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Ukr. J. Phys. 2015, Vol. 60, N 10, p.1062-1074
doi:10.15407/ujpe60.10.1062    Paper

Golubjeva O.N.1, Sidorov S.V.1, Bar'yakhtar V.G.2

1 People’s Friendship University of Russia
(Moscow 117198, Russia; e-mail: ogol2013@gmail.com)
2 Institute of Magnetism, Nat. Acad. of Sci. of Ukraine
(36, Academician Vernadsky Blvd., Kyiv 03142, Ukraine; e-mail: baryakhtar@gmail.com)

Numerical Simulation of Relaxation of Quantum Thermal Fluctuations

Section: General Problems of Theoretical Physics
Original Author's Text: Ukrainian

Abstract: A generalization of quantum-mechanical equations expressed in the hydrodynamic form by introducing terms that involve the diffusion velocity at zero and finite temperatures, as well as the diffusion pressure energy in a warm vacuum, into the Lagrangian density has been proposed. It is used as a basis for constructing a system of equations similar to the Euler equations, but making allowance for quantum-mechanical and thermal effects, for the model of one-dimensional hydrodynamics. The equations obtained generalize the equations of the Nelson stochastic mechanics. A numerical analysis of the solutions of this system allowed a conclusion to be drawn about its validity for the description of the relaxation of quantum thermal fluctuations.

Key words: (ћ, k)-dynamics, quantum thermostat, cold and warm vacua, effective action, self-diffusion, diffusion pressure energy density, drift and diffusion velocities, numerical analysis.