dorsal/arxiv
View SchemaResonant and non-resonant Tunneling through a double barrier
| Authors | Vladislav S. Olkhovsky, Erasmo Recami, A. K. Zaichenko |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410128 |
| URL | https://arxiv.org/abs/quant-ph/0410128 |
| DOI | 10.1209/epl/i2004-10523-8 |
| Journal | Europhysics Letters 70 (2005) 712-718 |
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.
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"abstract": "An explicit expression is obtained for the phase-time corresponding to\ntunneling of a (non-relativistic) particle through two rectangular barriers,\nboth in the case of resonant and in the case of non-resonant tunneling. It is\nshown that the behavior of the transmission coefficient and of the tunneling\nphase-time near a resonance is given by expressions with \"Breit-Wigner type\"\ndenominators. By contrast, it is shown that, when the tunneling probability is\nlow (but not negligible), the non-resonant tunneling time depends on the\nbarrier width and on the distance between the barriers only in a very weak\n(exponentially decreasing) way: This can imply in various cases, as well-known,\nthe highly Superluminal tunneling associated with the so-called \"generalized\nHartman Effect\"; but we are now able to improve and modify the mathematical\ndescription of such an effect, and to compare more in detail our results with\nthe experimental data for non-resonant tunneling of photons. Finally, as a\nsecond example, the tunneling phase-time is calculated, and compared with the\navailable experimental results, in the case of the quantum-mechanical tunneling\nof neutrons through two barrier-filters at the resonance energy of the set-up.",
"arxiv_id": "quant-ph/0410128",
"authors": [
"Vladislav S. Olkhovsky",
"Erasmo Recami",
"A. K. Zaichenko"
],
"categories": [
"quant-ph"
],
"doi": "10.1209/epl/i2004-10523-8",
"journal_ref": "Europhysics Letters 70 (2005) 712-718",
"title": "Resonant and non-resonant Tunneling through a double barrier",
"url": "https://arxiv.org/abs/quant-ph/0410128"
},
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