Time Evolution of Tunneling in Thermal Medium -- Environment-driven Excited Tunneling --

Time evolution of tunneling phenomena proceeding in thermal medium is studied using a standard model of environment interaction. A semiclassical probability formula for the particle motion in a metastable state of one dimensional system put in thermal medium is combined with the formula of quantum penetration factor through a potential barrier, to derive the tunneling rate in medium. Effect of environment, its influence on time evolution in particular, is clarified in a 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. 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.