Timescales for thermalization, quantum chaos, and self-averaging

This chapter discusses the conditions and timescales under which isolated many-body quantum systems, initially far from equilibrium, ultimately reach thermal equilibrium. We also examine quantities that, during the relaxation process, exhibit dynamical manifestations of spectral correlations as in random matrix theory and investigate how these manifestations affect their equilibration times. We refer to systems presenting these spectral correlations as chaotic quantum systems, although the correct term to be employed, whether chaotic or ergodic quantum systems, is debatable and both have limitations.