dorsal/arxiv
View SchemaWigner Functions with Boundaries
| Authors | Nuno Costa Dias, Joao Nuno Prata |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0012140 |
| URL | https://arxiv.org/abs/quant-ph/0012140 |
| DOI | 10.1063/1.1504885 |
| Journal | J. Math. Phys. 43 (2002) 4602-4627 |
Abstract
We consider the general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the "star-genvalue" equation and to the time evolution equation. These corrections can be cast in the form of a boundary potential contributing to the total Hamiltonian which together with a subsidiary boundary condition is responsible for the discretization of the energy levels. We show that a completely analogous formulation (in terms of boundary potentials) is also possible in standard operator quantum mechanics and that the Wigner and the operator formulations are also in one-to-one correspondence in the confined case. In particular, we extend Baker's converse construction to bounded systems. Finally, we elaborate on the applications of the formalism to the subject of Wigner trajectories, namely in the context of collision processes and quantum systems displaying chaotic behavior in the classical limit.
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"abstract": "We consider the general Wigner function for a particle confined to a finite\ninterval and subject to Dirichlet boundary conditions. We derive the boundary\ncorrections to the \"star-genvalue\" equation and to the time evolution equation.\nThese corrections can be cast in the form of a boundary potential contributing\nto the total Hamiltonian which together with a subsidiary boundary condition is\nresponsible for the discretization of the energy levels. We show that a\ncompletely analogous formulation (in terms of boundary potentials) is also\npossible in standard operator quantum mechanics and that the Wigner and the\noperator formulations are also in one-to-one correspondence in the confined\ncase. In particular, we extend Baker\u0027s converse construction to bounded\nsystems. Finally, we elaborate on the applications of the formalism to the\nsubject of Wigner trajectories, namely in the context of collision processes\nand quantum systems displaying chaotic behavior in the classical limit.",
"arxiv_id": "quant-ph/0012140",
"authors": [
"Nuno Costa Dias",
"Joao Nuno Prata"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1504885",
"journal_ref": "J. Math. Phys. 43 (2002) 4602-4627",
"title": "Wigner Functions with Boundaries",
"url": "https://arxiv.org/abs/quant-ph/0012140"
},
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