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Physical Review A

Phase transitions in the problem of the decay of a metastable state

Eugene M. Chudnovsky

Published Dec 1, 1992• 130 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.46.8011

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•May 24, 2019•2 citations
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.
We have investigated the dynamics of underdamped Josephson junctions with a relatively small Josephson coupling EJ{E}_{J}EJ​. In addition to the usual crossover between macroscopic quantum tunneling and thermally activated (TA) behavior we observe, for the first time, the transition from TA behavior to underdamped phase diffusion. Above the crossover temperature, the threshold for switching into the finite-voltage state becomes extremely sharp. We propose a (TTT, EJ{E}_{J}EJ​) phase diagram with various regimes and show that for a proper description of it, dissipation and level quantization in a metastable well are crucial.
The problem of metastability due to quantum and thermal fluctuations in a weakly damped system is treated within Feynman's influence-functional theory. It is shown that quite generally the nonequilibrium density matrix may be written as a single path integral. For a cubic metastable potential it has the form of a Feynman propagator with a complex Lagrangian containing second-order derivatives in time and terms noninvariant under time reversal. Dissipative tunneling and thermal activation emerge together as different solutions of the associated Lagrange equations. The low-temperature correction to the exponent of the tunneling rate behaves as Tn+1{T}^{n+1}Tn+1 for a spectrum of bath excitations vanishing as ${\ensuremath{\omega}}^{n}$. It is shown, moreover, how this result may be understood in terms of environment-assisted tunneling. Thus the low-temperature behavior of the tunneling rate provides a method to measure the dissipation mechanism in the quantum regime.
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.