Mobile impurities in integrable models

TL;DR

This paper employs a mobile impurity model to analyze elementary excitations in 1D integrable systems, expressing key interaction parameters via Bethe Ansatz solutions and showing the absence of certain inelastic scattering processes.

Contribution

It introduces a phenomenological description of mobile impurities in integrable models, linking parameters to Bethe Ansatz solutions and revealing the suppression of two-phonon scattering.

Findings

Parameters N and J expressed in terms of Bethe Ansatz

Absence of two-phonon scattering at leading order

Vanishing inelastic scattering rates for impurities

Abstract

We use a mobile impurity or depleton model to study elementary excitations in one-dimensional integrable systems. For Lieb-Liniger and bosonic Yang-Gaudin models we express two phenomenological parameters characterising renormalised inter- actions of mobile impurities with superfluid background: the number of depleted particles, $N$ and the superfluid phase drop $\pi J$ in terms of the corresponding Bethe Ansatz solution and demonstrate, in the leading order, the absence of two-phonon scattering resulting in vanishing rates of inelastic processes such as viscosity experienced by the mobile impurities