Séminaires de l’année 2003

18 dec. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Ignacio Cirac (Max Planck Inst. Munich)
Quantum Information Processing. Implementation to physical systems
17 dec. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Olivier Brodier (C.B.P.F. Rio de Janeiro)
Symplectic evolution of Wigner functions in Markovian open systems
The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a nonhamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyse the consequences of this in the three generic cases of elliptic, hyperbolic and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distriibution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of the linear entropy. We finally discuss the possibility of recovering the initial state.
16 dec. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Ignacio Cirac (Max Planck Inst. Munich)
Quantum Information Processing. General Introduction. Theoretical aspects.
9 dec. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Christophe Mora (LPT ENS)
Phases de Fulde-Ferrell-Larkin-Ovchinnikov dans les supraconducteurs et dans les gaz d'atomes froids fermioniques
Nous considérerons dans cet exposé une simple extension de la fameuse théorie BCS des supraconducteurs où l'on s'autorise des potentiels chimiques différents pour les deux états de spin de l'électron. En plus de décrire la physique de nombreux supraconducteurs, la théorie BCS peut aussi s'appliquer, sous certaines conditions, à la description de l'état superfluide pour les nouveaux systèmes expérimentaux que sont les gaz d'atomes froids fermioniques. Dans notre discussion de la réaction du système à un déséquilibre des potentiels chimiques, nous verrons apparaître naturellement les phases de Fulde-Ferrell-Larkin-Ovchinnikov, ou phases FFLO, qui correspondent à un paramètre d'ordre inhomogène, c'est-à-dire qu'elles brisent la symétrie d'invariance par translation. Après une introduction détaillée de la théorie BCS et des phases FFLO, nous présenterons nos résultats récents sur la description de ces phases. On décrira notamment à 2D une cascade d'une infinité de transitions à basse température et nous montrerons à 3D une méthode que nous avons mise au point pour étudier numériquement la compétition entre différentes formes du paramètre d'ordre.
2 dec. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Sébastien Camalet (ENS Lyon)
Transport quantique en présence d'un champ oscillant
Pour étudier le transport cohérent à travers un système mésocopique soumis à un champ oscillant, nous avons utilisé une approche de Floquet généralisée. Nous avons ainsi obtenu les premières expressions explicites du courant moyen et de la composante à fréquence nulle du spectre de puissance des fluctuations de courant. Je présenterai ces expressions et l'approche utilisée pour les obtenir. Nous avons montré que le courant moyen et le bruit à fréquence nulle peuvent être supprimés en appliquant un champ bien choisi au conducteur. En effet, il existe un régime de hautes fréquences, que je présenterai, dans lequel le transport peut être décrit à l'aide d'un conducteur statique effectif dont les couplages tunnel internes dépendent des paramètres du champ oscillant appliqué.
25 nov. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Jean-Michel Maillet ( ENS Lyon)
Fonctions de corrélation des modèles intégrables quantiques: progrès récents
Après une revue rapide du problème du calcul des fonctions de corrélation des modèles intégrables quantiques, je présenterai les résultats récents obtenus pour la chaine de spin-1/2 XXZ. La méthode utilisée s'appuie sur l'Ansatz de Bethe algébrique et la résolution dans ce cadre du problème inverse quantique. Elle permet d'obtenir des représentations sous forme d'intégrales multiples de toutes les fonctions de corrélations de la chaine de spin-1/2 XXZ. Je discuterai dans ce contexte le comportement asymptotique de ces fonctions de corrélations et donnerai plusieurs résultats explicites.
