Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. II. Applications

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

DOI:https://doi.org/10.1103/PHYSREVA.82.023611· OSTI ID:21448551

Rau, Stefan; Main, Joerg; Cartarius, Holger; Koeberle, Patrick; Wunner, Guenter ^[1]

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

Bose-Einstein condensates with an attractive 1/r interaction and with dipole-dipole interaction are investigated in the framework of the Gaussian variational ansatz introduced by S. Rau, J. Main, and G. Wunner [Phys. Rev. A 82, 023610 (2010)]. We demonstrate that the method of coupled Gaussian wave packets is a full-fledged alternative to direct numerical solutions of the Gross-Pitaevskii equation, or even superior in that coupled Gaussians are capable of producing both stable and unstable states of the Gross-Pitaevskii equation and thus of giving access to yet unexplored regions of the space of solutions of the Gross-Pitaevskii equation. As an alternative to numerical solutions of the Bogoliubov-de Gennes equations, the stability of the stationary condensate wave functions is investigated by analyzing the stability properties of the dynamical equations of motion for the Gaussian variational parameters in the local vicinity of the stationary fixed points. For blood-cell-shaped dipolar condensates it is shown that on the route to collapse the condensate passes through a pitchfork bifurcation, where the ground state itself turns unstable, before it finally vanishes in a tangent bifurcation.

• OSTI ID: 21448551
• Journal Information: Physical Review. A, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevA.82.023611; (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
74 ATOMIC AND MOLECULAR PHYSICS
BIFURCATION
BOSE-EINSTEIN CONDENSATION
DIPOLES
ENERGY LEVELS
EQUATIONS OF MOTION
GAUSS FUNCTION
INTERACTION RANGE
NUMERICAL SOLUTION
STABILITY
VARIATIONAL METHODS
WAVE EQUATIONS
WAVE FUNCTIONS
WAVE PACKETS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DISTANCE
EQUATIONS
FUNCTIONS
MATHEMATICAL SOLUTIONS
MULTIPOLES
PARTIAL DIFFERENTIAL EQUATIONS