Quantum Gases of Dipoles, Quadrupoles and Octupoles in Gross–Pitaevskii Formalism with Form Factor
| Autor: | Stanislav L. Ogarkov, Artem A. Alexandrov, Alina U. Badamshina |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Plane wave FOS: Physical sciences scalar QFT quantum field theory (QFT) 01 natural sciences Instability 010305 fluids & plasmas Gross–Pitaevskii (GP) formalism octupoles Quantum mechanics 0103 physical sciences Physics::Atomic Physics Quantum field theory 010306 general physics Wave function Quantum Convergent series Condensed Matter - Statistical Mechanics Physics Condensed Matter::Quantum Gases form factor Optical lattice dipoles quadrupoles Statistical Mechanics (cond-mat.stat-mech) Condensed Matter Physics lcsh:QC1-999 Electronic Optical and Magnetic Materials Dipole High Energy Physics - Theory (hep-th) nonlocal QFT Euclidean QFT quantum gases lcsh:Physics |
| Zdroj: | Condensed Matter Volume 5 Issue 4 Condensed Matter, Vol 5, Iss 61, p 61 (2020) |
| ISSN: | 2410-3896 |
| DOI: | 10.3390/condmat5040061 |
| Popis: | Here, classical and quantum field theory of dipolar, axisymmetric quadrupolar and octupolar Bose gases is considered within a general approach. Dipole, axisymmetric quadrupole and octupole interaction potentials in the momentum representation are calculated. These results clearly demonstrate attraction and repulsion areas in corresponding gases. Then the Gross&ndash Pitaevskii (GP) equation, which plays a key role in the present paper, is derived from the corresponding functional. The zoology of the form factors appearing in the GP equation is studied in details. The proper classes for the description of spatially non-uniform condensates form factors are chosen. In the Thomas&ndash Fermi approximation a general solution of the GP equation with a quasilocal form factor is obtained. This solution has an interesting form in terms of a double rapidly converging series that universally includes all the interactions considered. Plots of condensate density functions for the exponential-trigonometric form factor are given. For the sake of completeness, in this paper we consider the GP equation with an optical lattice potential in the limit of small condensate densities. This limit does not distinguish between dipolar, quadrupolar and octupolar gases. An important analysis of the condensate stability, in other words the study of condensate excitations, is also performed in this paper. In the Gaussian approximation (from the Gross&ndash Pitaevskii functional), a functional describing the perturbations of the condensate is derived in detail. This problem is an analog of the Bogolubov transformation used in the study of quantum Bose gases in operator formalism. For a probe wave function in the form of a plane wave, a spectrum of (Bogoliubov) excitations was obtained, from which an equation describing the threshold momentum for the emergence of instability was derived. An important result of this paper is the dependence of the threshold on the momentum of a stationary condensate. For completeness of the presentation, the approximating expression in the form of a rapidly converging series is obtained for the corresponding dependence, and plots of the corresponding series for the exponential-trigonometric form factor are given. Finally, in the conclusion a quantum hydrodynamic theory for dipolar, axisymmetric quadrupolar and octupolar gases is briefly presented, giving a clue to the experimental determination of the form factors. |
| Databáze: | OpenAIRE |
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