18 nov. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Achim Richter (Darmstadt University of Technology)
Spectral Properties of Billiards and Nuclei: Elementary Nuclear Dipole Excitations and Isospin Symmetry Breaking
12 nov. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Alexander Fetter (Stanford)
Annular Structures in rapidly Rotating Bose-Einstein Condensates
Rotating superfluids are interesting largely because they cannot achieve the uniform vorticity that is associated with a classical fluid in solid-body rotation. In a rotating annular container, for example, superfluid He-4 makes a transition from irrotational flow around the inner boundary (a giant vortex) to a one-dimensional array of quantized vortices as the angular velocity increases; experiments confirm this predicted behavior in considerable detail. For Bose-Einstein condensates in harmonic traps, the radial trap frequency sets an upper bound on the allowed rotation speed. An anharmonic trap allows greater rotation speeds, and the condensate eventually acquires an annular shape. For still larger angular velocity, the system makes a transition to a giant vortex, which now occurs in the opposite order to that in superfluid He-4. Even in harmonic traps, annular condensates can be created metastably, and they are observed to exhibit core oscillations. This dynamical behavior is modeled with variational trial functions.
21 oct. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Paul Zinn-Justin (LPTMS)
Gravité Lorentzienne 3D et Modèle de Matrices ABAB
21 oct. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Stéphane Ouvry (LPTMS)
Famille d'intégrales multiples et leur relation a zeta (impair)
21 oct. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Patricio Leboeuf (LPTMS)
Résonances de Ruelle-Pollicott, orbites périodiques, zeta dynamiques
14 oct. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Grégoire Misguich (SPht CEA Saclay)
Quantum dimer models on the kagome lattice
Quantum dimer models (QDM) were introduced by Rokhsar and Kivelson (1988) in the context of the resonating valence bond theories for the high-temperature superconductors, and are expected to describe the dynamics of singlets bonds in quantum disordered spin 1/2 antiferromagnets. They can describe at least two generic phases: the valence-bond crystals, with long range dimer-dimer correlations and dimer liquids with no broken symmetry. The later have attracted a lot of interest because they display both fractional excitations (spinons and visons) and topological order. The first realization of a dimer liquid in a microscopic model was found recently by Moessner and Sondhi (2001) in a triangular-lattice QDM. In this talk, we present the first completely solvable QDM {GM,Serban and Pasquier, Phys. Rev. Lett. 89, 137202 (2002)} Using the special properties of the underlying lattice (kagome is a lattice made by corner sharing triangles) the ground-state as well as all the excited states wave-functions are determined exactly. It allows to investigate the interplay between topology, ground-state degeneracy, Z_2 gauge theory and particle de-confinement in a simple way. A second QDM on the kagome lattice with an extensive ground-state degeneracy will be briefly presented { GM, Serban and Pasquier, Phys. Rev. B 67, 214413 (2003)}. This second model may have some relation with the physics of the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice.
7 oct. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Christophe Texier (LPTMS)
Weak localization in networks of diffusive wires
The transport properties of a phase coherent network of quasi one-dimensional diffusive wires can be described by a conductance matrix. At a classical level, the network is equivalent to a classical resistance network. Additionally, there exists a small correction coming from the quantum interferences: the weak localization correction. This question has been first addressed theoretically by Doucot & Rammal {Phys. Rev. Lett. 55 (1985) 1148} to describe quantitatively experiments demonstrating Altshuler, Aronov, Spivak oscillations in networks. This approach has been later made more efficient by Pascaud & Montambaux {Phys. Rev. Lett. 82 (1999) 4512}. However, in these two works, the cooperon is integrated uniformly over the network, which does not take into account the nontrivial weights that should be given to the different wires of the network when integrating the cooperon. We show that it may be important for networks whose wires are not all equivalent and provide a formalism allowing a systematic calculation of the weak localization correction to the conductances of networks.
3 oct. 2003 à 11h00 LPTMS-Bât.100-ORSAY
Italo Guarneri ( University of Como, Italy)
Cold atoms optics, arithmetics, and complex poles
A theory developed by Fishman, Rebuzzini and IG has explained the quantum accelerator modes observed in experiments with kicked cold atoms in terms of classical transporting islands. IFurther, recent analysis has shown that the genesis of such islands follows a Farey ordering. The quantal counterpart of the islands are complex eigenvalues of the evolution operator, which appear when the operator is hosted in a different functional space than Hilbert's.
