These are notes based on lectures given at the 2021 summer school on Fundamental
Problems in Statistical Physics XV. Their purpose is to give a very brief introduction to …

Many experimentally relevant quantum spin chains are approximately integrable, and
support long-lived quasiparticle excitations. A canonical example of integrable model of …

The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of
weakly interacting solitons in the framework of Korteweg–de Vries (KdV) equation. In this …

Conventional hydrodynamics describes systems with few long-lived excitations. In one
dimension, however, many experimentally relevant systems feature a large number of long …

At large scales of space and time, the nonequilibrium dynamics of local observables in
extensive many-body systems is well described by hydrodynamics. At the Euler scale, one …

These Lecture Notes discuss the recent theoretical advances in the understanding of open
quantum many-body physics in platforms where both dissipative and coherent processes …

We consider the quantum nonequilibrium dynamics of systems where fermionic particles
coherently hop on a one-dimensional lattice and are subject to dissipative processes …

Soliton gases represent large random soliton ensembles in physical systems that display
integrable dynamics at leading order. We report hydrodynamic experiments in which we …

We revisit the exact thermodynamic description of the classical sine-Gordon field theory, a
well-known integrable model. We found that existing results in the literature based on the …

The sine-Gordon model captures the low-energy effective dynamics of a wealth of one-
dimensional quantum systems, stimulating the experimental efforts in building a versatile …