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 $T=0$ by a factor exp[A(T)Mω₀q₀²], where M is the mass of the system, ω₀ is the frequency of small oscillations about the metastable state, and q₀ is the tunneling distance. For an undamped system $A(T)$ is exponentially small, A(T)∝exp(-ω₀kBT), whereas for a dissipative system $A(T)$ grows algebraically with temperature.