2 research outputs found
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
Quasiclassical Study of the Quantum Mechanical Two-Coulomb-Centre Problem
A recurrent scheme for finding the quasiclassical solutions of the onedimensional equation got by the separation of variables from the Schrödinger equation in prolate spheroidal coordinates has been elaborated. By means of this scheme, WKB expansion quasiclassical two-Coulomb-centre wave functions at large distances between the fixed positive charges (nuclei) have been constructed for the entire space of the negative particle (electron). Our method provides simple uniform estimates of the eigenfunctions at arbitrary internuclear distances R, R ≫ 1 included. In contrast to the perturbation theory, the interaction need not be very small in the quasiclassical approximation. Its applicability domain is hence wider. That permits analyzing qualitative laws for the behavior and properties of quantum mechanical systems