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International Journal of Quantum Chemistry

Transmissivity and degeneracy of quasi‐energies

R. Lefèbvre

Published May 4, 2005• 0 citations
Publisher

Abstract

Abstract We examine the transmissivity through a triple barrier of a particle interacting with an oscillating field. This study is motivated by the well‐documented coherence suppression of tunneling in a double well under the effect of such a field. Since the work of Hänggi and colleagues, it is known that localization of the particle in one of the wells can be correlated with a degeneracy of two quasi‐energies of Floquet theory. When the quasi‐energies are complex, we can at least produce an equality of their real parts. Since the particle meets a double‐well potential on its way, one may expect some effect on the transmission. It is found that there is effectively some significant reduction in the integrated transmission probabilities in the neighborhood of the energy crossing. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

DOI
10.1002/qua.20634

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Abstract We examine the transmissivity through a triple barrier of a particle interacting with an oscillating field. This study is motivated by the well‐documented coherence suppression of tunneling in a double well under the effect of such a field. Since the work of Hänggi and colleagues, it is known that localization of the particle in one of the wells can be correlated with a degeneracy of two quasi‐energies of Floquet theory. When the quasi‐energies are complex, we can at least produce an equality of their real parts. Since the particle meets a double‐well potential on its way, one may expect some effect on the transmission. It is found that there is effectively some significant reduction in the integrated transmission probabilities in the neighborhood of the energy crossing. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
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
We examine the transmissivity through a double-barrier potential with two resonances present in the intermediate well. The particle interacts with an oscillating field. Satellites are produced when the particle needs to emit or absorb one or more quanta of the field to reach the resonant energy which favours transmissivity. We show that as the frequency of the field goes from an off-resonance to the resonant situation, where there is matching with the energy separation of the well levels, the discontinuities responsible for the energy exchanges are first the most external ones, but finally the most internal ones. We also conclude that, even in the presence of an oscillating field, the propagation within the barriers is well accounted for by free waves.
Nonadiabatic tunneling is an effect occurring when two potentials are crossing each other with opposite slopes. It is characterized by the vanishing of the transmission probability at a set of energies (or nodes) that can be identified as the resonance energies of the system. We investigate the modification of this probability induced by the interaction of the particle with an oscillating field. The main result of this study is the presence of additional dips in the transmissivity, representing replicas of the nodal structure. They are due to processes implying an absorption (or emission) followed by an emission (or absorption) of one or even more than one quantum.
Abstract The quantum dynamics of a charged particle in a harmonic trap in the presence of discontinuous reversals of a homogeneous or an inhomogeneous electric field is studied. The dynamics reveals classically expected patterns in harmonic wells. In a symmetric double‐well potential, the discontinuously switched low intensity homogeneous electric field does not appear to assist tunneling, whereas an inhomogeneous electric field is found to assist the process. Resonance like enhancement is noticed at a critical reversal frequency. Dynamics in a triple well is also analyzed under similar conditions. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
Time-dependent wave packet resonant scattering for the double square barrier has been studied in terms of Bohm quantum trajectories. The high transmission probability for the wave packet with a resonant energy can be explained by the behavior of the quantum trajectories under the influence of the relatively slow formation of a node within the first barrier. This node splits the trajectories into reflected and transmitted components. During this stage, many particle trajectories pass through the double-barrier region and contribute to the transmitted part of the wave packet. Due to the transient nature of the nodes, trajectories in the reflected wave packet bunch together between the nodes for a finite period of time so that temporary structure (localization of particles and accompanying increase in the probability density) develops on small length scales. These calculations also show that the particles gain high momentum near the nodal points, and they reach a uniform momentum distribution after transmitting the barrier region. We have found that the presence of a node between the two barriers influences the different lifetimes of the quasi-bound states. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 206–213, 2001
Abstract One generally expects that the transmissivity through a symmetric arrangement of barriers and wells should go to unity when the energy of the incident particle coincides with a resonance energy of the system. It has been noticed before that for a symmetric triple barrier, there are conditions that lead to a merging of the two lowest unit transmissivity peaks, accompanied by a collapse of the transmissivity profile. This feature has been interpreted as meaning that there is a reduction of the number of resonances under these conditions. We reanalyze this situation with the help of a model that involves the same number of bound and continuum states, but which possesses an analytic solution. Because the transition probability in this case is expressed entirely in terms of resonance parameters (positions and widths), it is possible to calculate with the expression derived from the model a profile that agrees completely with that calculated with the transfer matrix method. The resonance parameters are obtained from the poles of the transition amplitude. This shows that the merging of the peaks and the collapse of the transmissivity occurs without a reduction in the number of resonances.