dorsal/arxiv
View SchemaQuantization of Non-Hamiltonian Systems
| Authors | Vasily E. Tarasov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108120 |
| URL | https://arxiv.org/abs/quant-ph/0108120 |
Abstract
In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables can be derived as a specific case of suggested quantization if dynamical operator is an operator of multiplication on a function. This approach allows to define consistent Weyl quantization of non-Hamiltonian and dissipative systems. Examples of the harmonic oscillator with friction and a system which evolves by Fokker-Planck-type equation are considered.
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"abstract": "In this paper a generalization of Weyl quantization which maps a dynamical\noperator in a function space to a dynamical superoperator in an operator space\nis suggested. Quantization of dynamical operator, which cannot be represented\nas Poisson bracket with some function, is considered. The usual Weyl\nquantization of observables can be derived as a specific case of suggested\nquantization if dynamical operator is an operator of multiplication on a\nfunction. This approach allows to define consistent Weyl quantization of\nnon-Hamiltonian and dissipative systems. Examples of the harmonic oscillator\nwith friction and a system which evolves by Fokker-Planck-type equation are\nconsidered.",
"arxiv_id": "quant-ph/0108120",
"authors": [
"Vasily E. Tarasov"
],
"categories": [
"quant-ph"
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"title": "Quantization of Non-Hamiltonian Systems",
"url": "https://arxiv.org/abs/quant-ph/0108120"
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