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

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.023610· OSTI ID:21448550

Rau, Stefan; Main, Joerg; Wunner, Guenter ^[1]

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1. Institut fuer Theoretische Physik 1, Universitaet Stuttgart, D-70550 Stuttgart (Germany)

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.

• OSTI ID: 21448550
• Journal Information: Physical Review. A, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevA.82.023610; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

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