Crossover from generalized to conventional hydrodynamics in nearly integrable systems under relaxation time approximation

TL;DR

This paper investigates how nearly integrable systems transition from generalized hydrodynamics to conventional Navier-Stokes hydrodynamics using a simplified collision operator, identifying key scales and observable signatures of this crossover.

Contribution

It introduces a relaxation time approximation for the collision term in GHD, providing explicit transport coefficients and analyzing the crossover to NS hydrodynamics.

Findings

Explicit computation of transport coefficients in the relaxation time approximation

Identification of characteristic scales for GHD to NS transition

Demonstration of crossover effects in charge density dynamics and two-point functions

Abstract

Upon breaking the integrability, the equations of generalized hydrodynamics (GHD) are supplemented by a Boltzmann collision term. Such terms are typically complicated and stem from a perturbative treatment of integrability-breaking terms in the hamiltonian. In our work, we study a simplified version of the collision operator in a form of relaxation time approximation familiar from kinetic theory. We explicitly compute transport coefficients which characterize the Navier-Stokes (NS) hydrodynamic regime emerging at large space-time scales. We also thoroughly study the crossover between GHD and NS hydrodynamic descriptions, identifying relevant characteristic space-time scales for the transition. In particular, we show how the emergence of NS hydrodynamics is visible in dynamics of conserved and non-conserved charge densities, and in hydrodynamic two-point functions.