Crossover from thermal to quantum decay

Eugene M. Chudnovsky

The decay of a metastable state is studied by means of a functional-integral approach. Depending on the shape of the potential barrier, the crossover from thermal activation to thermally assisted quantum tunneling is either a first- or second-order phase transition on temperature. Below the crossover temperature, first-order transitions between different tunneling regimes are possible. The general features of these transitions, and the possibilities to observe them, are discussed.

E. Torrontegui, Juan Gonzalo Muga, Joan Martorell +1 more

Hermann Grabert, Ulrich Weiß

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.

Gastón García‐Calderón

Gastón García‐Calderón, R. Bijker, Octavio Castaños +2 more

Alvise Verso, Joachim Ankerhold

Thermal escape out of a metastable well is considered in the weak friction regime, where the bottleneck for decay is energy diffusion, and at lower temperatures, where quantum tunneling becomes relevant. Within a systematic semiclassical formalism an extension of the classical diffusion equation is derived starting from a quantum mechanical master equation. In contrast to previous approaches finite barrier transmission also affects transition probabilities. The decay rate is obtained from the stationary nonequilibrium solution and captures the intimate interplay between thermal and quantum fluctuations above the crossover to the deep quantum regime.