The dynamical-quantization approach to open quantum systems

TL;DR

This paper develops a dynamical-quantization framework to derive non-Markovian quantum equations for open systems, solving specific cases and exploring phenomena like quantum forces and escape rates.

Contribution

It introduces a novel dynamical-quantization approach to derive non-Markovian quantum master and Smoluchowski equations for open quantum systems.

Findings

Existence of non-equilibrium thermal quantum force in studied systems

Solutions for quantum Brownian particle in gravitational field

Analysis of escape rate over potential barrier for non-inertial Brownian particles

Abstract

On the basis of the dynamical-quantization approach to open quantum systems, we can derive a non-Markovian Caldeira-Leggett quantum master equation as well as a non-Markovian quantum Smoluchowski equation in phase space. On the one hand, we solve our Caldeira-Leggett equation for the case of a quantum Brownian particle in a gravitational field. On the other hand, we solve our quantum Smoluchowski equation for a harmonic oscillator. In both physical situations we come up with the existence of a non-equilibrium thermal quantum force. Further, as a physical application of our quantum Smoluchowski equation we take up the phenomenon of escape rate of a non-inertial Brownian particle over a potential barrier. Key-words: Quantum Brownian motion; Non-Markovian effects; Caldeira-Leggett quantum master equation; Quantum Smoluchowski equation; Quantum tunneling