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Conference publicationsAbstractsXXI conferenceA study of some models of stochastic quantum hydrodynamicsRussian University of Peoples' Friendship Educational and Research Institute of Gravitation and Cosmology Russia , 117198, Moscow, ul . Maclay , 6. 1 pp. (accepted)A STUDY OF SOME MODELS OF STOCHASTIC QUANTUM HYDRODYNAMICS
Golubeva O.N., Sidorov S.V.
Russian University of Peoples' Friendship Educational and Research Institute of Gravitation and Cosmology Russia , 117198, Moscow, ul . Maclay , 6. E-mail: ogol@mail.ru, sidorovsv@mail.ru
In recent years, much attention is paid to the new universal property of matter nearly perfect fluidity (NPF), which manifests itself in such diverse environments as quark -gluon plasma, ultracold gases in traps, and even possibly graphene . One of the approaches to the study of this phenomenon is based on the construction of stochastic hydrodynamics, based on the study of quantum mechanics and quantum thermal fluctuations of the macro parameters [1]. In this paper we consider the theoretical possibility of some hydrodynamic models derived from the equations of quantum mechanics in the Lagrangian form, to describe the evolution of quantum thermal fluctuations: 1) Nelson equation [2 ]
(1)
2) with the self-diffusion equation [3 ]
(2)
where is u diffusion velocity , v the drift velocity , (x) the external potential . Found that the hydrodynamic equations in the model (1) have an elliptical type and are not suitable for describing the evolution of macroscopic fluctuations . Equation (2) refer to the parabolic type and basically allow us to study the quantum fluctuations of macro parameters . These considerations are illustrated by numerical simulation.
Literature 1. Sukhanov A.D. A quantum generalization of equilibrium statistical thermodynamics. Effective macroparameters . / / Theor . Mat. Physics, 2008, 154, pp. 185. 2. Nelson E. Dynamical theory of Brownian motions. Princeton: Princ. Univ. Press, 1967. 3. Golubjeva O.N., Sukhanov A.D. Derivation of stochastic hydrodynamics equations. arXiv: 1112.1598v1 [cond.-mat, stat-mech] ( 2011)
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