dorsal/arxiv
View SchemaQuantum-classical correspondence on compact phase space
| Authors | Martin Horvat, Tomaz Prosen, Mirko Degli Esposti |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0601139 |
| URL | https://arxiv.org/abs/quant-ph/0601139 |
| DOI | 10.1088/0951-7715/19/6/013 |
Abstract
We propose to study the $L^2$-norm distance between classical and quantum phase space distributions, where for the latter we choose the Wigner function, as a global phase space indicator of quantum-classical correspondence. For example, this quantity should provide a key to understand the correspondence between quantum and classical Loschmidt echoes. We concentrate on fully chaotic systems with compact (finite) classical phase space. By means of numerical simulations and heuristic arguments we find that the quantum-classical fidelity stays at one up to Ehrenfest-type time scale, which is proportional to the logarithm of effective Planck constant, and decays exponentially with a maximal classical Lyapunov exponent, after that time.
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"abstract": "We propose to study the $L^2$-norm distance between classical and quantum\nphase space distributions, where for the latter we choose the Wigner function,\nas a global phase space indicator of quantum-classical correspondence. For\nexample, this quantity should provide a key to understand the correspondence\nbetween quantum and classical Loschmidt echoes. We concentrate on fully chaotic\nsystems with compact (finite) classical phase space. By means of numerical\nsimulations and heuristic arguments we find that the quantum-classical fidelity\nstays at one up to Ehrenfest-type time scale, which is proportional to the\nlogarithm of effective Planck constant, and decays exponentially with a maximal\nclassical Lyapunov exponent, after that time.",
"arxiv_id": "quant-ph/0601139",
"authors": [
"Martin Horvat",
"Tomaz Prosen",
"Mirko Degli Esposti"
],
"categories": [
"quant-ph",
"nlin.CD"
],
"doi": "10.1088/0951-7715/19/6/013",
"title": "Quantum-classical correspondence on compact phase space",
"url": "https://arxiv.org/abs/quant-ph/0601139"
},
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