Influence of Dissipation on Quantum Tunneling in Macroscopic Systems

A quantum system which can tunnel, at $T=0$, out of a metastable state and whose interaction with its environment is adequately described in the classically accessible region by a phenomenological friction coefficient $\ensuremath{\eta}$, is considered. By only assuming that the environment response is linear, it is found that dissipation multiplies the tunneling probability by the factor $\mathrm{exp}[\ensuremath{-}\frac{A\ensuremath{\eta}{(\ensuremath{\Delta}q)}^{2}}{\ensuremath{\hbar}}]$, where $\ensuremath{\Delta}q$ is the "distance under the barrier" and $A$ is a numerical factor which is generally of order unity.

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