Self-consistent field theory of polarized BEC: dispersion of collective excitation

We suggest the construction of a set of the quantum hydrodynamics equations for the Bose-Einstein condensate (BEC), where atoms have the electric dipole moment. The contribution of the dipole-dipole interactions (DDI) to the Euler equation is obtained. Quantum equations for the evolution of medium polarization are derived. Developing mathematical method allows to study effect of interactions on the evolution of polarization. The developing method can be applied to various physical systems in which dynamics is affected by the DDI. Derivation of Gross-Pitaevskii equation for polarized particles from the quantum hydrodynamics is described. We showed that the Gross-Pitaevskii equation appears at condition when all dipoles have the same direction which does not change in time. Comparison of the equation of the electric dipole evolution with the equation of the magnetization evolution is described. Dispersion of the collective excitations in the dipolar BEC, either affected or not affected by the uniform external electric field, is considered using our method. We show that the evolution of polarization in the BEC leads to the formation of a novel type of the collective excitations. Detailed description of the dispersion of collective excitations is presented. We also consider the process of wave generation in the polarized BEC by means of a monoenergetic beam of neutral polarized particles. We compute the possibilities of the generation of Bogoliubov and polarization modes by the dipole beam.Comment: 16 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1106.082

Soliton appearing in boson-fermion mixture at the third order of the interaction radius

In this paper we consider an ultra-cold mixture of boson and fermion atoms on the basis of quantum hydrodynamics. Small one-dimensional perturbations in such systems are being analyzed. A possibility is shown for soliton solutions of a new type to appear if the third order of the interaction radius is taken into account in the analysis of interactions. A fermion-fermion interaction occurs in explicit form if this approximation is accepted. The conditions that lead to occurrence of this type of soliton in a mixture of boson and fermion atoms were investigated. Restrictions on the fermion-fermion interaction were found that are necessary for this kind of perturbations to appear in the system. Conditions determining whether perturbances would be a condensed soliton or a rarefied soliton are shown