Out of equilibrium properties of systems with long-range interactions – LORIS

Statistical mechanics is the unique theoretical approach that allows us to investigate the macroscopic behaviour of systems composed of a large number of microscopically coupled elements. Using the tools of statistical mechanics, it is possible to accurately predict and describe the asymptotic stage of the evolution which is eventually reached for very long times, the so-called thermodynamic equilibrium. However, many interesting physical properties occur out-of-equilibrium and deserve to be carefully addressed. This is particularly true for systems subject to long-range forces, for which the pair potential decays as a power at large distances. Surprisingly, systems with long-range interactions may be trapped in quasi-stationary states, which last virtually forever and which differ from the corresponding equilibrium configuration at both the microscopic and the macroscopic level. Quasi-stationary states are self-organized macroscopic regimes that have been recently reported in many fields of broad theoretical and applied relevance (e.g. unscreened plasmas, free electron lasers, gravitational systems, two-dimensional fluids). This proposal aims at developing a coherent and comprehensive theoretical picture that should elucidate the universal mechanisms behind the formation and persistence in time of quasi-stationary states. On this general theoretical topic I will mainly collaborate with Thierry Dauxois and Freddy Bouchet, both at ENS-Lyon. Moreover, I will study the effect of external perturbations of quasi-stationary states (linear response theory, fluctuation-dissipation relations), also in collaboration with Eric Bertin of ENS-Lyon. In order to achieve this goal, theoretical approaches will be tested on toy models that have become paradigmatic for the study of long-range interactions, like the Hamiltonian Mean Field (HMF) model. Besides that, one of the test grounds for the developed theoretical approaches will be the characterization of coherent structures in 2D fluid mechanics, using as a model the 2D Navier-Stokes (NS) equation with weak stochastic forces and dissipation, which turns out to be relevant for ocean and atmosphere dynamics (here the long-range nature of the force arises because of the logarithmic decay of the Green function). On this latter topic, I will mainly collaborate with Freddy Bouchet. The characterization of Non Equilibrium Steady States (NESS) in these two paradigmatic long-range systems (HMF and NS), when forcing becomes large, will be tackled in collaboration with Eric Bertin. The involvement in the project of an experienced senior researcher, Thierry Dauxois, who has been a driving force in the development of the research on long-range interactions, and of two young researchers, Freddy Bouchet and Eric Bertin, with different specific competences (statistical mechanics of fluid flows and non equilibrium statistical mechanics, respectively) guarantees that the project will have a long-lasting impact on the research activity at the Physics Laboratory of ENS-Lyon, leading possibly to the formation of a new team working on non equilibrium properties of systems with long range interactions. This will be conjugated with an extensive teaching activity at master and doctoral level, which will form younger newcomers in this quickly developing new research field.