We present, in the framework of canonical quantization, a class of nonlinear Schrrdinger 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 an N-body classical system where the underlined nonlinear kinetics is governed by a kinetic interaction principle (KIP) [20]. The KIP imposes both 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.
Canonical quantization of classical systems with generalized entropies
AM Scarfone
2005
Abstract
We present, in the framework of canonical quantization, a class of nonlinear Schrrdinger 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 an N-body classical system where the underlined nonlinear kinetics is governed by a kinetic interaction principle (KIP) [20]. The KIP imposes both 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.File in questo prodotto:
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