30 sept. 2003 à 15h00 LPTMS-Bât.100-ORSAY
Jané Kondev ( Brandeis university)
Mechanics of DNA packaging in viruses
Viruses self-assemble inside the host cell which they have infected. An important part of the self-assembly process is the packaging of the viral genome, which is tens of microns long, into the viral capsid, a protein shell only thirty or so nanometers in diameter. In some bacterial viruses this amazing feat is accomplished with the assistance of a protein machine, the portal motor, which, recent experiments have shown, is capable of producing forces in excess of 50pN. In this talk I will review the physics and biology of DNA packaging in viruses, and present a theorical model which accounts for the measured forces and provides quantitative predictions for new experiments.
23 sept. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Dimitri S. Petrov (FOM Institute Amsterdam)
Strongly interacting two-component Fermi gas
Recent success in cooling two-component atomic Fermi gases to well below the temperature of quantum degeneracy stimulaled a search for superfluid transition in this system. These gases are very cold and dilute, and for an attractive intercomponent interaction (negative s-wave scattering length a) the most efficient should be the superfluid s-wave pairing between atoms of different components. However, the superfluid BCS transition temperature T_c, being exponentially small compared to the Fermi temperature T_F, is beyond experimental reach for ordinary comparatively small values of the scatteringlength. Large negative or positive values of the scattering lengthare achieved by using Feshbach resonances providing a strong coupling between (zero-energy) continuum states of colliding atoms and a weakly bound molecular state of another hyperfine domain. We are especially interested in the case in which the scattering length is positive and the formation of weakly bound dimers of two different fermions is energetically favorable. One then has a weakly interacting gas of these composite bosons and encounters the problem of their Bose-Einstein condensation (BEC). The BEC regime of the bosonic dimers is interesting from a fundamental point of view as it couples the problem of superfluidity in Fermi gases to the problem of molecular condensates. We investigate the stability of the gas of dimers with regard to elastic dimer-dimer interactions, and the decay of the gas due to relaxation of the dimers to lower bound states. For that we solve the three and four-body problems for fermions. Our findings lead to a positive intermolecular scattering length, which means that the interaction between weakly bound dimers is repulsive and their Bose-Einstein condensate will be stable with respect to collapse. We show that the relaxation of the weakly bound dimers to deep bound states is much slower compared to the case of bosons. We conclude that due to fermionic correlations one has a rather stable gas of diatomic molecules in the highest rovibrational state, and, therefore, there is a potential opportunity to achieve and maintain BEC in this system.
16 sept. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Antonio Garcia (LPTMS)
Search for the Anderson transition in quantum chaos and chromodynamics
The QCD Dirac operator is modeled as a chiral banded matrix model with power law decay. Agreement between this model and a full instanton liquid simulation is observed at all scales. At finite temperature it is argued that the spectral correlations od the QCD Dirac operator resemble those of a system at an Anderson transition. In the second part of the talk I discuss quantum effects of classical intermittency. I present closed expressions for the spectral correlations in the semiclassical limit. It is shown that the spectral correlations associated with classical 1/f noise are similar to those of an Anderson transition. Finally I remark that in the context of Hamiltonian systems classical intermittency is related to the presence of cantori in the classical phase space.
9 sept. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Dibyendu Das (University of Wisconsin, Madison, USA)
Two dimensional loop models in a staggered field
We have studied the critical properties of the two-dimensional O(n) model on hexagonal lattice, subjected to a staggered field. As a function of the latter new parameter, the model exhibits new critical points distinct from the original loop model on the hewagonal lattice. We have also studied compact loops on triangular lattice with constraints; using staggered fields, various loop models of the latter type can be constructed with different integer central charges.
