Authors: Sergey Kamenshchikov
In this paper we consider a nonlinear stochastic approach to the description of quantum systems. It is shown that a possibility to derive quantum properties - spectrum quantization, zero point positive energy and uncertainty relations, exists in frame of Zaslavsky phase liquid. This liquid is considered as a projection of continuous medium into a Hilbert phase space. It has isotropic minimal diffusion defined by Planck constant. Areas of probability condensation, formed by phase liquid turbulence, may produce clustering centers–particles, which preserve boundaries. These areas are described as strange attractors with fractal transport properties. The stability of attractors has been shown in frame of the first order perturbation theory. Quantum peculiarities of considered systems have been strictly derived from markovian Fokker-Planck equation. It turned out that the positive zero point energy has volumetric properties and grows for higher time resolutions. We have shown that a quasi stable condensate may be applied as a satisfactory model of an elementary quantum system. The conditions of attractor stability are defined on the basis of Nonlinear Prigogine Theorem. It is shown that the integrity of classical and quantum approaches is recovered while existence of particles is derived in terms of mechanical model.
Comments: 6 Pages.
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[v1] 2015-03-03 07:43:57
[v2] 2015-03-10 12:09:38
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