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From Fermi-Pasta-Ulam Problem to Long-Range Interacting Systems

This talk will focus on the relaxation to equilibrium. We will discuss first an example with short-range interactions, namely the Fermi-Pasta-Ulam problem, of central importance in the theories of solitons and chaos. In the second part, we will consider similarities and differences in long-range interacting systems (gravitation, 2D hydrodynamics, charged and dipolar systems, ...) in which one might encounter ergodicity breaking and very slow relaxation to equilibrium. We will stress the importance of quasi-stationary states, described by the Vlasov equation.

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