From non equilibrium quantum Brownian motion to impurity dynamics in 1D quantum liquids

TL;DR

This paper develops a theoretical framework to analyze impurity dynamics in 1D quantum liquids, connecting quantum Brownian motion with experimental impurity-Luttinger liquid systems, and deriving correlation functions under various conditions.

Contribution

It introduces a generating functional for non-equilibrium correlation functions of quantum Brownian particles with Gaussian initial states, applied to impurity dynamics in 1D quantum liquids.

Findings

Derived a general non-equilibrium correlation function for quantum Brownian particles.

Modeled impurity-Luttinger liquid systems as quantum Brownian motion in a super-Ohmic bath.

Demonstrated the framework's applicability to various dynamical scenarios in 1D quantum liquids.

Abstract

Impurity motion in one dimensional ultra cold quantum liquids confined in an optical trap has attracted much interest recently. As a step towards its full understanding, we construct a generating functional from which we derive the position non equilibrium correlation function of a quantum Brownian particle with general Gaussian non-factorizing initial conditions. We investigate the slow dynamics of a particle confined in a harmonic potential after a position measurement; the rapid relaxation of a particle trapped in a harmonic potential after a quantum quench realized as a sudden change in the potential parameters; and the evolution of an impurity in contact with a one dimensional bosonic quantum gas. We argue that such an impurity-Luttinger liquid system, that has been recently realized experimentally, admits a simple modeling as quantum Brownian motion in a super Ohmic bath.