2016 International Symposium on Nanofluid Heat and Mass Transfer in Textile Engineering and 5th International Symposium on Nonlinear Dynamics


Journal: Nonlinear Science Letters A
(ISSN 2519-9072(Online), ISSN 2076-2275 (Print))          Vol. 1 No. 4
A Quantum Mechanical Approach to Description of Initial Gravitational Interactions Based on the Statistical Theory of Spheroidal Bodies
A. M. Krot
Laboratory of Self-Organization System Modeling, United Institute of Informatics Problems, National Academy of Sciences of Belarus, Surganov Str. 6, 220012 Minsk, Belarus
E-mail: alxkrot@newman.bas-net.by
Abstract: A quantum mechanical interpretation of the statistical theory is proposed for initial gravitational interactions of particles inside the forming cosmological bodies (molecular clouds) which have fuzzy contours and are represented by spheroidal forms. The equation for quasi-equilibrium gravitational compression of a spheroidal body in a vicinity of its mechanical equilibrium is derived initially. This process of quasi-equilibrium gravitational compression of a spheroidal body in space as a Wiener’ process but in a space-frequency domain is also investigated by means of the so-called “vibrating strainer” model. As shown in this paper, interactions of oscillations of particles inside a spheroidal body lead to the resonance increase of a parameter of gravitational compression in time under carrying out the special quantum mechanical conditions. According to the proposed model of “vibrating strainer”, the special quantum mechanical conditions stimulate the coherent motion of oscillatory particles inducing an antidiffusion mass flow inside a slowly compressible gravitating spheroidal body. In this connection, the notions of antidiffusion mass flow density as well as antidiffusion particle velocity in a spheroidal body are introduced. The equations for calculating the partial derivative of the antidiffusion velocity (in the cases of absence or presence of an ordinary hydrodynamic velocity) as well as the complete derivative of the common (hydrodynamic plus antidiffusion) velocity with respect to time are obtained. As shown in this paper, these equations are more general than the analogous equations derived in Nelson’ stochastic mechanics. They are used for the derivation of nonlinear time-dependent Schrödinger equation describing a gravitational formation of a cosmological body. The main results of the proposed statistical theory are in agreement with the conclusions of modern quantum gravity theories considered in this paper.

Keywords: Molecular clouds; initial gravitational interactions; spheroidal bodies; quasi-equilibrium gravitational compression; “vibrating strainer” model; special quantum mechanical conditions; coherent motion of oscillatory particles; antidiffusion velocity; nonlinear Schrödinger equation

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