Quantization of non-Hamiltonian and Dissipative Systems

Details Quantization of non-Hamiltonian and Dissipative Systems Quantization of non-Hamiltonian and Dissipative Systems

2003-11-24

arxiv.org/abs/quant-ph/0311159v1

Physics Letters A 288 (2001) 173-182

Physics

Quantum Physics

9p., LaTeX

Scientific paper

10.1016/S0375-9601(01)00548-5

A generalization of canonical quantization which maps a dynamical operator to a dynamical superoperator is suggested. Weyl quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables is a specific case of suggested quantization. This approach allows to define consistent quantization procedure for non-Hamiltonian and dissipative systems. Examples of the harmonic oscillator with friction (generalized Lorenz-Rossler-Leipnik-Newton equation), the Fokker-Planck-type system and Lorenz-type system are considered.

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