The mobility and diffusion of a particle coupled to a Luttinger liquid

TL;DR

This paper investigates the mobility and diffusion of a particle in a one-dimensional Luttinger liquid, revealing temperature-dependent behaviors and the formation of a polarization cloud due to fermion interactions.

Contribution

It models the particle-Luttinger liquid system as an acoustic polaron, deriving explicit temperature-dependent mobility and diffusion coefficients influenced by fermion interactions.

Findings

Mobility and diffusion follow specific power laws with temperature.

A polarization cloud (soliton) forms at strong coupling.

Finite mobility exists due to residual bosonic mode scattering.

Abstract

We study the mobility of a particle coupled to a one dimensional interacting fermionic system, a Luttinger liquid. We bosonize the Luttinger liquid and find the effective interaction between the particle and the bosonic system. We show that the dynamics of this system is completely equivalent to the acoustic polaron problem where the interaction has purely electronic origin. This problem has a zero mode excitation, or soliton, in the strong coupling limit which corresponds to the formation of a polarization cloud due to the fermion-fermion interaction around the particle. We obtain that, due to the scattering of the residual bosonic modes, the soliton has a finite mobility and diffusion coefficient at finite temperatures which depend on the fermion-fermion interaction. We show that at low temperatures the mobility and the diffusion coefficient are proportional to $T^{-4}$ and $T^5$ respectively and at high temperatures the mobility vanishes as $T^{-1}$ while the diffusion increases as $T$.