Resonant and non-resonant Tunneling through a double barrier

Abstract

An explicit expression is obtained for the phase-time corresponding to tunneling of a (non-relativistic) particle through two rectangular barriers, both in the case of resonant and in the case of non-resonant tunneling. It is shown that the behavior of the transmission coefficient and of the tunneling phase-time near a resonance is given by expressions with "Breit-Wigner type" denominators. By contrast, it is shown that, when the tunneling probability is low (but not negligible), the non-resonant tunneling time depends on the barrier width and on the distance between the barriers only in a very weak (exponentially decreasing) way: This can imply in various cases, as well-known, the highly Superluminal tunneling associated with the so-called "generalized Hartman Effect"; but we are now able to improve and modify the mathematical description of such an effect, and to compare more in detail our results with the experimental data for non-resonant tunneling of photons. Finally, as a second example, the tunneling phase-time is calculated, and compared with the available experimental results, in the case of the quantum-mechanical tunneling of neutrons through two barrier-filters at the resonance energy of the set-up.

replaced with some improvements in the text and in the references: pdf (11 pages) produced from a source-file in Word; including one Figure

References in corpus (4)

• Unified time analysis of photon and (nonrelativistic) particle Tunnelling, and the Superluminal group-velocity problem
• Measurement of Superluminal optical tunneling times in double-barrier photonic bandgaps
• Superoscillations and tunneling times
• Multibarrier tunneling

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• Stationary phase method and delay times for relativistic and non-relativistic tunneling particles
• Resonant laser tunnelling
• Soliton-like solutions to the ordinary Schroedinger equation
• Interaction of a wave packet with potential structures moving with acceleration
• Transmission singularities in resonant electron tunneling through double complex potential barrier
• Wave and Particle Limit for Multiple Barrier Tunneling
• On a Time-Space Operator (and other Non-Selfadjoint Operators) for Observables in QM and QFT
• Delay Times for Symmetrized and Antisymmetrized Quantum Tunneling Configurations
• The Exact Correspondence between Phase Times and Dwell Times in a Symmetrical Quantum Tunneling Configuration