Quantization of non-Hamiltonian and dissipative systems

A generalization of canonical quantization which maps a dynamical operator to a dynamical superoperator is suggested. Weyl quantization of dynamical o perator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables is a specific ca se of suggested quantization. This approach allows to define consistent qua ntization procedure for non-Hamiltonian and dissipative systems. Examples o f the harmonic oscillator with friction (generalized Lorenz-Rossler-Leipnik -Newton equation), the Fokker-Planck-type system and Lorenz-type system are considered. (C) 2001 Elsevier Science B.V. All rights reserved.