Approximated center-of-mass motion for systems of interacting particles with space- and velocity-dependent friction and anharmonic potential

We study the center-of-mass motion in systems of trapped interacting particles with space- and velocity-dependent friction and anharmonic traps. Our approach, based on a dynamical ansatz assuming a fixed density profile, allows us to obtain information at once for a wide range of binary interactions and interaction strengths, at linear and nonlinear levels. Our findings are first tested on different simple models by comparison with direct numerical simulations. Then, we apply the method to characterize the motion of the center of mass of a magneto-optical trap and its dependence on the number of trapped atoms. Our predictions are compared with experiments performed on a large Rb85 magneto-optical trap.Comment: 9 pages, 8 figure

Breathing mode for systems of interacting particles

We study the breathing mode in systems of trapped interacting particles. Our approach, based on a dynamical ansatz in the first equation of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy allows us to tackle at once a wide range of power law interactions and interaction strengths, at linear and non linear levels. This both puts in a common framework various results scattered in the literature, and by widely generalizing these, emphasizes universal characters of this breathing mode. Our findings are supported by direct numerical simulations.Comment: 4 pages, 4 figure

Breathing Dynamics for Systems of Interacting Particles in the Microcanonical and Canonical Descriptions

International audienceBy means of a dynamical ansatz, we study the breathing dynamics in systems of trapped interacting particles in a unified context, including a wide range of power law interactions and interaction strengths, at linear and non linear levels. We present detailed numerical tests of the general theory, and, motivated by Magneto-Optical Traps modeling, we extend it to the case of space dependent friction and diffusion

Anisotropic long-range interaction investigated with cold atoms

In two dimensions, a system of self-gravitating particles collapses and forms a singularity in finite time below a critical temperature $T_c$. We investigate experimentally a quasi two-dimensional cloud of cold neutral atoms in interaction with two pairs of perpendicular counter-propagating quasi-resonant laser beams, in order to look for a signature of this ideal phase transition: indeed, the radiation pressure forces exerted by the laser beams can be viewed as an anisotropic, and non-potential, generalization of two-dimensional self-gravity. We first show that our experiment operates in a parameter range which should be suitable to observe the collapse transition. However, the experiment unveils only a moderate compression instead of a phase transition between the two phases. A three-dimensional numerical simulation shows that both the finite small thickness of the cloud, which induces a competition between the effective gravity force and the repulsive force due to multiple scattering, and the atomic losses due to heating in the third dimension, contribute to smearing the transition.Comment: 11 pages, 8 figures, accepted in Physical Review

Landau damping and inhomogeneous reference states

Landau damping is a fundamental phenomenon in plasma physics, which also plays an important role in astrophysics, and sometimes under different names, in fluid dynamics and other fields. Its theoretical discussion in the framework of the Vlasov equation often assumes that the reference stationary state is homoge-neous in space. However, Landau damping around an inhomogeneous reference stationary state, a natural setting in astrophysics for instance, induces new mathematical difficulties and physical phenomena. The goal of this article is provide an introduction to these problems and the questions they raise

Algebraic damping in the one-dimensional Vlasov equation

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.Comment: 26 pages, 8 figures; text slightly modified, references added, typos correcte

Effets collectifs et particules en interaction : Des systèmes à longue portée aux atomes froids

