Time evolution of tunneling phenomena proceeding in a thermal medium is studied using a standard model of environmental interaction. A semiclassical probability formula for the particle motion in a metastable state of a one-dimensional system put in a thermal medium is combined with the formula of the quantum penetration factor through a potential barrier to derive the tunneling rate in the medium. The effect of environment, its influence on time evolution in particular, is clarified in our real-time formalism. A nonlinear resonance effect is shown to enhance the tunneling rate at finite times of order $2/\eta ,$ with $\eta$ the friction coefficient unless $\eta$ is too small. In the linear approximation this effect has relevance to the parametric resonance. This effect enhances the possibility of early termination of the cosmological phase transition much prior to the typical Hubble time.

• Received 29 July 2003

DOI:https://doi.org/10.1103/PhysRevD.69.123514