Canonical quantization of classical systems with generalized entropies
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.
Cite
@article{arxiv.cond-mat/0503684,
title = {Canonical quantization of classical systems with generalized entropies},
author = {A. M. Scarfone},
journal= {arXiv preprint arXiv:cond-mat/0503684},
year = {2009}
}
Comments
11 pages, no figures, RevTeX4, accepted on Rep. Math. Phys