dorsal/arxiv
View SchemaQuantum Chaos and Quantum-Classical Correspondence
| Authors | Joseph Emerson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211035 |
| URL | https://arxiv.org/abs/quant-ph/0211035 |
Abstract
The quantum dynamics of a classically chaotic model are studied in the approach to the macroscopic limit. The quantum predictions are compared and contrasted with the classical predictions of both Newtonian and Liouville mechanics. The time-domain scaling of the optimal quantum-classical correspondence is analyzed in detail in the case of both classical theories. In both cases the correspondence for observable quantities is shown to break down on a time-scale that increases very slowly (logarithmically) with increasing system size. In the case of quantum-Liouville correspondence such a short time-scale does not imply a breakdown of correspondence since the largest quantum-Liouville differences reached on this time-scale decrease rapidly (as an inverse power) with increasing system size. Therefore the statistical properties of chaotic dynamics are, as expected, well described by quantum theory in the macroscopic limit. In contrast, the largest quantum-Newtonian differences reached on the log time-scale actually increase in proportion to the system size. Since the invariance properties of the Hamiltonian impose functional constraints on the time-varying chaotic coordinates, it is possible to show, moreover, that if the quantum predictions are believed to describe the coordinates of individual chaotic systems, then they also predict macroscopic violations of any kinematic or dynamic constants of the motion. These results for chaotic systems indicate that a valid description of the time-varying properties of individual macroscopic bodies is not available within the standard interpretive framework of quantum theory.
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"abstract": "The quantum dynamics of a classically chaotic model are studied in the\napproach to the macroscopic limit. The quantum predictions are compared and\ncontrasted with the classical predictions of both Newtonian and Liouville\nmechanics. The time-domain scaling of the optimal quantum-classical\ncorrespondence is analyzed in detail in the case of both classical theories. In\nboth cases the correspondence for observable quantities is shown to break down\non a time-scale that increases very slowly (logarithmically) with increasing\nsystem size. In the case of quantum-Liouville correspondence such a short\ntime-scale does not imply a breakdown of correspondence since the largest\nquantum-Liouville differences reached on this time-scale decrease rapidly (as\nan inverse power) with increasing system size. Therefore the statistical\nproperties of chaotic dynamics are, as expected, well described by quantum\ntheory in the macroscopic limit. In contrast, the largest quantum-Newtonian\ndifferences reached on the log time-scale actually increase in proportion to\nthe system size. Since the invariance properties of the Hamiltonian impose\nfunctional constraints on the time-varying chaotic coordinates, it is possible\nto show, moreover, that if the quantum predictions are believed to describe the\ncoordinates of individual chaotic systems, then they also predict macroscopic\nviolations of any kinematic or dynamic constants of the motion. These results\nfor chaotic systems indicate that a valid description of the time-varying\nproperties of individual macroscopic bodies is not available within the\nstandard interpretive framework of quantum theory.",
"arxiv_id": "quant-ph/0211035",
"authors": [
"Joseph Emerson"
],
"categories": [
"quant-ph"
],
"title": "Quantum Chaos and Quantum-Classical Correspondence",
"url": "https://arxiv.org/abs/quant-ph/0211035"
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