Dynamical quantization of the non-Markovian Smoluchowski equation and the quantum tunneling phenomenon

TL;DR

This paper derives a non-Markovian quantum Smoluchowski equation for a harmonic oscillator in a thermal environment and investigates quantum tunneling, revealing potential non-dissipative tunneling at low temperatures and non-exponential decay of escape rates.

Contribution

It introduces a dynamical quantization approach to non-Markovian quantum Brownian motion and analyzes quantum tunneling phenomena in this framework.

Findings

Quantum Kramers rate may be independent of friction in strong damping.

Possible existence of non-dissipative quantum tunneling at low temperatures.

Quantum escape rate exhibits non-exponential decay near dissipation-fluctuation breakdown.

Abstract

Based on the dynamical quantization method we derive a quantum phase-space non-Markovian Smoluchowski equation describing the non-inertial Brownian motion of a harmonic oscillator immersed in a generic environment. In the long-time regime we investigate the tunneling phenomenon by evaluating the quantum Kramers escape rate of a Brownian particle over a potential barrier. As far as a quantum thermal reservoir is concerned, it is found that our steady quantum Kramers rate may depend upon no friction constant in the strong friction domain. This preposterous feature may suggest the existence of non-dissipative quantum tunneling at the low-temperature range, including the zero temperature case. Lastly, we predict that our quantum escape rate non-exponentially decays on the edge of the breakdown of the dissipation-fluctuation relation.