dorsal/arxiv
View SchemaParameter scaling in the decoherent quantum-classical transition for chaotic systems
| Authors | Arjendu K. Pattanayak, Bala Sundaram |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206069 |
| URL | https://arxiv.org/abs/quant-ph/0206069 |
| DOI | 10.1103/PhysRevLett.90.014103 |
Abstract
The quantum to classical transition has been shown to depend on a number of parameters. Key among these are a scale length for the action, $\hbar$, a measure of the coupling between a system and its environment, $D$, and, for chaotic systems, the classical Lyapunov exponent, $\lambda$. We propose computing a measure, reflecting the proximity of quantum and classical evolutions, as a multivariate function of $(\hbar,\lambda,D)$ and searching for transformations that collapse this hyper-surface into a function of a composite parameter $\zeta = \hbar^{\alpha}\lambda^{\beta}D^{\gamma}$. We report results for the quantum Cat Map, showing extremely accurate scaling behavior over a wide range of parameters and suggest that, in general, the technique may be effective in constructing universality classes in this transition.
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"abstract": "The quantum to classical transition has been shown to depend on a number of\nparameters. Key among these are a scale length for the action, $\\hbar$, a\nmeasure of the coupling between a system and its environment, $D$, and, for\nchaotic systems, the classical Lyapunov exponent, $\\lambda$. We propose\ncomputing a measure, reflecting the proximity of quantum and classical\nevolutions, as a multivariate function of $(\\hbar,\\lambda,D)$ and searching for\ntransformations that collapse this hyper-surface into a function of a composite\nparameter $\\zeta = \\hbar^{\\alpha}\\lambda^{\\beta}D^{\\gamma}$. We report results\nfor the quantum Cat Map, showing extremely accurate scaling behavior over a\nwide range of parameters and suggest that, in general, the technique may be\neffective in constructing universality classes in this transition.",
"arxiv_id": "quant-ph/0206069",
"authors": [
"Arjendu K. Pattanayak",
"Bala Sundaram"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.90.014103",
"title": "Parameter scaling in the decoherent quantum-classical transition for chaotic systems",
"url": "https://arxiv.org/abs/quant-ph/0206069"
},
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