile model, and the corresponding mean height , are directly related to the probability P_{ret} that a loop-erased random walk passes through a nearest neighbour of the starting site (return probability). The exact values of these quantities on the square lattice have been conjectured, in particular = 25/8 and P_{ret} = 5/16. We provide a rigorous proof of this conjecture by using a local monomer–dimer formulation of these questions. The detailed calculations of the asymptotics of two-site corrélation functions for height variables in the two-dimensional Abelian sandpile model is presented. Combinatorial methods for the enumeration of spanning trees are used. We extend the well-known result for the corrélation \sigma_{1,1} of minimal height h_1=h_2=1 to \sigma_{1,h}=P_{1,h}-P_1P_h for height values h=2,3,4. These results confirm the dominant logarithmic behaviour \sigma_{1,h} \simeq (c_h\log r + d_h)/r^4 + {\cal O}(r^{-5}) for large r, predicted by logarithmic conformal field theory based on field identifications obtained previously. We obtain, from our lattice calculations, the explicit values for the coefficients c_h and d_h.
9 décembre à 14h30 Vladimir Gritsev (University of Fribourg)
Séminaire exceptionnel Dynamical deviation from integrability
  When classical many-body integrable system is weakly perturbed by the non-integrable perturbation, its properties remain similar to the unperturbed one, the statement known as a Kolmogorov-Arnold-Moser theorem. What happens when quantum integrable many-body system is perturbed? Recently these questions have been raised by several experiments with ultracold atomic systems. I am going to discuss our approach to deviation from integrability in quantum many-body systems. Our understanding is based on a finding that behind every quantum integrable many-body system there is an effective hidden classical one which for small deviation from integrability determines the behavior of a quantum system.
6 décembre à 11h Arul Lakshminarayan (IIT Madras)
  On the spectra of partial transposed density matrices
  The spectrum of the partial transposes of random density matrices from the measure induced by the Haar measure on pure states is studied. It is shown how a simple random matrix models predicts an observed transition from dominantly Negative Partial Transpose (NPT) phase to a dominantly Positive Partial Transpose (PPT) one. We use the theory of extreme eigenvalues of random matrices, and the Tracy-Widom distribution in particular, to find the fraction of NPT states in the critical cases. A model of coupled rotors is studied as a dynamical example. Substantial deviations from random states are found in the critical cases and form a very stringent test of the Bohigas-Giannoni-Schmit conjecture that random matrices describe fluctuation properties of quantized chaotic systems.
29 novembre à 11h Luca Peliti (Universita di Napoli)
  The fate of beneficial mutations in a range-expansion wave
  Recent theoretical and experimental studies have shown that range expansions can have severe consequences for the gene pool of the expanding population. Due to strongly enhanced genetic drift at the advancing frontier, neutral and weakly deleterious mutations can reach large frequencies in the newly colonized regions, as if they were surfing the front of the range expansion. These findings raise the question under which conditions beneficial mutations may be able to prevail at shifting range margins, thereby promoting adaptation. Here, we study, by means of individual-based simulations, wave-like range expansions in linear habitats, and show that the surfing probability of non-neutral mutations becomes substantial only when the mutation appears further than a certain distance ahead of the bulk of the wave. This characteristic distance is proportional to the inverse fitness of the mutant type, and only weakly (logarithmically) dependent on the carrying capacity. Moreover, we show that the surfing of beneficial mutations is to an excellent approximation captured by a branching process within a moving field of growth rates. In order to quantify the rate of adaptation, our results are finally used to predict, for a given mutation rate, how frequently substitutions by beneficial mutations occur at invasion fronts. Importantly, we find that small amounts of genetic drift increase the fixation rate of beneficial mutations at the advancing front, and thus should be important for adaptation during species invasions.
28 novembre à 16h Francis Corson (The Rockefeller University)
Séminaire exceptionnel Génétique, géométrie et développement
