Crossover from Thermal Hopping to Quantum Tunneling

Consider a macroscopic system rendered unstable by both thermal fluctuation and quantum tunneling. Kramer's classical theory of the rate of decay by thermal activation is extended to lower temperatures where quantum tunneling prevails. By means of a functional-integral approach, a general formula for the decay rate is derived which describes the transition between the high- and low-temperature regimes. The influence of dissipation on the decay rate is emphasized.