Thermalization and Quantum Quenches

Giulio Biroli, Saclay

The understanding of thermalization phenomena and of the conditions to reach thermalization for isolated quantum systems are fundamental issues in quantum statistical mechanics. Recently, there has been a renewal of interest in these problems because of their experimental relevance for cold atomic systems. In particular, a lot of attention has been focused on the evolution of an isolated quantum system after a sudden parameter change, a so-called quantum quench. In this talk I will discuss the pre-requisites for thermalization after a quantum quench focusing on the statistical properties of the time-averaged density matrix and of the expectation values of observables in the final eigenstates. I will show that eigenstates, which are very rare compared to the typical ones sampled by the Gibbs distributions, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some finite size non-integrable systems, such as the Bose-Hubbard model.