Stochastic quantization of interacting classical particles system

Details Stochastic quantization of interacting classical particles system Stochastic quantization of interacting classical particles system

2007-03-05

arxiv.org/abs/cond-mat/0703115v1

J. Stat. Mech. (2007) P03012

Physics

Condensed Matter

Statistical Mechanics

16 pages, IOP macro style, version accepted on Journal of Statistical Mechanics: Theory and Experiment

Scientific paper

Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a quantum system of interacting particles. The time evolution of the main physical observables is analyzed by means of the Ehrenfest equations showing that, in general, this family of equations takes into account dissipative and damped effects due to the interaction of the system with the background. We explore the presence of steady states by means of solitons, describing conservative solutions. The results are specialized to the case of a system governed by the Boltzmann-Gibbs entropy.

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