Tunneling with dissipation in open quantum systems

TL;DR

This paper derives a closed-form expression for tunneling rates in open quantum systems considering environmental dissipation, revealing how dissipation can both inhibit and facilitate tunneling depending on system parameters.

Contribution

It introduces a new analytical expression for tunneling rates in open quantum systems using path integrals, highlighting the role of dissipation.

Findings

Dissipation can prohibit tunneling in open quantum systems.

Dissipation can decrease barrier crossing for energies above the barrier.

Application to decay from metastable states demonstrates practical relevance.

Abstract

Based on the general form of the master equation for open quantum systems the tunneling is considered. Using the path integral technique a simple closed form expression for the tunneling rate through a parabolic barrier is obtained. The tunneling in the open quantum systems strongly depends on the coupling with environment. We found the cases when the dissipation prohibits tunneling through the barrier but decreases the crossing of the barrier for the energies above the barrier. As a particular application, the case of decay from the metastable state is considered.