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

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.

published version

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• Hydrodynamical phase transition for domain-wall melting in the XY chain
• Non-equilibrium quantum transport in presence of a defect: the non-interacting case
• Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems
• Front dynamics in the XY chain after local excitations
• Disorder-induced Enhancement of Entanglement Growth in One Dimension: Information Leakage at the scale of localization length
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Thermodynamic Bethe Ansatz and Generalised Hydrodynamics in the sine-Gordon model
• Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory
• Inhomogeneous quantum quenches in the sine-Gordon theory