Over the last decade impressive progress has been made in the theoretical understanding
of transport properties of clean, one-dimensional quantum lattice systems. Many physically …

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 …

Understanding the general principles underlying strongly interacting quantum states out of
equilibrium is one of the most important tasks of current theoretical physics. With …

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

We give a pedagogical introduction to the generalized hydrodynamic approach to
inhomogeneous quenches in integrable many-body quantum systems. We review recent …

We extend beyond the Euler scales the hydrodynamic theory for quantum and classical
integrable models developed in recent years, accounting for diffusive dynamics and local …

Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems
when prepared in generic inhomogeneous initial states. However, the ballistic contribution …

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-
particle systems from local to global equilibrium. In a quantum integrable system, local …

We review the non-equilibrium dynamics of many-body quantum systems after a quantum
quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We …