2001/09/01 by Vasily E. Tarasov · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Canonical quantization #Classical mechanics #Dissipative operator #Dissipative system #Geometric quantization #Hamiltonian (control theory) #Mathematical physics #Mathematics #Nonlinear Dynamics and Pattern Formation #Observable #Physics #Poisson bracket #Pure mathematics #Quantization (signal processing) #Quantum #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Quantum mechanics #cond-mat.stat-mech #hep-th #math-ph #math.MP #physics.chem-ph #quant-ph
paper · pdf · doi:10.1016/s0375-9601(01)00548-5
published as Physics Letters A 288 (2001) 173-182 · 9p., LaTeX
openalex publication_date 2001/09/01 · arxiv created 2003/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.