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Communications in Theoretical Physics

Quantum Dissipative Threshold and Its Effect on Decay of Metastable State

Jing-Dong Bao

Published Oct 1, 2005• 0 citations
Publisher

Abstract

The coupling between system and reservoir is considered to be linear in the coordinates of the bath but nonlinear in the system's coordinate. A dissipative threshold is observed at finite temperatures due to nonlinear dissipation. The quantum decay rate of a metastable state including higher-order expanded terms of the coupling form function is proposed, which can be strongly decreased at finite temperatures when the quantum dissipative threshold is added to the saddle point of the potential.

DOI
10.1088/6102/44/4/697

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The coupling between system and reservoir is considered to be linear in the coordinates of the bath but nonlinear in the system's coordinate. A dissipative threshold is observed at finite temperatures due to nonlinear dissipation. The quantum decay rate of a metastable state including higher-order expanded terms of the coupling form function is proposed, which can be strongly decreased at finite temperatures when the quantum dissipative threshold is added to the saddle point of the potential.
We develop the fast-Fourier-transformation path-integral approach to investigate the quantum decay of a nonlinear dissipative system. The action of the bounce trajectory, i.e. the exponential factor of decay rate, is obtained. In the case of the nonlinear coupling f(x)=tanh［λ(x-xb)］ between the system and its environment, we find that the nonlinear coupling suppresses the decay rate. In contrast to the usual linear coupling, the action will not abide by the law SB=a［1-b(T/Tc)2］ and the crossover temperature rebounds, which means that the system steps into the quantum tunneling region at a higher temperature.
We have studied the quantum stochastic dynamics of a system whose interaction with a reservoir is non-linear in system coordinates. In addition, the bath particles are driven by external noise with finite correlation. The effects of the space dependent friction and correlation of the external noise on the rate of decay of a particle from a metastable well have been examined. At a critical value of the correlation, the variation of the quantum decay rate versus the external noise strength exhibits a resonance.
A quantum-activated rate process in the presence of a nonlinear dissipative environment is studied with a Feynman path-integral technique. The nonlinear dissipation arises from specific nonlinear couplings between the reaction coordinate and a many-dimensional bath of effective harmonic oscillators. Such coupling results in a nonlinear influence functional for the effective Feynman path integral along the reaction coordinate. Large nonlinear effects on the rate constant are found at low temperatures.
The recently developed Lindblad approach for quantum dynamics of an open system with linear dissipation has been extended to a model of nonlinear coupling. The coupling term ${H}_{i}={\ensuremath{\sum}}_{k}{C}_{k}{f(x)q}_{k}$ is an arbitrary function of the system coordinate, but remains to be linear in bath coordinates. A Lindblad master equation and its associated stochastic differential equation have been obtained. To study dissipative surface dynamics, a general form of f(x)f(x)f(x) has been proposed. It is shown that such a nonlinear-coupling model is crucial to qualitatively describe gas-surface dynamics, when a gas molecule impinging or leaving a surface goes beyond the linear-coupling regime.
Finite temperatures are incorporated into the calculation of the tunneling rate in the presence of linear dissipation. A theory of finite-temperature tunneling is introduced which is based on the density matrix which provides an approximate description of the metastable state. Semiclassical functional integral methods are used to calculate the density matrix and the Wentzel-Kramers-Brillouin approximation is used to derive the tunnel current from the density matrix. Dissipation appropriate to superconducting quantum-interference devices is introduced into the calculation by the use of the existing model of a heat bath consisting of a prescribed distribution of harmonic oscillators linearly coupled to the tunneling variable. The finite-temperature tunnel escape rate obtained is of the form \ensuremath{\Gamma}=A exp(-S/\ensuremath{\Elzxh}). S is determined from the solution of a nonlinear integro-differential equation. An existing numerical technique was modified to achieve this. The quantity A is approximately evaluated.