  Le développement des organismes multicellulaires repose sur des réseaux génétiques et moléculaires complexes, dont le comportement résiste à une interprétation intuitive et à une analyse systématique. La théorie des systèmes dynamiques suggère qu’il est possible de caractériser les traits essentiels de ce comportement de manière géométrique, en faisant abstraction des détails de l’architecture moléculaire sous-jacente. Le développement de la vulve du nématode C. elegans est un exemple classique de la spécification de différentes « identités cellulaires » par deux signaux moléculaires. Un modèle géométrique minimal permet d’expliquer l’effet de mutations connues affectant ces signaux, et prédit des interactions fortes et parfois contre-intuitives lorsque deux mutations sont introduites chez un même animal. En outre, il permet de distinguer des sources intrinsèques et extrinsèques de variation dans les expériences où le devenir d’une cellule diffère d’un animal à l’autre. Cette approche géométrique, qui pourrait aisément être transposée à d’autres systèmes, permet d’aborder l’étude des voies de développement et de leur évolution à l’échelle du phénotype (des caractères observables), complémentaire d’une description mécaniste à l’échelle moléculaire.
23 novembre à 14h30 Zoran Ristivojevic (ENS, Paris)
Séminaire "Fluides quantiques" du LPTMS Interacting electrons in one dimension beyond the Luttinger liquid paradigm: relaxation rates and transport
  In contrast to higher dimensional systems where pair collisions provide finite relaxation rate and lifetime, the situation in one dimension is peculiar. A one-dimensional electron gas requires three-particle collisions for finite relaxation due to constraints imposed by the conservation laws. At zero temperature the fastest relaxation is provided by the interbranch processes which enable energy exchange between counterpropagating particles. At sufficiently high temperatures the leading mechanism is due to the intrabranch scattering of comoving electrons. We derive the corresponding relaxation rates that strongly depend whether one considers screened or unscreneed Coulomb interaction. The abovementioned relaxation processes are responsible for interaction-induced modifications of electrical and thermal conductance in quantum wires. Our approach is based on the Boltzmann equation that is beyond the Luttinger-liquid theory.
22 novembre à 11h Claude Loverdo (UCLA)
  Influence des mécanismes de réplication des virus sur la dynamique évolutionnaire intra-hôte
  Les virus répliquent leurs génomes via différents mécanismes, d'où différentes distributions de mutants parmi leur progéniture. Cependant, dans les modèles d'évolution des virus, souvent seul le taux moyen de mutation est considéré. Pour déterminer quand et comment les mécanismes de réplication influent sur l'évolution virale, nous analysons le début d'une infection virale dans un hôte dans deux cas limites: quand tous les virions produits par une cellule infectée ont le même génôme, muté ou pas; et quand chaque virion porte des mutations indépendamment des autres virions. La corrélation entre mutants pour les autres mécanismes est intermédiaire entre ces deux extrêmes. En utilisant les processus de branchement, nous étudions analytiquement la probabilité que l'infection virale s'établisse quand les mutations sont létales, et dans le cas plus général de deux souches qui ont un succès reproductif différent. Pour un taux moyen de mutation donné, nous montrons qu'une lignée où les mutations sont corrélées a une probabilité de survie plus faible, mais quand elle survit, la population virale croît plus vite. Ce résultat est valable pour n'importe quelle combinaison des paramètres, mais l'effet est quantitativement significatif quand les effets stochastiques sont importants et quand les mutations sont cruciales pour la survie du virus.
16 novembre à 14h30 Patrick Cheinet (Laboratoire Aimé-Cotton)
Séminaire "Fluides quantiques" du LPTMS Studying many body physics and correlated matter with Rydberg atoms
  Cold Rydberg atoms are known for their large interaction properties thanks to long range dipole-dipole interactions. This property enables to study many-body effects and could lead to novel quantum simulations on correlated matter.
In a first part, I will present new results on a 4-body resonant energy transfer detected by the observation of a previously unpopulated Rydberg level which thus constitutes a direct signature of the 4-body process. We exploit here the occurrence of an accidental quasi-coincidence of the electric fields of two 2-body Förster resonances in Cesium excited to the n=23 Rydberg level, leading to a strong 4-body interaction. I will present our study of this 4-body interaction and further prospects to study many-body physics.
