dorsal/arxiv
View SchemaBounds on integrals of the Wigner function: the hyperbolic case
| Authors | J. G. Wood, A. J. Bracken |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411028 |
| URL | https://arxiv.org/abs/quant-ph/0411028 |
| DOI | 10.1063/1.1851971 |
| Journal | J. Math. Phys., 46, (2005) 042103. |
Abstract
Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly-solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total ``quasiprobability'' on such a region can be greater than 1 or less than zero.
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"abstract": "Wigner functions play a central role in the phase space formulation of\nquantum mechanics. Although closely related to classical Liouville densities,\nWigner functions are not positive definite and may take negative values on\nsubregions of phase space. We investigate the accumulation of these negative\nvalues by studying bounds on the integral of an arbitrary Wigner function over\nnoncompact subregions of the phase plane with hyperbolic boundaries. We show\nusing symmetry techniques that this problem reduces to computing the bounds on\nthe spectrum associated with an exactly-solvable eigenvalue problem and that\nthe bounds differ from those on classical Liouville distributions. In\nparticular, we show that the total ``quasiprobability\u0027\u0027 on such a region can be\ngreater than 1 or less than zero.",
"arxiv_id": "quant-ph/0411028",
"authors": [
"J. G. Wood",
"A. J. Bracken"
],
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"quant-ph"
],
"doi": "10.1063/1.1851971",
"journal_ref": "J. Math. Phys., 46, (2005) 042103.",
"title": "Bounds on integrals of the Wigner function: the hyperbolic case",
"url": "https://arxiv.org/abs/quant-ph/0411028"
},
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