Exact ground state of finite Bose-Einstein condensates on a ring

Journal Article · Thu Sep 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.033613· OSTI ID:20718601

Sakmann, Kaspar; Streltsov, Alexej I; Alon, Ofir E; Cederbaum, Lorenz S ^[1]

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1. Theoretische Chemie, Universitaet Heidelberg, 69120 Heidelberg (Germany)

The exact ground state of the many-body Schroedinger equation for N bosons on a one-dimensional ring interacting via a pairwise {delta}-function interaction is presented for up to 50 particles. The solutions are obtained by solving Lieb and Liniger's system of coupled transcendental equations numerically for finite N. The ground-state energies for repulsive and attractive interactions are shown to be smoothly connected at the point of zero interaction strength, implying that the Bethe ansatz can be used also for attractive interactions for all cases studied. For repulsive interactions the exact energies are compared to (i) Lieb and Liniger's thermodynamic limit solution and (ii) the Tonks-Girardeau gas limit. It is found that the energy of the thermodynamic limit solution can differ substantially from that of the exact solution for finite N when the interaction is weak or when N is small. A simple relation between the Tonks-Girardeau gas limit and the solution for finite interaction strength is revealed. For attractive interactions we find that the true ground-state energy is given to a good approximation by the energy of the system of N attractive bosons on an infinite line, provided the interaction is stronger than the critical interaction strength of mean-field theory.

• OSTI ID: 20718601
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN CONDENSATION
BOSONS
DELTA FUNCTION
EXACT SOLUTIONS
GROUND STATES
MANY-BODY PROBLEM
MEAN-FIELD THEORY
ONE-DIMENSIONAL CALCULATIONS
SCHROEDINGER EQUATION