In a second part, I will present a new project to create a laser-controllable sample of Ytterbium Rydberg atoms. Ytterbium has the property to possess optical transitions suitable for all usual optical cold atoms techniques, both in the ground state and in the first ionized state. This gives the opportunity to use fluorescence or absorption imaging, optical cooling or trapping techniques on the Rydberg atom as if they were Ytterbium ions. It will enable a broad range of new quantum simulation experiments on highly correlated matter under long-range interactions. After presenting the required experimental set-up, I will develop some achievable studies like the diffusion of interacting Rydberg excitations in a randomly distributed sample, analogous to the diffusion in an amorphous solid.
15 novembre à 11h Ginestra Bianconi (Northeastern University)
  Entropy of network ensembles
  The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this talk we discuss recent works defining the Shannon entropy of a network ensemble and evaluating how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here play a crucial role for the formulation of null models of networks through maximum-entropy arguments and contribute to inference problems emerging in the field of complex networks.
8 novembre à 11h Yves Couderc (LMSC, Université Paris-Diderot)
  Quelques questions posées par l'observation d'une dualité onde-particule à échelle macroscopique
  On pense habituellement que la dualité onde-particule quantique n'a pas d'équivalent possible en physique classique. Ceci concerne aussi bien le caractère probabiliste de la mécanique quantique que la quantification même. Nous avons été amené à revisiter ces questions lorsque nous avons trouvé un système expérimental dans lequel une goutte rebondissant sur une surface liquide oscillante se couple aux ondes qu'elle émet et devient auto-propulsée. Ayant repris dans ce système des expériences telles que la diffraction en particule unique ou le confinement dans une boite, nous observons des comportements probabilistes quasi quantiques. Dans ce système les comportements statistiques résultent du chaos des trajectoires individuelles. Ce chaos est lui-même un effet de la "mémoire de chemin" contenue dans la structure du champ d'ondes. Nous montrerons qu'une autre manifestation de ces effets de mémoire est la quantification des orbites.
25 octobre à 11h Alessandro Pelizzola (Politecnico di Torino)
  An Ising-like model for the kinetics of protein mechanical unfolding
  Many features of protein folding have been shown to be described by an Ising-like model (one-dimensional, with long-range, multispin interactions) whose equilibrium thermodynamics is exactly solvable. We have generalized such a model to the problem of mechanical unfolding. The equilibrium thermodynamics is still exactly solvable, and the characteristic kinetic responses found in force ramp and force clamp experiments are well reproduced.
Unfolding and refolding pathways and intermediates can also be studied, again with good agreement with experiments. Applications to various proteins and RNA fragments will be discussed.
18 octobre à 11h Demian Levis (LPTHE, Université Pierre et Marie Curie)
  Phase ordering dynamics after a quench in 2d spin-ice
  Spin-ice materials are frustrated magnets that have the Pauling's zero temperature entropy of water ice. This type of materials provide a variety of novel states, one of the most surprising one is the emergence of de-confined magnetic monopoles as thermal excitations. We introduce a general 2d vertex model on a square lattice to study the dynamics of this kind of systems. It is a generalization of the extensively studied six and eight vertex models, which are integrable. The numerical results of the equilibrium phase diagram of our sixteen-vertex model are presented. The phases of the system and the nature of the phase transitions are radically modified by allowing defects breaking the ice-rules. Once the equilibrium phases have been identified, we study the phase ordering dynamics of 2d spin-ice following a quench from a disordered initial condition into its paramagnetic (close to a quasi long-range order), ferromagnetic and antiferromagnetic phases. We analyze the evolution of the density of topological defects and we show that these take finite density over very long periods of time in all kind of quenches. This behaviour was also found in 3d dipolar spin-ice. We identify the leading mechanisms involved in the ordering process, involving the growth of domains. We evaluate the (anisotropically) growing lengths involved in dynamical scaling.
4 octobre à 11h Leonid Pastur (ILTPE Kharkov)
  On Disordered Systems with Large Number of Orbitals, Large Hopping Radius or Large Dimension
13 septembre à 11h Etienne Bernard (LPS-ENS)
  Transition de phase des systèmes bidimensionnels : le cas des disques durs

