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Title: Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept

Abstract

The variational method of coupled Gaussian functions is applied to Bose-Einstein condensates with long-range interactions. The time dependence of the condensate is described by dynamical equations for the variational parameters. We present the method and analytically derive the dynamical equations from the time-dependent Gross-Pitaevskii equation. The stability of the solutions is investigated using methods of nonlinear dynamics. The concept presented in this article will be applied to Bose-Einstein condensates with monopolar 1/r and dipolar 1/r{sup 3} interaction in the subsequent article [S. Rau et al., Phys. Rev. A 82, 023611 (2010)], where we will present a wealth of phenomena obtained using the ansatz with coupled Gaussian functions.

Authors:
; ;  [1]
  1. Institut fuer Theoretische Physik 1, Universitaet Stuttgart, D-70550 Stuttgart (Germany)
Publication Date:
OSTI Identifier:
21448550
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 82; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.82.023610; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; GAUSS FUNCTION; INTERACTION RANGE; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; STABILITY; TIME DEPENDENCE; VARIATIONAL METHODS; WAVE EQUATIONS; CALCULATION METHODS; DIFFERENTIAL EQUATIONS; DISTANCE; EQUATIONS; FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS

Citation Formats

Rau, Stefan, Main, Joerg, and Wunner, Guenter. Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.82.023610.
Rau, Stefan, Main, Joerg, & Wunner, Guenter. Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept. United States. https://doi.org/10.1103/PHYSREVA.82.023610
Rau, Stefan, Main, Joerg, and Wunner, Guenter. 2010. "Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept". United States. https://doi.org/10.1103/PHYSREVA.82.023610.
@article{osti_21448550,
title = {Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept},
author = {Rau, Stefan and Main, Joerg and Wunner, Guenter},
abstractNote = {The variational method of coupled Gaussian functions is applied to Bose-Einstein condensates with long-range interactions. The time dependence of the condensate is described by dynamical equations for the variational parameters. We present the method and analytically derive the dynamical equations from the time-dependent Gross-Pitaevskii equation. The stability of the solutions is investigated using methods of nonlinear dynamics. The concept presented in this article will be applied to Bose-Einstein condensates with monopolar 1/r and dipolar 1/r{sup 3} interaction in the subsequent article [S. Rau et al., Phys. Rev. A 82, 023611 (2010)], where we will present a wealth of phenomena obtained using the ansatz with coupled Gaussian functions.},
doi = {10.1103/PHYSREVA.82.023610},
url = {https://www.osti.gov/biblio/21448550}, journal = {Physical Review. A},
issn = {1050-2947},
number = 2,
volume = 82,
place = {United States},
year = {Sun Aug 15 00:00:00 EDT 2010},
month = {Sun Aug 15 00:00:00 EDT 2010}
}