Quantum Tunneling in Dissipative Systems at Finite Temperatures

Abstract

A quantum system which can tunnel out of a metastable state, and which interacts with an environment at temperature $T$, is considered. It is found that heat enhances the tunneling probability at $T=0$ by a factor $\mathrm{exp}[A(T)M{\ensuremath{\omega}}_{0}\frac{{q}_{0}^{2}}{\ensuremath{\hbar}}]$, where $M$ is the mass of the system, ${\ensuremath{\omega}}_{0}$ is the frequency of small oscillations about the metastable state, and ${q}_{0}$ is the tunneling distance. For an undamped system $A(T)$ is exponentially small, $A(T)\ensuremath{\propto}\mathrm{exp}(\frac{\ensuremath{-}\ensuremath{\hbar}{\ensuremath{\omega}}_{0}}{{k}_{B}T})$, whereas for a dissipative system $A(T)$ grows algebraically with temperature.