La physique à basse dimension dévoile de nombreux comportements étonnants : fluctuations importantes, systèmes fortement corrélés bien que désordonnés, ou encore absence d'universalité au sens fort. Les solides bidimensionnels par exemple sont des cristaux orientés mais dont les positions par rapport au réseau subissent des fluctuations infinies.

Depuis la découverte de tels solides dans des simulations numériques en 1962, la nature de leur transition de phase liquide-solide n'est toujours pas connue, et notamment pour le modèle le plus simple, celui des disques durs. Deux scénarios étaient jusqu'à présent envisagés : soit une transition du premier ordre classique, discontinue, entre la phase solide et la phase liquide, soit deux transitions successives continues de type KT, avec une phase intermédiaire dite hexatique (ce qui correspond au scénario dit KTHNY).

Ce problème pourrait être résolu à l'aide de simulations de type Monte-Carlo, mais les difficultés de thermalisation de ce système fortement corrélé ont été un obstacle à leur succès. Grâce à notre nouvel algorithme "Event-chain", je montrerai que la transition liquide-solide des disques durs suit un scénario inattendu : si la transition s'effectue bien en deux étapes, et qu'une transition continue KT hexatique-solide est bien observée, la transition
hexatique-liquide est, elle, discontinue[E. P. Bernard and W. Krauth arXiv:1102.4094].
Ce résultat n'invalide pas forcément le scénario KTHNY pour d'autres modèles, il confirme l'existence de la phase hexatique, et pose une nouvelle base théorique aux expériences sur les solides bidimensionnels.

6 septembre à 11h Boris Shapiro (Technion Institute)
  Cold atoms in the presence of disorder
  The discussion will focus on three topics:
1. A disorder induced superfluid-insulator transition.2. Dynamics of cold atoms (mostly Bose-Einstein condensates, but also Fermi gases) in the presence of a random potential, and the related issue of the Anderson localization.3.Free expansion of a condensate, with an initial density modulation, and possible developments of matter wave caustics.
21 juillet à 14h30 Dingping Li (Beijing University)
  Theory of Vortex Matter of Type II superconductors
5 juillet à 11h Steve Tomsovic (Washington state University)
  Random matrix theory for underwater sound propagation
  Ocean acoustic propagation, motivated by basic ocean communication and monitoring issues, can be formulated as a wave guide with a weakly random medium generating multiple scattering. Twenty years ago, this was recognized as a quantum chaos problem, and yet random matrix theory, one pillar of quantum or wave chaos studies, has never been introduced into the subject. The modes of the wave guide provide a representation for the propagation, which in the parabolic approximation is unitary. Scattering induced by the ocean's internal waves leads to a power-law random banded unitary matrix ensemble for long-range deep ocean acoustic propagation. The ensemble has similarities, but differs, from those introduced for studying the Anderson metal-insulator transition. The resulting long-range propagation ensemble statistics agree well with those of full wave propagation using the parabolic equation.
16 juin à 11h Karyn Le Hur (Yale University)
  Entanglement and Fluctuations in Many-Body Quantum Systems

The study of quantum many-body systems has traditionally involved the analysis of ground state and excited state energies, correlation functions, and symmetry-breaking order parameters to characterize different states ofmatter. Recently, there has been great interest in using a different feature of quantum many-body systems to understand their nature, particularly at zero temperature and especially for phases of matter such astopologically ordered states where conventional order parameters are not sufficient to define the state of the system: quantum entanglement. One important challenge is to provide a better characterization of entanglementin many-body quantum systems and to find a connection between the entanglement and physical observables. In this Talk, we summarize our recent results on bipartite fluctuations in many-body quantum systems. A connectionbetween fluctuations and entanglement in many-body quantum systems such as mesoscopic systems and cold atoms is addressed.

7 juin à 11h John Dudley (Institut FEMTO-ST, Université de Franche-Comté)
  Extreme events in nature, rogue wave in optics

A central challenge in understanding extreme events in physics is to develop rigorous models linking the complex generation dynamics and the associated statistical behavior. Quantitative studies of extreme phenomena, however, are often hampered in two ways: (i) the intrinsic scarcity of the events under study and (ii) the fact that such events often appear in environments where measurements are difficult. A particular case of interest concerns the infamous oceanic rogue or freak waves that have been associated with many catastrophic maritime disasters. Studying rogue waves under controlled conditions is problematic, and the phenomenon remains a subject of intensive research.
On the other hand, there are many qualitative and quantitative links between wave propagation in optics and in hydrodynamics, because a nonlinearly-induced refractive index perturbation to an optical material behaves like a moving fluid and is described mathematically by the same propagation equation as nonlinear waves on deep water. In this context, significant experiments have been reported in optics over the last two years, where advanced measurement techniques have been used to quantify the appearance of extreme localised optical fields that have been termed "optical rogue waves". The analogy between the appearance of localized structures in optics and the rogue waves on the ocean?s surface is both intriguing and attractive, as it opens up possibilities to explore the extreme value dynamics in a convenient benchtop optical environment. The purpose of this talk will be to discuss these results that have been obtained in optics, and to consider both the similarities and the differences with oceanic rogue wave counterparts. The talk will provide suitable introduction to specialist aspects of ocean physics and optics, and will be accessible to non-specialists.

