Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

Journal Article · Fri Oct 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.043622· OSTI ID:20646416

Cherny, A Yu ^[1]; Brand, J ^[1]

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1. Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden (Germany)

A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g., in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behavior of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, crossover regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial.

• OSTI ID: 20646416
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN CONDENSATION
BOSONS
CORRELATIONS
COUPLING CONSTANTS
EVALUATION
FUNCTIONAL ANALYSIS
HARTREE-FOCK METHOD
HARTREE-FOCK-BOGOLYUBOV THEORY
POTENTIALS
RENORMALIZATION
TRAPPING
TWO-BODY PROBLEM
VARIATIONAL METHODS
WAVE EQUATIONS
WAVE FUNCTIONS