dorsal/arxiv
View SchemaUnravelling quantum carpets: a travelling wave approach
| Authors | Michael J. W. Hall, Martina S. Reineker, Wolfgang P. Schleich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906107 |
| URL | https://arxiv.org/abs/quant-ph/9906107 |
| DOI | 10.1088/0305-4470/32/47/307 |
| Journal | J.Phys.A32:8275-8291,1999 |
Abstract
Quantum carpets are generic spacetime patterns formed in the probability distributions P(x,t) of one-dimensional quantum particles, first discovered in 1995. For the case of an infinite square well potential, these patterns are shown to have a detailed quantitative explanation in terms of a travelling-wave decomposition of P(x,t). Each wave directly yields the time-averaged structure of P(x,t) along the (quantised)spacetime direction in which the wave propagates. The decomposition leads to new predictions of locations, widths depths and shapes of carpet structures, and results are also applicable to light diffracted by a periodic grating and to the quantum rotator. A simple connection between the waves and the Wigner function of the initial state of the particle is demonstrated, and some results for more general potentials are given.
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"abstract": "Quantum carpets are generic spacetime patterns formed in the probability\ndistributions P(x,t) of one-dimensional quantum particles, first discovered in\n1995. For the case of an infinite square well potential, these patterns are\nshown to have a detailed quantitative explanation in terms of a travelling-wave\ndecomposition of P(x,t). Each wave directly yields the time-averaged structure\nof P(x,t) along the (quantised)spacetime direction in which the wave\npropagates. The decomposition leads to new predictions of locations, widths\ndepths and shapes of carpet structures, and results are also applicable to\nlight diffracted by a periodic grating and to the quantum rotator. A simple\nconnection between the waves and the Wigner function of the initial state of\nthe particle is demonstrated, and some results for more general potentials are\ngiven.",
"arxiv_id": "quant-ph/9906107",
"authors": [
"Michael J. W. Hall",
"Martina S. Reineker",
"Wolfgang P. Schleich"
],
"categories": [
"quant-ph",
"physics.optics"
],
"doi": "10.1088/0305-4470/32/47/307",
"journal_ref": "J.Phys.A32:8275-8291,1999",
"title": "Unravelling quantum carpets: a travelling wave approach",
"url": "https://arxiv.org/abs/quant-ph/9906107"
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