Influence of Dissipation on Quantum Tunneling in Macroscopic Systems

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