dorsal/arxiv
View SchemaBounds and enhancements for the Hartman effect
| Authors | J. G. Muga, I. L. Egusquiza, J. A. Damborenea, F. Delgado |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206181 |
| URL | https://arxiv.org/abs/quant-ph/0206181 |
| DOI | 10.1103/PhysRevA.66.042115 |
Abstract
The time of passage of the transmitted wave packet in a tunneling collision of a quantum particle with a square potential barrier becomes independent of the barrier width in a range of barrier thickness. This is the Hartman effect, which has been frequently associated with ``superluminality''. A fundamental limitation on the effect is set by non-relativistic ``causality conditions''. We demonstrate first that the causality conditions impose more restrictive bounds on the negative time delays (time advancements) when no bound states are present. These restrictive bounds are in agreement with a naive, and generally false, causality argument based on the positivity of the ``extrapolated phase time'', one of the quantities proposed to characterize the duration of the barrier's traversal. Nevertheless, square wells may in fact lead to much larger advancements than square barriers. We point out that close to thresholds of new bound states the time advancement increases considerably, while, at the same time, the transmission probability is large, which facilitates the possible observation of the enhanced time advancement.
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"abstract": "The time of passage of the transmitted wave packet in a tunneling collision\nof a quantum particle with a square potential barrier becomes independent of\nthe barrier width in a range of barrier thickness. This is the Hartman effect,\nwhich has been frequently associated with ``superluminality\u0027\u0027. A fundamental\nlimitation on the effect is set by non-relativistic ``causality conditions\u0027\u0027.\nWe demonstrate first that the causality conditions impose more restrictive\nbounds on the negative time delays (time advancements) when no bound states are\npresent. These restrictive bounds are in agreement with a naive, and generally\nfalse, causality argument based on the positivity of the ``extrapolated phase\ntime\u0027\u0027, one of the quantities proposed to characterize the duration of the\nbarrier\u0027s traversal. Nevertheless, square wells may in fact lead to much larger\nadvancements than square barriers. We point out that close to thresholds of new\nbound states the time advancement increases considerably, while, at the same\ntime, the transmission probability is large, which facilitates the possible\nobservation of the enhanced time advancement.",
"arxiv_id": "quant-ph/0206181",
"authors": [
"J. G. Muga",
"I. L. Egusquiza",
"J. A. Damborenea",
"F. Delgado"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.042115",
"title": "Bounds and enhancements for the Hartman effect",
"url": "https://arxiv.org/abs/quant-ph/0206181"
},
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