dorsal/arxiv
View SchemaSemiclassical quantization of non-Hamiltonian dynamical systems without memory
| Authors | E. D. Vol |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509159 |
| URL | https://arxiv.org/abs/quant-ph/0509159 |
| DOI | 10.1103/PhysRevA.73.062113 |
Abstract
We propose a new method of quantization of a wide class of dynamical systems that originates directly from the equations of motion. The method is based on the correspondence between the classical and the quantum Poisson brackets, postulated by Dirac. This correspondence applied to open (non-Hamiltonian) systems allows one to point out the way of transition from the quantum description based on the Lindblad equation to the dynamical description of their classical analogs by the equations of motion and vice versa. As the examples of using of the method we describe the procedure of the quantization of three widely considered dynamical systems: 1) the harmonic oscillator with friction, 2) the oscillator with a nonlinear damping that simulates the process of the emergence of the limit cycle, and 3) the system of two periodic rotators with a weak interaction that synchronizes their oscillations. We discuss a possible application of the method for a description of quantum fluctuations in Josephson junctions with a strong damping and for the quantization of open magnetic systems with a dissipation and a pumping.
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"abstract": "We propose a new method of quantization of a wide class of dynamical systems\nthat originates directly from the equations of motion. The method is based on\nthe correspondence between the classical and the quantum Poisson brackets,\npostulated by Dirac. This correspondence applied to open (non-Hamiltonian)\nsystems allows one to point out the way of transition from the quantum\ndescription based on the Lindblad equation to the dynamical description of\ntheir classical analogs by the equations of motion and vice versa. As the\nexamples of using of the method we describe the procedure of the quantization\nof three widely considered dynamical systems: 1) the harmonic oscillator with\nfriction, 2) the oscillator with a nonlinear damping that simulates the process\nof the emergence of the limit cycle, and 3) the system of two periodic rotators\nwith a weak interaction that synchronizes their oscillations. We discuss a\npossible application of the method for a description of quantum fluctuations in\nJosephson junctions with a strong damping and for the quantization of open\nmagnetic systems with a dissipation and a pumping.",
"arxiv_id": "quant-ph/0509159",
"authors": [
"E. D. Vol"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.062113",
"title": "Semiclassical quantization of non-Hamiltonian dynamical systems without memory",
"url": "https://arxiv.org/abs/quant-ph/0509159"
},
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