Quantum Tunneling in Dissipative Systems at Finite Temperatures

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 $T=0\mathrm{}$ by a factor $\exp \left[A\mathrm{}\right(T\left)M{\omega }_0\frac{q_0^2}{\hslash }\right]$, where $M$ is the mass of the system, ${\omega }_0$ is the frequency of small oscillations about the metastable state, and $q_0$ is the tunneling distance. For an undamped system $A\mathrm{}\left(T\right)\mathrm{}$ is exponentially small, $A\mathrm{}\left(T\right)\mathrm{}\propto \exp \left(\frac{-\hslash {\omega }_0}{k_{B}T}\right)$, whereas for a dissipative system $A\mathrm{}\left(T\right)\mathrm{}$ grows algebraically with temperature.