Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench

TL;DR

This paper develops a semiclassical framework to analyze out-of-equilibrium spin transport in quantum systems with massive quasiparticles, revealing ballistic and diffusive behaviors and the emergence of a second, slower front.

Contribution

It introduces an analytic semiclassical approach for inhomogeneous quantum quenches and explores the effects of non-trivial scattering beyond the universal limit.

Findings

Analytic expressions for spin density and current profiles.

Identification of a second, slower propagating front.

Observation of local equilibration near the second front.

Abstract

We use a semiclassical approach to study out of equilibrium dynamics and transport in quantum systems with massive quasiparticle excitations having internal quantum numbers. In the universal limit of low energy quasiparticles, the system is described in terms of a classical gas of colored hard-core particles. Starting from an inhomogeneous initial state, in this limit we give analytic expressions for the space and time dependent spin density and spin current profiles. Depending on the initial state, the spin transport is found to be ballistic or diffusive. In the ballistic case we identify a `second front' that moves more slowly than the maximal quasiparticle velocity. Our analytic results also capture the diffusive broadening of this ballistically propagating front. To go beyond the universal limit, we study the effect of non-trivial scattering processes in the $O(3)$ non-linear sigma model by performing Monte Carlo simulations, and observe local equilibration around the second front in terms of the densities of the particle species.