Environment-dependent dissipation in quantum Brownian motion

TL;DR

This paper analyzes how different environmental spectra influence the energy dissipation and thermalization dynamics of a quantum Brownian particle without relying on the Markovian approximation.

Contribution

It provides analytic results linking environmental spectral types to quantum system thermalization, highlighting non-Markovian effects.

Findings

Derived energy evolution for Ohmic, sub-Ohmic, super-Ohmic environments

Established connection between environment spectrum and thermalization dynamics

Identified regimes where non-Markovian effects dominate

Abstract

The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic and super-Ohmic environments, without performing the Markovian approximation. Our results allow to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.