Hydrodynamics of weak integrability breaking

TL;DR

This paper reviews recent developments in understanding how nearly integrable models transition from generalized hydrodynamics to conventional hydrodynamics when integrability is weakly broken, highlighting key theoretical approaches and open questions.

Contribution

It summarizes recent progress in incorporating small integrability breaking effects into GHD, elucidating the transition to standard hydrodynamics and identifying open research directions.

Findings

Transition from GHD to standard hydrodynamics with weak integrability breaking

Role of residual conserved quantities in thermalization

Impact of bound-state recombination on hydrodynamic behavior

Abstract

We review recent progress in understanding nearly integrable models within the framework of generalized hydrodynamics (GHD). Integrable systems have infinitely many conserved quantities and stable quasiparticle excitations: when integrability is broken, only a few residual conserved quantities survive, eventually leading to thermalization, chaotic dynamics and conventional hydrodynamics. In this review, we summarize recent efforts to take into account small integrability breaking terms, and describe the transition from GHD to standard hydrodynamics. We discuss the current state of the art, with emphasis on weakly inhomogeneous potentials, generalized Boltzmann equations and collision integrals, as well as bound-state recombination effects. We also identify important open questions for future works.