Scattering of hole excitations in a one-dimensional spinless quantum liquid

TL;DR

This paper investigates how high-energy hole excitations in one-dimensional quantum liquids scatter off thermally excited bosons, using a mobile impurity model within Luttinger liquid theory, to understand their role in system equilibration.

Contribution

It introduces a method to evaluate hole-boson scattering probabilities at arbitrary interaction strengths, extending Luttinger liquid theory to include high-energy excitations.

Findings

Derived scattering probabilities in terms of hole spectrum and fluid parameters.

Provided explicit formulas for Galilean invariant systems.

Applied results to analyze quantum liquid equilibration processes.

Abstract

Luttinger liquid theory accounts for the low energy boson excitations of one-dimensional quantum liquids, but disregards the high energy excitations. The most important high energy excitations are holes which have infinite lifetime at zero temperature. At finite temperatures they can be scattered by thermally excited bosons. We describe the interaction of the hole with the bosons by treating it as a mobile impurity in a Luttinger liquid. This approach enables us to evaluate the scattering probability at arbitrary interaction strength. In general, the result is expressed in terms of the hole spectrum, its dependence on the density and momentum of the fluid, and the parameters of the Luttinger liquid Hamiltonian. In the special case of Galilean invariant systems the scattering probability is expressed in terms of only the hole spectrum and its dependence on the fluid density. We apply our results to the problem of equilibration of one-dimensional quantum liquids.