Non-Markovian weak coupling limit of quantum Brownian motion

TL;DR

This paper derives an analytical non-Markovian master equation for quantum Brownian motion, showing its equivalence to a harmonic oscillator in a squeezed thermal bath, which preserves positivity and links decoherence to environment interactions.

Contribution

It introduces a novel analytical solution for the non-Markovian dynamics of quantum Brownian motion under weak coupling and high temperature conditions.

Findings

Positivity of the density operator is preserved during evolution.

The non-Markovian master equation is equivalent to a harmonic oscillator in a squeezed thermal bath.

Connection established between Schrödinger cat state dynamics and environment-induced decoherence.

Abstract

We derive and solve analytically the non-Markovian master equation for harmonic quantum Brownian motion proving that, for weak system-reservoir couplings and high temperatures, it can be recast in the form of the master equation for a harmonic oscillator interacting with a squeezed thermal bath. This equivalence guarantees preservation of positivity of the density operator during the time evolution and allows one to establish a connection between the dynamics of Schr\"odinger cat states in squeezed environments and environment-induced decoherence in quantum Brownian motion.