Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the
experimental investigation of ultracold gases made of highly magnetic atoms has …

The approach to thermal equilibrium, or thermalization, in isolated quantum systems is
among the most fundamental problems in statistical physics. Recent theoretical studies have …

We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ
spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state …

We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

We review the dynamics after quantum quenches in integrable quantum spin chains. We
give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the …

How do closed quantum many-body systems driven out of equilibrium eventually achieve
equilibration? And how do these systems thermalize, given that they comprise so many …

We overview the concept of dynamical phase transitions (DPTs) in isolated quantum
systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized …

We analyze quantum dynamics of strongly interacting, kinetically constrained many-body
systems. Motivated by recent experiments demonstrating surprising long-lived, periodic …

Isolated quantum many-body systems with integrable dynamics generically do not
thermalize when taken far from equilibrium. As one perturbs such systems away from the …

We review the imaginary time path integral approach to the quench dynamics of conformal
field theories. We show how this technique can be applied to the determination of the time …