The influence of non-linear dissipation on non-equilibrium quantum tunneling processes

The influence that linear and non-linear coupling to a heat bath has on the dynamics of the tunneling of a particle out of a meta-stable state is examined. The tunneling rate is calculated using the dilute bounce gas method, for finite temperatures. The action corresponding to the bounce is evaluated with the aid of a variational method. It is found that the linear coupling to the heat bath has the effect of decreasing the characteristic cross-over temperature between the regime of thermally activated hopping and the quantum tunneling regime. The linear coupling is found to suppress the decay rate in the quantum tunneling regime, and causes energy to be dissipated. The non-linear coupling has the effect of removing the normal modes of the heat bath to higher energies, and thus reduces the effectiveness of the linear coupling, and thereby increases the tunneling rate.