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, is considered. By only assuming that the environment response is linear, it is found that dissipation multiplies the tunneling probability by the factor exp[-A(q)2], where q is the "distance under the barrier" and A is a numerical factor which is generally of order unity.