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Journal of Physics C Solid State Physics

Activated tunnelling decay of metastable states

V V Melnikov, András Sütö

Published Mar 10, 1984• 4 citations
Publisher

Abstract

The authors consider a particle in a potential well of depth U 0 and level splitting omega <
DOI
10.1088/0022-3719/17/7/005

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This chapter considers one important physical example of that kind, quantum dissipative decay of a metastable state. It demonstrates how to evaluate the quantum decay rate of a metastable state for a quantum particle in the presence of dissipation. In the presence of phase fluctuations, however, such current states become unstable and decay simply because the “particle” can escape from the local potential minimum either by thermal activation or by quantum tunneling. The chapter also considers sufficiently low temperatures in which case the decay is due to quantum tunnelling. Classical process of thermally activated decay of supercurrent in Josephson junctions was first demonstrated in 1974, and the results turned out to be in a good agreement with theoretical predictions. Later experiments allowed to quantitatively verify a number of important theoretical predictions, for example, ones concerning the effect of temperature and damping on the quantum decay rate.
The spin-bath induced decay of a quantum system out of a metastable state, which can tunnel and undergo thermal activation, is considered. The treatment is based on the c-number description of bath degrees of freedom and a canonical thermal distribution of the associated c-number variables. We show that, apart from the usual frequency prefactor and its dynamical modification in the spatial diffusion-limited regime, i.e., the Grote-Hynes factor, the rate coefficient contains two other factors. One is a quantum correction to the dynamical factor resulting from quantum transmission and reflection of the particle at the finite barrier. This term exhibits exponential rate enhancement at low temperature. The other one is a quantum corrected Arrhenius factor, which incorporates the effect of thermal saturation. At 0 K, dissipation due to tunneling multiplies the tunneling probability by a factor that gets exponentially damped by friction, implying that, at this temperature, the behavior of spin bath is almost identical to that of a harmonic bath.