dorsal/arxiv
View SchemaWigner functions for curved spaces I: On hyperboloids
| Authors | Miguel Angel Alonso, George S. Pogosyan, Kurt Bernardo Wolf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0205041 |
| URL | https://arxiv.org/abs/quant-ph/0205041 |
| DOI | 10.1063/1.1518139 |
Abstract
We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature --in this paper on hyperboloids--, which returns the correct marginals and has the covariance of the Shapiro functions under SO(D,1) transformations. To the free systems obeying the Laplace-Beltrami equation on the hyperboloid, we add a conic-oscillator potential in the hyperbolic coordinate. As an example, we analyze the 1-dimensional case on a hyperbola branch, where this conic-oscillator is the Poschl-Teller potential. We present the analytical solutions and plot the computed results. The standard theory of quantum oscillators is regained in the contraction limit to the space of zero curvature.
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"abstract": "We propose a Wigner quasiprobability distribution function for Hamiltonian\nsystems in spaces of constant curvature --in this paper on hyperboloids--,\nwhich returns the correct marginals and has the covariance of the Shapiro\nfunctions under SO(D,1) transformations. To the free systems obeying the\nLaplace-Beltrami equation on the hyperboloid, we add a conic-oscillator\npotential in the hyperbolic coordinate. As an example, we analyze the\n1-dimensional case on a hyperbola branch, where this conic-oscillator is the\nPoschl-Teller potential. We present the analytical solutions and plot the\ncomputed results. The standard theory of quantum oscillators is regained in the\ncontraction limit to the space of zero curvature.",
"arxiv_id": "quant-ph/0205041",
"authors": [
"Miguel Angel Alonso",
"George S. Pogosyan",
"Kurt Bernardo Wolf"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1518139",
"title": "Wigner functions for curved spaces I: On hyperboloids",
"url": "https://arxiv.org/abs/quant-ph/0205041"
},
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