Canonical quantization of classical systems with generalized entropies
arXiv:cond-mat/0503684 · doi:10.1016/S0034-4877(05)00012-1
Abstract
We present, in the framework of the canonical quantization, a class of nonlinear Schroedinger equations with a complex nonlinearity describing, in the mean field approximation, systems of collectively interacting particles. The quantum evolution equation is obtained starting from the study of a N-body classical system where the underlined nonlinear kinetics is governed by a kinetic interaction principle (KIP) recently proposed [G. Kaniadakis: Physica A 296 (2001), 405--425]. The KIP, both imposes the form of the generalized entropy associated to the classical system, and determines the Fokker-Planck equation describing the kinetic evolution of the system towards equilibrium. Keywords: Nonlinear Schroedinger equation, Nonlinear kinetics, Generalized entropy.
11 pages, no figures, RevTeX4, accepted on Rep. Math. Phys
References in corpus (5)
- Statistical mechanics in the context of special relativity
- Non Linear Kinetics underlying Generalized Statistics
- H-Theorem and Generalized Entropies Within the Framework of Non Linear Kinetics
- Cole-Hopf Like Transformation for Schrödinger Equations Containing Complex Nonlinearities
- Nonlinear gauge transformation for a class of Schroedinger equations containing complex nonlinearities