INTERactions à LOngue Portée : dynamique hors équilibre, aspects non conservatifs et liens avec l'expérience – INTERLOP

Long range interactions between components of a physical system are at the origin of several peculiarities, both at equilibrium (negative specific heat, inequivalence between statistical ensembles...), and out of equilibrium (violent relaxation, Landau damping, quasi stationary states...). They play a role in many different physical fields: self gravitating systems, plasma physics, 2D fluid dynamics (vortices interact at long range), wave-particles interactions... The recognition that these a priori very different systems actually have many phenomena in common stimulated in recent years to a flurry of researches on generic long range interacting systems. These developments brought together researchers with various backgrounds, and led to significant progresses, both in equilibrium and out of equilibrium. However, many questions remain open, and the experimental connections of the developed theories are not so frequent: in this sense, the dream of a tunable tabletop galaxy remains elusive. The goal of this project is to foster new research directions in the field, when possible in connections with experiments. Starting with Lynden-Bell works in an astrophysical context in the 60's, much effort has been devoted to the understanding of the violent relaxation process and its usual result: the Quasi Stationary States. These states are usually described as stable stationary solutions of the Vlasov equation corresponding to the discrete system. First, motivated by recent numerical investigations, we will look for periodic generalizations of these well known Quasi Stationary States, which would correspond to asymptotically stable periodic solutions of the Vlasov equation. We shall also explore the possibility of glassy dynamics in some cases, before the system reaches the thermodynamic equilibrium. Second, we will focus on non conservative long range interacting systems, whereas most studies so far concentrate on the Hamiltonian case. This includes dissipative systems, with a Langevin, or a more complicated, forcing; in this case the main questions are: do the QSS survive and how to describe them' Are there out-of-equilibrium phase transitions related to the forcing' Motivated by modeling issues, we will also consider other types of non conservative systems, including forces which do not derive from a potential, or mixing position and velocity. In this situations, yet unexplored, we expect a rich out of equilibrium dynamics and new physical regimes. One of the main idea of the project is to make connections with an original experimental system: a cloud of cold atoms in a Magneto Optic Trap (MOT). MOTs were invented in the 80's, and are now very well controlled experimentally. Beyond a Langevin force and a friction, the trapped atoms experience a Coulomb like repulsion as well as a two-body attractive long range force which does not derive from a potential. Still far from the ultimate goal of a tabletop galaxy, MOTs are a potential application field for the theories on long range interacting systems, as well as a source of inspiration to develop new research directions, including for instance non conservative forces. In some parts of the project, we plan to obtain analytical and numerical results directly comparable with experiments on MOTs; we may mention here a correlation analysis (is there equivalent of a Debye length in a MOT'), or a computation of low frequency excitation of a long range interacting atomic cloud. The project team includes theoretical physicists specialists of long range interacting systems (J. Barré, F. Bouchet), an expert of self gravitating systems (B. Marcos) with a strong experience in long range forces numerical simulations, which will be crucial for the success of the project, and an experimentalist, expert in MOT physics (R. Kaiser).