Thermalization and typicality in integrable systems

M.Baldovin (CNR-ISC Rome)

The success of Statistical Mechanics in describing the equilibrium behaviour of macroscopic systems is often ascribed to the chaotic nature of the underlying microscopic dynamics, which guarantees ergodicity. In this respect, integrable systems should be regarded as pathological, since the presence of an extensive number of conserved quantities prevents the dynamics from being ergodic. Nonetheless, empirical evidence suggests that relevant macroscopic observables typically follow a good thermodynamic behavior even for this class of models.

We investigate numerically and analytically the thermalization properties of integrable systems in the classical domain. The main finding is that thermalization is typical, even when the system is prepared in far-from-equilibrium initial conditions, provided that the considered observable has a global nature and the total number of degrees of freedom is large. The reason for this behaviour lies in the dephasing of normal modes, which is responsible for an "effective" ergodicity. Our results support the scenario proposed by Khinchin to give mathematical foundations to the Statistical Mechanics of large non-interacting systems.