Dissipative dynamics of a particle coupled to field via internal degrees of freedom

TL;DR

This paper investigates the non-equilibrium dissipative behavior of a particle's center of mass coupled to a quantum field via its internal degrees of freedom, using an influence functional approach to derive a quantum Langevin equation.

Contribution

It introduces a perturbative method to model the coupled dynamics of internal degrees, field, and center of mass, accounting for backaction and deriving a generalized fluctuation-dissipation relation.

Findings

Derived a second order effective action for the system

Established a generalized fluctuation-dissipation relation

Analyzed dissipation and noise from the composite environment

Abstract

We study the non-equilibrium dissipative dynamics of the center of mass of a particle coupled to a field via its internal degrees of freedom. We model the internal and external degrees of freedom of the particle as quantum harmonic oscillators in 1+1 D, with the internal oscillator coupled to a scalar quantum field at the center of mass position. Such a coupling results in a nonlinear interaction between the three pertinent degrees of freedom -- the center of mass, internal degree of freedom, and the field. It is typically assumed that the internal dynamics is decoupled from that of the center of mass owing to their disparate characteristic time scales. Here we use an influence functional approach that allows one to account for the self-consistent backaction of the different degrees of freedom on each other, including the coupled non-equilibrium dynamics of the internal degree of freedom and the field, and their influence on the dissipation and noise of the center of mass. Considering a weak nonlinear interaction term, we employ a perturbative generating functional approach to derive a second order effective action and a corresponding quantum Langevin equation describing the non-equilibrium dynamics of the center of mass. We analyze the resulting dissipation and noise arising from the field and the internal degree of freedom as a composite environment. Furthermore, we establish a generalized fluctuation-dissipation relation for the late-time dissipation and noise kernels. Our results are pertinent to open quantum systems that possess intermediary degrees of freedom between system and environment, such as in the case of optomechanical interactions.