P. A. Andreev, L. S. Kuzmenkov
Further development of the method of the quantum hydrodynamics in application to a Bose-Einstein condensate is presented. To consider evolution of polarization direction along with particles movement we have developed the set of quantum hydrodynamics equations, which includes equation of the polarization evolution and the polarization current evolution along with the continuity equation and the Euler equation (momentum balance equation). Dispersion properties of transverse waves including the electromagnetic waves propagating through the BEC are considered. For this purpose we consider whole system of the Maxwell's equations for field dynamic description. This approximation gives us possibility to consider electromagnetic waves along with matter waves. We show that in the electrically polarized BEC we have a splitting of the electromagnetic waves on two branches. We have four solution, two for the electromagnetic waves and two for the matter waves, the last two are the concentration-polarization waves. In this approximation we find anisotropy in dispersion dependencies for the all four waves. Whereas in the longitudinal approximation we have two matter waves only which show no anisotropy.
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http://arxiv.org/abs/1208.1000
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