6 juin à 14h Alexander Mozeika (The Non-linearity and Complexity Research Group, Aston University, Birmingham, United Kingdom)
Séminaire exceptionnel "Systèmes complexes" Phase transitions and memory effects in the dynamics of Boolean networks
  The generating functional method is employed to investigate the dynamics of Boolean networks (BN), providing an exact result for the evolution of macroscopic order parameters. The topology of the networks studied and its constituent Boolean functions represent the system's quenched disorder and are sampled from a given distribution. The framework accommodates a variety of topologies and Boolean function distributions and can be used to study both the noisy and noiseless regimes; it enables one to calculate correlation functions at different times that are inaccessible using commonly used annealed approximation. It is also used to determine conditions for the annealed approximation to be valid, explore phases of the system under different levels of noise and obtain results for models with strong memory effects, where existing approximations break down. Links between BN and noisy Boolean formulas are identified and common results to both system types are highlighted.
31 mai à 11h Anatoly M. Kamchatnov (Russian Academy of Sciences)
  The Theory of dispersive shock waves
  Generation of solitons is a common phenomenon in nonlinear physics which has found many applications. Recently, much attention was attracted to dispersive shock waves which have been observed in experiments on evolution of Bose-Einstein condensates and other nonlinear media with strong dispersive properties. Dispersive shock waves can be considered as dense lattices of solitons or, in other words, as nonlinear modulated waves which connect two regions of smooth flows with different parameters, and in this sense dispersive shock wave replace viscous shocks well-known in physics of waves in viscous media. In this talk I will present a short introduction to the theory of dispersive shocks based on the Whitham approach to nonlinear waves modulations. Generalization of such well-known notions of the linear modulation theory as “group velocity” and “dispersive widening” of wave packets to the nonlinear case is quite nontrivial and demands development of appropriate mathematics. Without going into much details, I will illustrate the general method by simple examples and their applications to description of real phenomena.
17 mai à 11h Denis Vion ( Quantronics group, CEA-Saclay)
  La mesure en mécanique quantique des circuits électriques
  La mesure idéale en mécanique quantique est projective, non destructive (QND) et limitée quantiquement dans le sens où elle ne perturbe le système que pour en extraire de l’information utile à la mesure. Les circuits électriques quantiques à base de jonctions Josephson permettent aujourd’hui d’illustrer ces concepts et de les éclairer sous un jour nouveau : Le cas simple de la lecture d’un qubit de type transmon par réflectométrie micro-onde sur un résonateur désaccordé du qubit (lecture dite dispersive), met en jeu un premier étage de détection limitée quantiquement. Cette méthode de lecture offre de plus une preuve expérimentale du non-réalisme du monde, via la violation d’une inégalité de Bell en temps. Le cas d’une lecture plus performante en pratique mais moins bien comprise théoriquement, impliquant une physique non linéaire du résonateur de lecture, est également intéressant : une tentative d’analyse des caractères QND ou non, et limité quantiquement ou non de cette mesure sera présentée.
12 avril à 11h Nicolas Rougerie (Université de Cergy Pontoise)
  Vortex géants et cercles de vortex dans un condensat de Bose-Einstein en rotation rapide
  On étudie un condensat de Bose-Einstein en rotation dans le cadre de la théorie de Gross-Pitaevskii bi-dimensionnelle. Nous discuterons de l'existence de trois vitesses de rotation critiques marquant des transitions de phases caractérisées par des changements radicaux de la répartition des vortex dans le condensat.
En particulier nous démontrons rigoureusement l'apparition d'une phase de type vortex géant lorsque la vitesse de rotation dépasse un seuil que nous calculons et détaillons la nature de la transition de phase en montrant que l'apparition du vortex géant est précédée par une phase contenant un cercle de vortex.
29 mars à 11h Mohammad A. Rajabpour (SISSA, Trieste)
  Conformal symmetry in Non-local field theories

