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Tunneling of heavy particles in condensed media. Fluctuation effects in barrier preparation, and the role of excited vibrational states of the tunneling species

Alexey Kuznetsov

Published Aug 1, 1986• 0 citations
OpenAlex

Abstract

The nonadiabatic-tunneling probability of heavy particles is calculated while allowing for a dependence of the resonance integral on the vibrational coordinates. It is shown that quantum fluctuations of the tunneling species in a transverse direction can be of distinct importance in preparing the barrier for tunneling. In the model of harmonic vibrations, expressions are obtained for the transition probability which include the contribution from excited vibrational states of the tunneling particle as well as the changes in their vibrational frequency and equilibrium coordinates which occur as the system moves toward the transition configuration.

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Physica Scripta•Apr 29, 2014•3 citations
The nonadiabatic-tunneling probability of heavy particles is calculated while allowing for a dependence of the resonance integral on the vibrational coordinates. It is shown that quantum fluctuations of the tunneling species in a transverse direction can be of distinct importance in preparing the barrier for tunneling. In the model of harmonic vibrations, expressions are obtained for the transition probability which include the contribution from excited vibrational states of the tunneling particle as well as the changes in their vibrational frequency and equilibrium coordinates which occur as the system moves toward the transition configuration.
There has been considerable interest recently in the low temperature dynamics of condensed phase tunneling phenomena. In this paper we consider the interplay between quasiparticle transport and vibrational relaxation; the former taking place via tunneling in a double well potential, and the latter occurring due to interactions of the tunneling system with a harmonic bath. Taking the system–bath interactions to be linear in the bath coordinates, and explicitly allowing for a vibrationally excited well, we present a unified treatment of the weak and strong coupling regimes and obtain reduced equations of motion for the tunneling particle position operator. Solutions are obtained for several important limiting cases. In particular, we find that at sufficiently low temperatures, the dynamical behavior strongly resembles that of multisite spin jump model.
Abstract The tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier is studied. For barriers fluctuating randomly in time we show by exact numerical calculation the significant effect of barrier fluctuation on the tunneling behavior of the particle. At nonzero temperatures the computed tunneling rate constant passes through a maximum when plotted against fluctuation frequency. The resonant frequency (at which the maximum appears) slowly decreases with increase in temperature and attains a constant value at higher temperature and it increases linearly with increase in barrier height of the potential. Another important observation is that in presence of barrier fluctuation the dependence of tunneling rate constant on temperature is strongly guided by the barrier fluctuation frequency. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 280–285, 2003
The effects of coupling to a harmonic oscillator on the quantum tunneling of a macroscopic motion are studied through the influence functional formalism of Feynman's path integral method for the general coupling form factor. As an example, we consider the model in which the potential barrier is parabolic and the coupling Hamiltonian is linear in both coordinates of the macroscopic motion and of the intrinsic harmonic oscillator. The results are then compared with the exact solution obtained through the canonical transformation into normal coordinates in the limiting cases when the normal coordinates reduce to the original coordinates. We found that: (1) In the adiabatic case, i.e., when the recurrence time $\frac{\ensuremath{\pi}}{\ensuremath{\omega}}$ of the oscillator is much shorter than the transmission time through the macroscopic potential barrier, the effect of oscillator coupling can be well represented by an effective potential. The coupling enhances the tunneling probability on the whole. (2) There exists a critical energy, above which the tunneling probability is reduced because of the linear oscillator coupling. In the weak coupling limit and when $\ensuremath{\omega}\ensuremath{\rightarrow}0$, the critical energy becomes $\ensuremath{-}\ensuremath{\infty}$, so that the coupling to the oscillator always reduces the tunneling probability.NUCLEAR REACTIONS Quantum tunneling, coupling of macroscopic motion to intrinsic oscillators, semiclassical method, heavy ion fusion.
Some aspects of quantum tunnelling of a composite particle are clarified by a simple model. We calculate the probability that a couple of point particles bound to each other by a square well potential with a hard core tunnel through a rectangular potential barrier. It is shown that resonance structures appear in the transmission spectrum in some cases, which reflects the existence of quasi-bound-states of the centre of mass motion around the potential barrier. It is also shown that an inelastic tunnelling occurs in which the transitions in the relative motion are induced by the tunnelling of the centre of mass.
Abstract The tunneling of a hydrogen atom through the barrier of a three‐dimensional double‐well potential is considered. From the time‐dependent Schrödinger equation, expressions are derived for the ensemble‐averaged probability density and for the probability that the hydrogen atom is in the reactant region, in the barrier region, or in the product region. It is found that when thermal vibrations are not taken into account, the ensemble‐averaged probability density may oscillate with time about its equilibrium value. When thermal vibrations are included, the oscillations become damped and the probability density approaches equilibrium. The tunneling rate is found to decrease considerably for increasing barrier thickness and barrier height.
Quantum tunnelling of a cluster comprised of several identical particles, coupled via an oscillator-type potential, through short-range repulsive barrier potentials is studied in the s-wave approximation of the symmetrized coordinate representation. A procedure is briefly described that allows the construction of states, symmetric or asymmetric with respect to permutations of A identical particles, from the harmonic oscillator basis functions expressed via the newly introduced symmetrized coordinates. In the coupled-channel approximation of the -matrix approach, the effect of quantum transparency is analysed; it manifests itself in non-monotonic resonance dependence of the transmission coefficient upon the energy of the particles, their number A = 3, 4 and the symmetry types of their states. The total transmission coefficient is shown to demonstrate resonance behaviour with probability density growth in the vicinity of the potential energy local minima, which is a manifestation of the barrier quasi-stationary states, embedded in the continuum.