Thermalization of macroscopic quantum systems. Is it unavoidable?

Dynamics of quantum systems is typically a few orders of magnitude faster than the time-scales which are relevant for our everyday experience.  In particular, the relaxation times in solids with strong electronic correlations may be of the order of a few tens of femtoseconds. At longer time, quantum systems typically approach their thermal equilibrium. Thermalization may be avoided only in integrable models and, possibly, also in strongly disordered systems which are many-body localized. However, recent studies of disordered spin chains have experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization in macroscopic systems. During the talk I will discuss the basic concepts concerning thermalization in quantum systems and discuss transport in disordered chains with many-body interactions. In the case of the latter systems I will focus on the problem whether the thermalization may be completely eliminated or only slowed down.