dorsal/arxiv
View SchemaSemiquantum versus semiclassical mechanics for simple nonlinear systems
| Authors | A. J. Bracken, J. G. Wood |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511227 |
| URL | https://arxiv.org/abs/quant-ph/0511227 |
| DOI | 10.1103/PhysRevA.73.012104 |
| Journal | Phys. Rev. A 73(2006), 012104 |
Abstract
Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behaviour of expectation values of simple observables and of eigenvalues of the Groenewold operator, are calculated numerically and compared for the various semiclassical and semiquantum approximations.
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"abstract": "Quantum mechanics has been formulated in phase space, with the Wigner\nfunction as the representative of the quantum density operator, and classical\nmechanics has been formulated in Hilbert space, with the Groenewold operator as\nthe representative of the classical Liouville density function. Semiclassical\napproximations to the quantum evolution of the Wigner function have been\ndefined, enabling the quantum evolution to be approached from a classical\nstarting point. Now analogous semiquantum approximations to the classical\nevolution of the Groenewold operator are defined, enabling the classical\nevolution to be approached from a quantum starting point. Simple nonlinear\nsystems with one degree of freedom are considered, whose Hamiltonians are\npolynomials in the Hamiltonian of the simple harmonic oscillator. The behaviour\nof expectation values of simple observables and of eigenvalues of the\nGroenewold operator, are calculated numerically and compared for the various\nsemiclassical and semiquantum approximations.",
"arxiv_id": "quant-ph/0511227",
"authors": [
"A. J. Bracken",
"J. G. Wood"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.012104",
"journal_ref": "Phys. Rev. A 73(2006), 012104",
"title": "Semiquantum versus semiclassical mechanics for simple nonlinear systems",
"url": "https://arxiv.org/abs/quant-ph/0511227"
},
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