Non-local field theories as a method to describe the scaling limit of the long-range interacting systems are well-known for many years and they are much studied in statistical physics. The long-range spin systems and rough surfaces are just two examples from many that could be included. We show for a particular non-local free field theory that it has conformal symmetry in arbitrary dimensions. Using the local field theory counterparts of these field theories we find the Noether currents and the Ward identities of the translation, rotation and scale symmetries. The operator product expansion of the introduced energy-momentum tensor with quasi-primary fields is also investigated. We will have a close look to the rough surfeces as a physical example for our model.

22 mars à 11h Kris Van Houcke (Ghent University & UMass Amherst)
  Diagrammatic Monte Carlo for the Hubbart model, electron gas and unitary gas

Expansion in Feynman diagrams is a standard tool of quantum many-body theory. Usually, one is restricted to a few low-order diagrams. Diagrammatic Monte Carlo (DiagMC) is a new technique to perform the summation of diagrams up to high order. Contrarily to standard Monte Carlo approaches for fermions, the sign problem does not scale exponentially with the volume, but rather with the diagram order. We can thus calculate thermodynamic properties of strongly interacting fermions in the thermodynamic limit. Moreover, we use for the first time the "Bold DiagMC" method, where partial summation of classes of diagrams happens automatically by building the diagrams from fully dressed propagators, so that only skeleton diagrams need to be evaluated. We will give an introduction to the DiagMC technique, and show first unbiased results for the equation of state of three models of spin-1/2 fermions: -The Hubbard model, a key model for understanding high-temperature superconductivity -The electron gas, whose exchange-correlation energy is a basic input of density functional theory -The unitary gas, where interactions have infinite scattering length and zero range. This is not only a qualitative model for high-temperature superconductors and a semi-quantitative model for neutron matter, but also an accurate model for cold-atoms experiments at a Feshbach resonance. We use generalized "Tan relations" to treat analytically the high-momentum asymptotics.

