Phase liquid turbulence as novel quantum approach

Abstract

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 turbulent medium into a Hilbert phase space.It has isotropic minimal diffusion defined by Planck constant.Areas of probability condensation may produce clustering centers: quasi stable particles-attractors which preserve boundaries and scale-free fractal transport properties.The stability of particles 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 attractor 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. Finally the integrity of classical and quantum approaches is recovered: existence of particles is derived in terms of Zaslavsky quantum fluid.