skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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.

Authors:
 [1];  [1]
  1. Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden (Germany)
Publication Date:
OSTI Identifier:
20646416
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 70; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.70.043622; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL 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

Citation Formats

Cherny, A Yu, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, and Brand, J. Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation. United States: N. p., 2004. Web. doi:10.1103/PhysRevA.70.043622.
Cherny, A Yu, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, & Brand, J. Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation. United States. https://doi.org/10.1103/PhysRevA.70.043622
Cherny, A Yu, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, and Brand, J. 2004. "Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation". United States. https://doi.org/10.1103/PhysRevA.70.043622.
@article{osti_20646416,
title = {Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation},
author = {Cherny, A Yu and Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna and Brand, J},
abstractNote = {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.},
doi = {10.1103/PhysRevA.70.043622},
url = {https://www.osti.gov/biblio/20646416}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 70,
place = {United States},
year = {Fri Oct 01 00:00:00 EDT 2004},
month = {Fri Oct 01 00:00:00 EDT 2004}
}