dorsal/arxiv
View SchemaEarly times in tunneling
| Authors | Gaston Garcia-Calderon, Jorge Villavicencio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0008014 |
| URL | https://arxiv.org/abs/quant-ph/0008014 |
Abstract
Exact analytical solutions of the time-dependent Schr\"odinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value along the tunneling and transmitted regions of the potential. At the barrier width it exhibits, at early times, a distribution of traversal times that typically has a peak $\tau_p$ and a width $\Delta \tau$. Numerical results for other tunneling times, as the phase-delay time, fall within $\Delta \tau$. The B\"uttiker traversal time is the closest to $\tau_p$. Our results resemble calculations based on Feynman paths if its noisy behaviour is ignored.
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"abstract": "Exact analytical solutions of the time-dependent Schr\\\"odinger equation with\nthe initial condition of an incident cutoff wave are used to investigate the\ntraversal time for tunneling. The probability density starts from a vanishing\nvalue along the tunneling and transmitted regions of the potential. At the\nbarrier width it exhibits, at early times, a distribution of traversal times\nthat typically has a peak $\\tau_p$ and a width $\\Delta \\tau$. Numerical results\nfor other tunneling times, as the phase-delay time, fall within $\\Delta \\tau$.\nThe B\\\"uttiker traversal time is the closest to $\\tau_p$. Our results resemble\ncalculations based on Feynman paths if its noisy behaviour is ignored.",
"arxiv_id": "quant-ph/0008014",
"authors": [
"Gaston Garcia-Calderon",
"Jorge Villavicencio"
],
"categories": [
"quant-ph"
],
"title": "Early times in tunneling",
"url": "https://arxiv.org/abs/quant-ph/0008014"
},
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"type": "Model",
"variant": "snapshot-2026-03-01",
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