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Physical Review A

Probability of passing through a parabolic barrier and thermal decay rate: Case of linear coupling both in momentum and in coordinate

R. A. Kuzyakin, Vazgen Valerikovich Sargsyan, G. G. Adamian, N. V. Antonenko

Published Sep 22, 2011• 18 citations
Publisher

Abstract

With the quantum diffusion approach, the probability of passing through the parabolic barrier and the quasistationary thermal decay rate from a metastable state are examined in the limit of linear coupling both in momentum and in coordinate between a collective subsystem and the environment. An increase of passing probability with friction coefficient is demonstrated to occur at subbarrier energies.

DOI
10.1103/physreva.84.032117

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With the quantum diffusion approach, the probability of passing through the parabolic barrier and the quasistationary thermal decay rate from a metastable state are examined in the limit of linear coupling both in momentum and in coordinate between a collective subsystem and the environment. An increase of passing probability with friction coefficient is demonstrated to occur at subbarrier energies.
Based on a master equation for the reduced density matrix of an open quantum collective system, the influence of coordinate-dependent microscopical diffusion coefficients on the decay rate from a metastable state is treated. For various frictions and temperatures larger than a crossover temperature, the quasistationary decay rates obtained with the coordinate-dependent microscopical set of diffusion coefficients are compared with those obtained with the coordinate-independent microscopical set of diffusion coefficients and coordinate-independent and -dependent phenomenological sets of diffusion coefficients. Neglecting the coordinate dependence of diffusion coefficients, one can strongly overestimate or underestimate the decay rate at low temperature. The coordinate-dependent phenomenological diffusion coefficient in momentum are shown to be suitable for applications.
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.
Quantum diffusion equations with transport coefficients explicitly depending on time are derived from the generalized non-Markovian Langevin equations. The asymptotic behavior of the friction and diffusion coefficients is investigated in the case of the FC and RWA couplings between the collective and internal subsystems. An asymptotic expression is obtained for the propagator of the density matrix of the open quantum system with the general quadratic Hamiltonian, linearly coupled (in coordinate and momentum) to internal degrees of freedom. The effect of different sets of transport coefficients on the decoherence and decay rate of the metastable state is investigated using the master equation for the reduced density matrix of open quantum systems. The developed approach is used to study the capture of the projectile nucleus by the target nucleus at energies near the Coulomb barrier. Capture cross sections in asymmetric reactions are well described with allowance for the calculated capture probabilities. Particular cases where dissipation favors penetration through the potential barrier are found. The generalized Kramers formula for the quasi-stationary decay rate of the quantum metastable systems is analytically derived.