A large number of physical systems present long range interactions : self-gravitating systems, plasmas, vortex interactions... and thus share some properties. In this thesis, we have another experimental system in view: cold atoms; in that case, absorption/emission of photons create effective long range interactions. During a specific time scale, the out-of-equilibrium dynamics of a long range system is described by the Vlasov, or Vlasov-Fokker-Planck, equation. The goal here is to study the out-of-equilibrium behavior for several particles systems with long range interaction, from theoretical to experimental as well as numerical. Firstly, we study the dynamics of a system of particles close to an inhomogeneous stationary state using the Vlasov equation. We show that, while Landau damping is present for short time scales, the long time behavior is governed by a power law relaxation. We check and valid our predictions using numerical simulations for the HMF model (a prototype of long range system). Next, we consider the center-of-mass and breathing oscillations of interacting particles system. Assuming an invariant shape for the particles distribution, we obtain two equations which approximatively describe evolution of these two modes for a large number of systems (long/short range, with/without thermal bath, ...). Finally we use the previous result to explore an instability of a cloud of cold atoms in a magneto-optical trap and analyze a regime possibly analogous to a 1d self-gravitating system.Un grand nombre de systèmes physiques sont le siège d'interactions à longue portée : systèmes auto gravitants, plasmas, interactions entre vortex... et partagent de ce fait certaines propriétés. Dans cette thèse, un autre type de système expérimental est envisagé : des atomes froids ; dans ce cas, ce sont les échanges de photons qui peuvent induire des interactions effectives à longue portée. La dynamique de ces systèmes à longue portée est décrite sur une certaine échelle de temps par une équation de type Vlasov, ou Vlasov-Fokker-Planck. Le but de cette thèse est d'étudier le comportement hors équilibre de plusieurs systèmes de particules comportant en général des interactions à longue portée, d'un point de vue théorique, numérique et expérimental. Dans une première partie, nous étudions dans le cadre de l'équation de Vlasov la dynamique d'un système de particules au voisinage d'un état stationnaire inhomogène. Nous montrons que si un amortissement de type Landau apparaît aux temps courts, une relaxation vers un état stationnaire en loi de puissance domine toujours aux temps longs. Nous testons et validons ensuite nos prédictions par des simulations numériques du modèle HMF (archétype des systèmes à longue portée). Nous nous intéressons ensuite aux oscillations de respiration et du centre de masse d'un système de particules en interaction. En supposant une invariance de la forme de la distribution des particules, nous obtenons deux équations qui décrivent approximativement l'évolution de ces modes pour une grande gamme de systèmes (longue/courte portée, avec/sans thermostat, ...). Pour finir, nous présentons l'utilisation des résultats précédemment obtenus pour explorer un régime d'instabilité dans un piège magnéto-optique, et la possible existence de l'analogue d'un régime auto-gravitant 1d

Effets collectifs et particules en interaction (des systèmes à longue portée aux atomes froids)

Un grand nombre de systèmes physiques sont le siège d interactions à longue portée : systèmes autogravitants, plasmas, interactions entre vortex et partagent de ce fait certaines propriétés. Dans cette thèse, un autre type de système expérimental est envisagé : des atomes froids. Dans ce cas, ce sont les échanges de photons qui peuvent induire des interactions effectives à longue portée. La dynamique de ces systèmes à longue portée est décrite sur une échelle de temps par une équation de type Vlasov, ou Vlasov-Fokker-Planck. Le but de cette thèse est d étudier le comportement hors équilibre de plusieurs systèmes de particules comportant en général des interactions à longue portée, d un point de vue théorique, numérique et expérimental. Dans une première partie, nous étudions dans le cadre de l équation de Vlasov la dynamique d un système de particules au voisinage d un état stationnaire inhomogène. Nous montrons que si un amortissement de type Landau apparaît aux temps courts, une relaxation vers un état stationnaire en loi de puissance domine toujours aux temps longs. Nous testons et validons ensuite nos prédictions par des simulations numériques du modèle HMF (archétype des systèmes à longue portée). Nous nous intéressons ensuite aux oscillations de respiration et du centre de masse d un système de particules en interaction. En supposant une invariance de la forme de la distribution des particules, nous obtenons deux équations qui décrivent approximativement l évolution de ces modes pour une grande gamme de systèmes (longue/courte portée, avec/sans thermostat, ). Pour finir, nous présentons l utilisation des résultats précédemment obtenus pour explorer un régime d instabilité dans un piège magnéto-optique, et la possible existence de l analogue d un régime autogravitant 1d.A large number of physical systems present long range interactions : self-gravitating systems, plasmas, vortex interactions and thus share some properties. In this thesis, we have another experimental system in view : cold atoms ; in that case, absorption/emission of photons create effective long range interactions. During a specific time scale, the out-of-equilibrium dynamics of a long range system is described by the Vlasov, or Vlasov-Fokker-Planck, equation. The goal here is to study the out-of-equilibrium behaviour for several particles systems with long range interaction, theoretically, experimentally, and numerically. Firstly, we study the dynamics of a system of particles close to an inhomogeneous stationary state using the Vlasov equation. We show that, while Landau damping is present for short time scales, the long time behaviour is governed by a power law relaxation. We check and valid our predictions using numerical simulations for the HMF model (a prototype of long range system). Next, we consider the center-of-mass and breathing oscillations of interacting particles system. Assuming an invariant shape for the particles distribution, we obtain two equations which approximatively describe the evolution of these two modes for a large number of systems (long/short range, with/without thermal bath, ). Finally, we use the previous result to explore an instability of a cloud of cold atoms in a magneto-optical trap and analyze a regime possibly analogous to a 1d self-gravitating system.NICE-BU Sciences (060882101) / SudocSudocFranceF