24 juin 2003 à 14h30 LPTMS-Bât.100-ORSAY
Baha Balantekin (University of Wisconsin, Madison, USA)
Exactly solvable shape-invariant systems, Gaudin algebras, and pairing problems
Supersymmetric quantum mechanics is the study of pairs of Hamiltonians with identical energy spectra and with eigenstates that are different, but can be transformed into each other. Some, but not all; such pairs of Hamiltonians share an integrability condition called shape-invariance. An algebraic approach to shape-invariance is presented.In a parallel development Gaudin developed an approach to solve many-body spin Hamiltonians. Gaudin model can also be formulated algebraically. In this talk relationship between Gaudin's methods, algebraic methods developed to search for quasi-exactly solvable models and supersymmetric quantum mechanics will be explored.
20 juin 2003 à 11h30 LPTMS-Bât.100-ORSAY
Vito Latora ( Universita di Catania, ITALY)
Efficient Behavior of Small-World Networks
We introduce the concept of efficiency of a network, measuring how efficiently it exchanges information. Using this simple measure, we give a new unifying definition of small-world networks, as systems that are both globally and locally efficient. This allows to give a clear physical meaning to the concept of small-world, and also to perform a precise quantitative analysis of the system. We analyze different neural networks and man-made transportation systems: besides showing the subtle quantitative differences we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency.
17 juin 2003 à 14h30 LPTMS-Bât.100-ORSAY
Gleb Oshanin (LPTL Paris 6)
Stochastic and many-particle aspects of transport and reactions in inhomogeneous media
In this talk we overview recent research on the stochastic and many-particle aspects of transport and reactive phenomena taking place in inhomogeneous media. A special emphasis will be put on the fluctuation-induced kinetics of chemical reactions involving species which perform random transport. We demonstrate that here essential departures from the conventional mean-field behavior emerge, as exemplified, in particular, by anomalous power-law kinetic behavior in reversible reactions and by the breakdown of chemical equilibrium concept. We consider, as well, several models of transport in disordered systems and discuss the collective phenomena emerging during spreading of monolayers on solid surfaces. Finally, we address the question of the properties characterizing tracer diffusion in lattice gases and verify the fundamental Einstein relation between the tracer mobility and the diffusivity.
1er avril 2003 à 14h30 LPTMS-Bât.100-ORSAY
Thierry Jolicoeur (ENS Paris)
Effet Hall quantique fractionnaire dans les gaz de bose pièges en rotation
Il est possible de mettre en rotation les condensats de Bose d'atomes ultra-froids. Lorsque la force centrifuge compense la force de rappel harmonique du piège, les bosons ne subissent plus que la force de Coriolis qui est analogue à la force de Lorentz d'un champ magnétique fictif. Si les bosons vivent dans une galette quasi-bidimensionnelle du à un fort piègeage selon la direction perpendiculaire, il est possible d'observer l'effet Hall quantique fractionnaire des bosons. A fort remplissage du niveau de landau le plus bas la rotation conduit à la formation du reseau d'Abrikosov. Celui-ci peut (théoriquement) fondre en un liquide incompressible de Hall à faible remplissage. Nous montrons par des arguments spectroscopiques et des diagonalisations exactes la présence de la série principale de fractions n/n +- 1 et l'appariement des fermions composites lorsqu'il y a un quantum de vorticite par boson. Nous donnons des valeurs approchées des gaps des excitations neutres et chargées pour les fractions nu =1/2 (l'état de Laughlin pour les bosons) ainsi que nu =2/3 et nu =1 ou nu est le remplissage du niveau de landau le plus bas.
25 mars 2003 à 14h30 LPTMS-Bât.100-ORSAY
Carlos Lobo (LKB, ENS Paris)
Vortex Lattice Formation in Bose-Einstein Condensates
The nonlinear Schrodinger equation can simulate the formation of a vortex lattice in a superfluid. Starting from the experimental procedure used recently by the LKB (ENS) team I will show that the turbulent dynamics of the field produces an effective dissipation that allows for the lattice to be formed. At T=0 this process can be triggered by a dynamical instability of the condensate. At finite temperatures turbulence is present from the beginning of the simulation. These two regimes have a very different vortex dynamics and phenomenology.
