Quench dynamics of one-dimensional bosons in a commensurate periodic potential: A quantum kinetic equation approach

TL;DR

This paper investigates the non-equilibrium dynamics of one-dimensional bosons after a sudden quench, revealing how a periodic potential induces inelastic scattering and leads to thermalization with non-monotonic dependence on quench energy.

Contribution

It introduces a quantum kinetic equation approach to analyze boson dynamics post-quench in a periodic potential, highlighting multi-particle scattering effects and non-monotonic thermalization times.

Findings

Periodic potential causes multi-particle scattering and relaxation.

System thermalizes with a time depending non-monotonically on quench energy.

Large quenches lead to exponential approach to equilibrium.

Abstract

Results are presented for the dynamics arising due to a sudden quench of a boson interaction parameter with the simultaneous switching on of a commensurate periodic potential, the latter providing a source of non-linearity that can cause inelastic scattering. A quantum kinetic equation is derived perturbatively in the periodic potential and solved within the leading order gradient expansion. A two-particle irreducible formalism is employed to construct the stress-momentum tensor and hence the conserved energy. The dynamics is studied in detail in the phase where the boson spectrum remains gapless. The periodic potential is found to give rise to multi-particle scattering processes that relaxes the boson distribution function. At long times the system is found to thermalize with a thermalization time that depends in a non-monotonic way on the amount of energy injected into the system due to the quantum quench. This non-monotonic behavior arises due to the competing effect of an increase of phase space for scattering on the one hand, and an enhancement of the orthogonality catastrophe on the other hand as the quench amplitude is increased. The approach to equilibrium is found to be purely exponential for large quench amplitudes, and more complex for smaller quench amplitudes.