dorsal/arxiv
View SchemaTime dependence of evanescent quantum waves
| Authors | J. G. Muga, M. Buttiker |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0001039 |
| URL | https://arxiv.org/abs/quant-ph/0001039 |
| DOI | 10.1103/PhysRevA.62.023808 |
| Journal | Phys. Rev. A, 62 (2000) 023808 |
Abstract
The time dependence of quantum evanescent waves generated by a point source with an infinite or a limited frequency band is analyzed. The evanescent wave is characterized by a forerunner (transient) related to the precise way the source is switched on. It is followed by an asymptotic, monochromatic wave which at long times reveals the oscillation frequency of the source. For a source with a sharp onset the forerunner is exponentially larger than the monochromatic solution and a transition from the transient regime to the asymtotic regime occurs only at asymptotically large times. In this case, the traversal time for tunneling plays already a role only in the transient regime. To enhance the monochromatic solution compared to the forerunner we investigate (a) frequency band limited sources and (b) the short time Fourier analysis (the spectrogram) corresponding to a detector which is frequency band limited. Neither of these two methods leads to a precise determination of the traversal time. However, if they are limited to determine the traversal time only with a precision of the traversal time itself both methods are successful: In this case the transient behavior of the evanescent waves is at a time of the order of the traversal time followed by a monochromatic wave which reveals the frequency of the source.
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"abstract": "The time dependence of quantum evanescent waves generated by a point source\nwith an infinite or a limited frequency band is analyzed. The evanescent wave\nis characterized by a forerunner (transient) related to the precise way the\nsource is switched on. It is followed by an asymptotic, monochromatic wave\nwhich at long times reveals the oscillation frequency of the source. For a\nsource with a sharp onset the forerunner is exponentially larger than the\nmonochromatic solution and a transition from the transient regime to the\nasymtotic regime occurs only at asymptotically large times. In this case, the\ntraversal time for tunneling plays already a role only in the transient regime.\nTo enhance the monochromatic solution compared to the forerunner we investigate\n(a) frequency band limited sources and (b) the short time Fourier analysis (the\nspectrogram) corresponding to a detector which is frequency band limited.\nNeither of these two methods leads to a precise determination of the traversal\ntime. However, if they are limited to determine the traversal time only with a\nprecision of the traversal time itself both methods are successful: In this\ncase the transient behavior of the evanescent waves is at a time of the order\nof the traversal time followed by a monochromatic wave which reveals the\nfrequency of the source.",
"arxiv_id": "quant-ph/0001039",
"authors": [
"J. G. Muga",
"M. Buttiker"
],
"categories": [
"quant-ph",
"cond-mat"
],
"doi": "10.1103/PhysRevA.62.023808",
"journal_ref": "Phys. Rev. A, 62 (2000) 023808",
"title": "Time dependence of evanescent quantum waves",
"url": "https://arxiv.org/abs/quant-ph/0001039"
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