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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 expA (T) M₀q₀^{2}, where M is the mass of the system, ₀ 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) (-{₀}{k₁T}), whereas for a dissipative system A (T) grows algebraically with temperature.
Grabert et al. (Mon,) studied this question.