Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid

TL;DR

This paper investigates how nonlinear interactions in a strongly interacting one-dimensional quantum liquid lead to finite decay rates of bosonic excitations, providing a theoretical framework for thermalization with a relaxation rate scaling as T^5.

Contribution

It introduces a model that resolves divergence issues in decay rates by incorporating spectrum nonlinearity in strongly interacting Luttinger liquids.

Findings

Decay rate scales as T^5 at low energies.

Spectrum nonlinearity regularizes decay rate divergence.

Provides a theoretical description of thermalization process.

Abstract

We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is strong, and the excitation spectrum is nonlinear. Although at low energies the nonlinearity is weak, it regularizes the divergence in the decay rate. We develop a theoretical description of the approach of the system to thermal equilibrium. The typical relaxation rate scales as the fifth power of temperature.