Analytical solutions for the quantum Brownian motion of a particle during a quantum quench

TL;DR

This paper derives analytical solutions for the transient quantum Brownian motion of a particle in a harmonic potential interacting with a reservoir, providing insights into energy exchange and correlations during a quantum quench.

Contribution

It presents new analytical expressions for quantum correlations and energy dynamics of a particle undergoing Brownian motion during a quantum quench.

Findings

Derived explicit formulas for quantum correlations.

Analyzed energy conservation during the quantum quench.

Characterized transient Brownian motion in a harmonic trap.

Abstract

A particle subjected to a fluctuating force originated from its interaction with an external quantum system undergoes quantum Brownian motion. This phenomenon is investigated in detail for the case of a particle confined by a harmonic potential and allowed to interact with a reservoir modeled as a continuum of oscillators, with particular emphasis on transient effects. Assuming a linear coupling between the particle and the reservoir, canonical quantization of the system is implemented, and analytical expressions for the quantum correlations are derived. These correlations are then applied to analyze energy conservation, and the particle Brownian motion is characterized from the perspective of the energy extracted from the reservoir.