15 mars à 11h Hajime Yoshino (University of Osaka)
  Rigidity of glasses - a cloned liquid computation of shear modulus
  We discuss a first principle approach to compute elastic properties of glasses at finite temperatures based on the cloned liquid method which combines the replica method and the liquid theory. Shear modulus of metastable solids is found to depend strongly on temperature due to a non-affine correction term which reflects fluctuation of shear stress field induced by vibrations of particles inside cages. We discuss validity of the Born's conjecture on melting of metastable solids via "rigidity catastrophe" approaching spinodal temperatures from below.
1er mars à 11h Elisabeth Agoritsas (Université de Genève)
  Temperature-induced crossovers in the static roughness of a one-dimensional interface
  Interfaces are ubiquitous in nature, and display a large variety of characteristic lengthscales and different specific microphysics, ranging from domain walls in ferromagnets or ferroelectric materials, to the spread of imbibing coffee on a napkin. However, the generic framework of the "disordered elastic systems" allows to tackle theoretically the static and dynamic properties of such interfaces, by retaining essentially two physical ingredients in competition: the elasticity of the interface and the disorder of its underlying medium, blurred by thermal fluctuations at finite temperature.We actually explored the consequences of a finite correlation length of disorder, or alternatively a finite interface width (as it is always the case in experimental systems) on the geometrical fluctuations of a static 1D interface, by computing analytically its roughness using a replica approach and a Gaussian variational method (with full replica-symmetry breaking), and then probing its different scaling regimes depending on the lenghtscale of observation.The specific case of a 1D interface is in particular of special interest both for the experimental domain walls in thin ferromagnetic films, and for the theoretical study of 1+1 directed polymers in random media, which is just one of the many statistical physics models on which the 1D interface problem can be mapped.
16 février à 14h30 Séminaire "Fluides quantiques"
  Takao Morinari (Yukawa Institute for Theoretical Physics, Kyoto University)
  Acoustic Hawking radiation in dynamically expanding Bose-Einstein condensate
  Black holes do not just absorb but radiate. This phenomenon is called Hawking radiation. After Hawking published the paper[1] on this subject in 1974, a lot of researches have been done. However, the experimental verification for real black holes is almost hopeless because the characteristic temperature of the radiation is generally much lower than that of the cosmic microwave background radiation. On the other hand, Unruh pointed out [2] that the fluid dynamics equation describing fluctuations around a supersonic flow has the same form as that describing quantum fields in a curved space-time of the Schwarzschild black hole. So there is possibility of verifying the Hawking radiation using this acoustic black hole. In this talk, I will show numerical simulation results for a dynamically expanding Bose-Einstein condensate of cold atoms. An acoustic black hole is created by changing the trap potential [3]. I will show that the radiation spectrum obeys the Planck distribution function with a characteristic temperature on the order of 0.1nK. The origin of the radiation is also discussed.
[1] S. Hawking, Nature 248, 30 (1974); Commun. Math. Phys. 43, 199 (1975).
[2] W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981).
[3] Y. Kurita, M. Kobayashi, T. Morinari, M. Tsubota, and H. Ishihara, Phys. Rev. A 79, 043616 (2009); Y. Kurita and T. Morinari, Phys. Rev. A 76, 053603 (2007).
15 février à 11h Takami Tohyama (Yukawa Institute for Theoretical Physics, Kyoto University, Japan)
  Dynamical DMRG study of one-dimensional strongly correlated systems
  Among several numerical techniques for one-dimensional (1D) strongly correlated systems, the dynamical version of the density matrix renormalization group (DMRG) is a powerful method to examine the dynamics of spin and charge in the systems. Recently we have developed the dynamical DMRG at zero and finite temperatures [1]. In my talk, I firstly introduce the newly developed dynamical DMRG. Next I will show recent applications of this method to (i) the dynamics of vector-spin chirality in a spin-1/2 zigzag XY chain [2], which is the basis of recent 1D multiferroic materials, and (ii) the charge dynamics in a 1D Holstein Hubbard model at half filling [3,4], which describes a cuprate Mott insulator Sr_2CuO_3. The two topics demonstrate effectiveness of the dynamical DMRG for 1D strongly correlated systems.
[1] S. Sota and T. Tohyama, Phys. Rev. B 78, 113101 (2008).
[2] T. Sugimoto, S. Sota, and T. Tohyama, Phys. Rev. B 82, 035437 (2010).
[3] S. Sota and T. Tohyama, Phys. Rev. B 82, 195130 (2010).
[4] H. Matsueda, T. Tohyama, and S. Maekawa, arXiv:1005.1690.
1er février à 11h Benoit Estienne (ITFA Amsterdam)
  Quasihole wavefunctions in non-Abelian fractional quantum Hall states: from conformal field theory to Calogero-Sutherland Hamiltonians
  We consider the quasihole wavefunctions of the non-abelian Read-Rezayi quantum Hall states which are given by the conformal blocks of the minimal model WA_{k?1}(k+1,k+2) of the WA_{k?1} algebra. By studying the degenerate representations of this conformal field theories, we derive a second order differential equation satisfied by a general many-quasihole wavefunction. We find a surprising duality between the differential equations fixing the electron and quasihole wavefunctions: they both satisfy a Calogero-Sutherland type equation.
We use this equation to obtain an analytic expression for the generic wavefunction with one excess flux. This analysis also applies to the more general models WA_{k?1}(k + 1, k + r) corresponding to the recently introduced Jack states.
These results hints at some novel structure about non polynomial solutions of Calogero-Sutherland Hamiltonian.
25 janvier à 11h Sylvain Capponi (Laboratoire de Physique Théorique, Université de Toulouse III)
  Entanglement and Fidelity of Quantum Spin Systems: A Valence Bond Approach

We review the use of several quantum information concepts to tackle condensed matter issues such as quantum phase transitions in magnetic systems. In particular, we propose to use the valence-bond basis, which allows to describe any singlet state, in order to get more insights on the properties of various wave-functions.

First, we introduce a new measure of entanglement - the valence-bond entanglement entropy - which we analyze on various spin models, including frustrated ones in one dimension. We make a systematic comparison to the more usual von Neumann entropy when available.

Secondly, we describe recent developments to compute fidelity between two different ground-states. When a system undergoes a quantum phase transition, the ground-state shows a change of nature, which can be monitored using this fidelity concept. We will present two Quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. We have also developed a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length.