Quantum Brownian Motion in a Bath of Parametric Oscillators: A model for system-field interactions

TL;DR

This paper models quantum Brownian motion with a bath of time-dependent oscillators, deriving influence functionals and master equations that connect quantum field effects like decoherence and particle creation to statistical mechanics, with applications in cosmology and quantum optics.

Contribution

It introduces a novel approach to derive influence functionals for a system coupled to a parametric oscillator bath, linking quantum field phenomena to statistical processes.

Findings

Derived influence functional in terms of Bogolubov coefficients

Connected vacuum fluctuations to decoherence and dissipation

Provided exact evolution operator and master equation for the system

Abstract

The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes like decoherence, dissipation, particle creation, noise and fluctuation. We treat the case where the Brownian particle is coupled linearly to a bath of time dependent quadratic oscillators. While the bath mimics a scalar field, the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode or the scale factor of the universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients. This method enables one to trace the source of statistical processes like decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origin of quantum noise and thermal radiance from black holes and from uniformly- accelerated observers in Minkowski space as well as from the de Sitter universe discovered by Hawking, Unruh and Gibbons-Hawking. We also derive the exact evolution operator and master equation for the reduced density matrix of the system interacting with a parametric oscillator bath in an initial squeezed thermal state. These results are useful for decoherence and backreaction studies for systems and processes of interest in semiclassical cosmology and gravity. Our model and results are also expected to be useful for related problems in quantum optics. %\pacs {05.40.+j,03.65.Sq,98.80.Cq,97.60.Lf}