18 mars 2003 à 14h30 LPTMS-Bât.100-ORSAY
Stefano Bettelli (Univ. Paul Sabatier, Toulouse)
The simulation of chaotic quantum maps on quantum computers: entanglement and decoherence
The field of quantum computing studies the possibility of solving computational problems faster than with the classical Turing machine model. Although there is already a number of theoretical results for ideal (noiseless) quantum computers which prove the superiority of the quantum computational model over the classical one, no scalable quantum computer has been built so far, and the technological and (maybe) fundamental problems concerning their design indicate that in the foreseeable future the quantum computer community will not have access to devices with a memory larger than 10-15 qubits (the quantum "equivalent" of a bit). It is therefore interesting to try to design and study quantum algorithms with very limited memory requirements, which can however be used as a test-ground for error correction strategies. In this context, the quantum algorithms for the simulation of chaotic maps are ideal candidates, because they satisfy the previous requirement and have the ability to investigate non-trivial physics. In this talk, after a brief introduction to the quantum computational model and to the general approach for chaotic algorithms, a recent study about the links between the entangle- ment in the quantum computer memory and the properties of the underlying chaotic map will be illustrated (quant-ph/0301086).
11 mars 2003 à 14h30 LPTMS-Bât.100-ORSAY
Isabelle Bouchoule (Institut d'Optique, Orsay)
Fluctuations de phases introduites par les interactions dans un "laser a atomes" guide
Recent progress on micro-fabricated magnetic guides for atoms are stimulating efforts to realize high precision guided-atom interferometers. Phase coherence is a crucial property of such interferometers, and it may be affected by interactions between atoms. In this paper, we determine the magnitude of phase fluctuations caused by atom-atom interaction in a one-dimensional beam of bosonic atoms. In our model the beam is created with a large coherence length, and that interactions only act in a limited section of the beam. Using the Bogolioubov theory, we determine the magnitude and correlation length of the ensuing phase fluctuations in the beam after the interaction zone.
25 fev. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Andrea Pagnani (LPTMS)
Universality in 2 dimensional spin glasses
25 fev. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Jesper-Lykke Jacobsen (LPTMS)
Théories conformes parafermioniques basées sur des algèbres de Lie
25 fev. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Eugène Bogomolny (LPTMS)
Matrices de distance et plongements isométriques
28 janv. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Istvan Daruka
Grain Boundary De-faceting: A First Order Phase Transition by Atomic Shuffle
A multiscale theory of a grain boundary de-faceting phase transition in aluminum has been developed. At an atomic scale, molecular dynamics (MD) calculations revealed that the grain boundary can move only by a concerted shuffle of several atoms. This elementary excitation allowed rapid motion and equilibration of the grain boundary. The atomic understanding of the grain boundary motion then was mapped onto a simple lattice model which exhibited a first order phase transition. The results provide a detailed understanding of an experimentally observed grain boundary de-faceting transition including a statistical mechanical description.
21 janv. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Dimitri Gangardt ( LKB ENS )
Propriétés de correlations des gaz de Bose unidimensionnels
The model of bosons interacting via delta-like potential in one spatial dimension is relevant to the current experiments with cold gases. Being one of the first examples exactly soluble by using the Bethe Ansatz, this model exhibit interesting behaviour which, in particular, manifest itself in strong (beyond the mean field) correlations, as the strength of interaction increases. In this seminar, we discuss various correlation properties of one-dimensional bosons and concentrate on the new results for the local density correlations which are crucial for the decay rates of 1D Bose gases.
14 janv. 2003 à 14h30 LPTMS-Bât.100-ORSAY
Vladimir Korepin ( YITP Stony Brook )
Correlations in XXX Heisenberg spin chain and Riemann zeta function.