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 recent progress in understanding nearly integrable models within the framework
of generalized hydrodynamics (GHD). Integrable systems have infinitely many conserved …

The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of
a wealth of classical stochastic models. Surprisingly, KPZ universality was recently …

This review summarizes recent advances in our understanding of anomalous transport in
spin chains, viewed through the lens of integrability. Numerical advances, based on tensor …

The emergence of a special type of fluidlike behavior at large scales in one-dimensional
(1D) quantum integrable systems, theoretically predicted in OA Castro-Alvaredo et al …

We address the hydrodynamics of operator spreading in interacting integrable lattice
models. In these models, operators spread through the ballistic propagation of …

We show that hydrodynamic diffusion is generically present in many-body, one-dimensional
interacting quantum and classical integrable models. We extend the recently developed …

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

We address the nature of spin transport in the integrable XXZ spin chain, focusing on the
isotropic Heisenberg limit. We calculate the diffusion constant using a kinetic picture based …

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 …