From non equilibrium quantum Brownian motion to impurity dynamics in 1D quantum liquids

Impurity motion in one dimensional ultra cold quantum liquids confined in an optical trap has attracted much interest recently. As a step towards its full understanding, we construct a generating functional from which we derive the position non equilibrium correlation function of a quantum Brownian particle with general Gaussian non-factorizing initial conditions. We investigate the slow dynamics of a particle confined in a harmonic potential after a position measurement; the rapid relaxation of a particle trapped in a harmonic potential after a quantum quench realized as a sudden change in the potential parameters; and the evolution of an impurity in contact with a one dimensional bosonic quantum gas. We argue that such an impurity-Luttinger liquid system, that has been recently realized experimentally, admits a simple modeling as quantum Brownian motion in a super Ohmic bath.Comment: Published version, 23 pages, 2 figure

Critical Langevin dynamics of the O(N)-Ginzburg-Landau model with correlated noise

We use the perturbative renormalization group to study classical stochastic processes with memory. We focus on the generalized Langevin dynamics of the \phi^4 Ginzburg-Landau model with additive noise, the correlations of which are local in space but decay as a power-law with exponent \alpha in time. These correlations are assumed to be due to the coupling to an equilibrium thermal bath. We study both the equilibrium dynamics at the critical point and quenches towards it, deriving the corresponding scaling forms and the associated equilibrium and non-equilibrium critical exponents \eta, \nu, z and \theta. We show that, while the first two retain their equilibrium values independently of \alpha, the non-Markovian character of the dynamics affects the dynamic exponents (z and \theta) for \alpha < \alpha_c(D, N) where D is the spatial dimensionality, N the number of components of the order parameter, and \alpha_c(x,y) a function which we determine at second order in 4-D. We analyze the dependence of the asymptotic fluctuation-dissipation ratio on various parameters, including \alpha. We discuss the implications of our results for several physical situations

Resistive double-diffusive instability in the dead-zones of protostellar disks

We outline a novel linear instability that may arise in the dead-zones of protostellar disks, and possibly the fluid interiors of planets and protoplanets. In essence it is an axisymmetric buoyancy instability, but one that would not be present in a purely hydrodynamical gas. The necessary ingredients for growth include a negative radial entropy gradient (of any magnitude), weak magnetic fields, and efficient resistive diffusion (in comparison with thermal diffusion). The character of the instability is local, axisymmetric, and double-diffusive, and it attacks lengths much shorter than the resistive scale. Like the axisymmetric convective instability, it draws its energy from the negative radial entropy gradient; but by utilising the diffusing magnetic field, it can negate the stabilising influence of rotation. Its nonlinear saturated state, while not transporting appreciable angular momentum, could drive radial and vertical mixing, which may influence the temperature structure of the disk, dust dynamics and, potentially, planet formation.Comment: 16 pages, 5 figures. MNRAS Accepted. V2: cosmetic changes to bring in line with MNRAS versio

Transitions de phase diffusion dans des systèmes classiques et quantiques dissipatifs

Cette thèse est structurée autour de trois chapitres principaux. Dans le premier chapitre, je présente de nouveaux résultats obtenus pour la théorie S\phi^4S hors équilibre, dont la dynamique est décrite par une equation de Langevin en présence d'un bruit coloré. Les corrélations temporelles du bruit décroissent avec une loi de puissance déterminée par un certain exposant que j'appelerai SalphaS. Il s'avère qu'il y a un S\alpha_cS de transition qui dépend de la dimension SDS du système et qui sépare le plan S(\alpha, D)S en une région où la couleur du bruit modifie le comportement critique et une autre où cette couleur est non pertinente. Je discute également le comportement d'échelle des fonctions de corrélation hors équilibre. Dans le deuxième chapitre de ma thèse j'introduis un formalisme d'intégrale de chemin pour d'écrire le mouvement Brownien hors équilibre. Je présente de nouveaux résultats qui ont été obtenus pendant mon doctorat sur les fonctions de corrélation hors equilibre après une trempe quantique. La troisième partie de ma thèse est consacrée à la diffusion d'impuretés dans des liquides quantiques en une dimension, communément appelés des liquides de Luttinger. Après une introduction aux problèmes divers liés à un tel système composé d'une impureté et d'un liquide de Luttinger, je présente une nouvelle description de la dynamique de l'impureté en présence d'un piège harmonique. La densité du liquide de Luttinger non-homogène influence fortement la dynamique de l'impureté et mène à des comportements inédits. De tels systèmes physiques sont actuellement étudiés dans des expèriences d'atomes froids.This thesis is structured around three main chapters. In the first chapter I present new results which have been obtained for the out-of-equilibrium critical S\phi^4S-theory. Its dynamics are described by a Langevin equation driven by a colored noise. The temporal correlation of this noise features a power-law decrease which is governed by a certain exponent S\alphaS. It turns out that there exists a crossover S\alpha_cS which depends on the dimension SDS of the system and separates the S(\alpha, D)S-plane into a region where the color of the noise alters the critical behaviour and a region where the color is non relevant. I also discuss the scaling bahaviour of the non equilibrium correlation functions. In the second chapter I introduce a path integral formalism to describe non equilibrium quantum Brownian motion. I present the results which have been obtained during my PhD on the evolution of the non equilibrium correlation functions after a quantum quench. The third part of my thesis focuses on the impurity diffusion in one-dimensional quantum liquids which are commonly called Luttinger liquids. After an introductory part which covers the main issues related to such a system, I present a novel description of the impurity dynamics in the case where an external trapping potential is present. The non-homogeneous density profile of the Luttinger liquid then strongly influences on the impurity dynamics in a fascinating way. Such systems are currently being studied in cold atoms experiments.PARIS-BIUSJ-Biologie recherche (751052107) / SudocSudocFranceF