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Physical Review C

Dynamical norm method for nonadiabatic macroscopic quantum tunneling

N. Takigawa, K. Hagino, M. Abe

Published Jan 1, 1995• 24 citations
Publisher

Abstract

We present a method for macroscopic quantum tunneling, named dynamical norm method, which works over a very wide range of situations between the adiabatic and the sudden limits. We examine the validity of the method by studying the effects of linear oscillator coupling on the tunneling rate through an Eckart barrier. We then apply the method to discussing the effects of a nuclear intrinsic excitation on fission. This method shows that the adiabaticity of the tunneling process is governed not only by the relative time scale of the tunneling degree of freedom and of environmental degrees of freedom, but also by the properties of the coupling between them. We also show that the dynamical norm factor which represents nonadiabatic effects in our method is closely related to the dissipation factor in the Caldeira-Leggett theory for dissipative quantum tunneling.

DOI
10.1103/physrevc.51.187

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We present a method for macroscopic quantum tunneling, named dynamical norm method, which works over a very wide range of situations between the adiabatic and the sudden limits. We examine the validity of the method by studying the effects of linear oscillator coupling on the tunneling rate through an Eckart barrier. We then apply the method to discussing the effects of a nuclear intrinsic excitation on fission. This method shows that the adiabaticity of the tunneling process is governed not only by the relative time scale of the tunneling degree of freedom and of environmental degrees of freedom, but also by the properties of the coupling between them. We also show that the dynamical norm factor which represents nonadiabatic effects in our method is closely related to the dissipation factor in the Caldeira-Leggett theory for dissipative quantum tunneling.
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A semiclassical method is applied to the problem of quantum tunneling in the presence of internal oscillator degrees of freedom. Comparison with coupled channel calculations verifies the accuracy of the semi-classical method. Providing the coupling has a physically reasonable form factor, the coupling produces an enhancement in the tunneling rate. The enhancement becomes larger when the tunneling degree of freedom couples with a harmonic oscillator with lower frequency. The semiclassical method is found to be quite useful in situations where the coupled channel method becomes numerically difficult.
Quantum tunneling under the influence of an environment with nearly degenerate spectrum is considered. We first give a general derivation of the zero point motion formula in the sudden tunneling limit. The effects of a finite excitation energy of the environment are then considered by a perturbation method. Examples of linear oscillator coupling and rotational coupling show that the finite excitation energy can be represented by a dissipation factor and reduces the tunneling probability estimated in the limit of sudden tunneling. These examples clearly show that the applicability of the sudden tunneling approximation is governed by the details of the coupling as well as the relative time scales of the tunneling and the environmental degrees of freedom. We discuss some applications to heavy-ion fusion reactions.
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This paper studies the effect of the momentum conservation on tunneling with dissipation. Two coupled macroscopic particles, interacting with a thermal bath of harmonic oscillators are considered. The interaction between the particles is chosen such that it has minima at two different separations. The exact effective action is obtained for the linear coupling with the bath by the direct calculation of the imaginary-time path integral at arbitrary temperature, and by applying Leggett's prescription at T=0. The case of the Ohmic dissipation is studied in detail. It is proved that the tunneling, at any strength of the dissipation, has a simple description in terms of the effective reduced mass that depends on temperature and classical friction coefficients. The connection with the M\"ossbauer effect is discussed. \textcopyright{} 1996 The American Physical Society.
Quantum tunneling is known to play an important role in the dynamics of systems with nonadiabatic couplings. However, until recently, the time-domain properties of nonadiabatic scattering have been severely under-explored. Using numerically exact quantum methods, we study the impact that nonadiabatic couplings have on the time it takes to tunnel through a barrier. We find that the Wigner phase time is the appropriate measure to use when determining the tunneling flight time also when considering nonadiabatic systems. The central result of the present study is that in an avoided crossing system in one dimension, the nonadiabatic couplings speed up the tunneling event, relative to the adiabatic case in which all nonadiabatic coupling is ignored. This has implications for both the study of quantum tunneling times and for the field of nonadiabatic scattering and chemistry.