Dynamics of a Mobile Impurity in a One-Dimensional Bose Liquid

TL;DR

This paper develops a microscopic theory describing how a quantum impurity moves in a one-dimensional Bose liquid, revealing temperature-dependent friction effects and special cases where friction vanishes.

Contribution

It introduces a detailed microscopic model for impurity dynamics in 1D Bose liquids, including temperature-dependent friction and the integrable case where friction is absent.

Findings

Friction scales as T^4 or T^8 at low temperatures depending on parameters.

Friction is linear in temperature at high temperatures.

In the integrable case, the impurity is transparent and friction is zero.

Abstract

We develop a microscopic theory of a quantum impurity propagating in a one-dimensional Bose liquid. As a result of scattering off thermally excited quasiparticles, the impurity experiences the friction. We find that, at low temperatures, the resulting force scales either as the fourth or the eighth power of temperature, depending on the system parameters. For temperatures higher than the chemical potential of the Bose liquid, the friction force is a linear function of temperature. Our approach enables us to find the friction force in the crossover region between the two limiting cases. In the integrable case, corresponding to the Yang-Gaudin model, the impurity becomes transparent for quasiparticles and thus the friction force is absent. Our results could be further generalized to study other kinetic phenomena.