dorsal/arxiv
View SchemaDeformation quantization of linear dissipative systems
| Authors | V. G. Kupriyanov, S. L. Lyakhovich, A. A. Sharapov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505023 |
| URL | https://arxiv.org/abs/quant-ph/0505023 |
| DOI | 10.1088/0305-4470/38/37/008 |
Abstract
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding Poisson tensor is allowed to explicitly depend on time. Starting from this pseudo-Hamiltonian formulation we develop a consistent deformation quantization procedure involving a non-stationary star-product $*_t$ and an ``extended'' operator of time derivative $D_t=\partial_t+...$, differentiating the $\ast_t$-product. As in the usual case, the $\ast_t$-algebra of physical observables is shown to admit an essentially unique (time dependent) trace functional $\mathrm{Tr}_t$. Using these ingredients we construct a complete and fully consistent quantum-mechanical description for any linear dynamical system with or without dissipation. The general quantization method is exemplified by the models of damped oscillator and radiating point charge.
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"abstract": "A simple pseudo-Hamiltonian formulation is proposed for the linear\ninhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics,\nour approach is based on the use of non-stationary Poisson brackets, i.e.\ncorresponding Poisson tensor is allowed to explicitly depend on time. Starting\nfrom this pseudo-Hamiltonian formulation we develop a consistent deformation\nquantization procedure involving a non-stationary star-product $*_t$ and an\n``extended\u0027\u0027 operator of time derivative $D_t=\\partial_t+...$, differentiating\nthe $\\ast_t$-product. As in the usual case, the $\\ast_t$-algebra of physical\nobservables is shown to admit an essentially unique (time dependent) trace\nfunctional $\\mathrm{Tr}_t$. Using these ingredients we construct a complete and\nfully consistent quantum-mechanical description for any linear dynamical system\nwith or without dissipation. The general quantization method is exemplified by\nthe models of damped oscillator and radiating point charge.",
"arxiv_id": "quant-ph/0505023",
"authors": [
"V. G. Kupriyanov",
"S. L. Lyakhovich",
"A. A. Sharapov"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/38/37/008",
"title": "Deformation quantization of linear dissipative systems",
"url": "https://arxiv.org/abs/quant-ph/0505023"
},
"schema_id": "dorsal/arxiv",
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