Canonical quantization of classical systems with generalized entropies

Details Canonical quantization of classical systems with generalized entropies Canonical quantization of classical systems with generalized entropies

Publishing date

2005-03-29

URL

arxiv.org/abs/cond-mat/0503684v1

Science

Physics

Field

Condensed Matter

SubField

Statistical Mechanics

Additional info

11 pages, no figures, RevTeX4, accepted on Rep. Math. Phys

Type

Scientific paper

Digital Object Identifier

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.

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