Leticia Cugliándolo Sorbonne Université
Statistical measures for classical integrable systems
The pertinence of a statistical description of the long-term dynamics of a macroscopic system is not ensured in general, and much less so if the system is integrable. Great interest has been recently paid to check whether such an equilibrium-like approach could be useful to describe the temporal averages of well-chosen observables in the long term evolution of closed quantum systems. On the contrary, relatively little work has been devoted to the analysis of the same issue in the context of classical macroscopic integrable systems.
In this talk I will describe one particularly simple classical integrable interacting system, the so-called Neumann model, which can be related to the spherical Sherrington-Kirkpatrick (or p=2) model of disordered systems. With techniques of classical mechanics and disordered systems the Newtonian evolution after sudden quenches can be fully elucidated; in particular, in the long-times and large N limits. In parallel, a Generalized Gibbs Ensemble measure including all conserved charges can be used to evaluate statistical averages. The relevance of the latter approach can then be favourably put to the test for parameters in all sectors of the dynamic phase diagram, thus proving an extension of conventional statistical mechanics out of equilibrium.
Video of the lecture