Quantum resonances in physical tunneling

Michael Martin Nieto, Vincent P. Gutschick, Carl M. Bender +2 more

Er’el Granot

Resonant tunnelling (RT) is used as a pedagogical tool to emphasize the difference between quantum and classical physics. We calculate the RT reflection and transmission coefficients in both the classical and quantum scenarios, and RT is used to demonstrate the transition from the quantum domain to the classical one. We also use the classical result with a dimension analysis to derive the Landauer formula.

Marco Merkli

Boris I. Ivlev

Quantum tunneling through an almost classical potential barrier can be strongly enhanced by a nonstationary field so that the penetration through the barrier becomes not exponentially small. This constitutes an extremely unusual phenomenon of quantum physics called Euclidean resonance. A certain nonstationary barrier is proposed with a very low WKB tunneling rate. The quantum dynamics of this barrier is mapped on resonant tunneling across a static double barrier with a resonant level inside. The real penetration through the dynamical barrier is not exponentially small providing an example of Euclidean resonance. Therefore, the Schoedinger equation allows solutions of the type of Euclidean resonance. The counterintuitive phenomenon of Euclidean resonance is a dynamical analogue of static resonant tunneling.

Pavel M. Krassovitskiy, Ф. М. Пеньков

Probabilities of resonant tunneling through a potential barrier are compared for a rigid molecule and an excited molecule. It is shown that the resonance spectrum is mainly governed by the transmission resonance spectrum of the rigid molecule. Analytical expressions for the probability for the tunneling of the rigid molecule through a barrier allow resonance-spectrum-averaged observables, including quantum diffusion, to be estimated.

Antonio Defendi, Marco Roncadelli