2005/05/12 by Kaspar Sakmann, Alexej I. Streltsov, Ofir E. Alon +1 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #cond-mat.other
paper · pdf · doi:10.1103/physreva.72.033613
published as Phys. Rev. A 72, 033613 (2005) · 28 pages, 11 figures
arxiv created 2005/05/12 · openalex publication_date 2005/09/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The exact ground state of the many-body Schr"odinger equation for N bosons on a one-dimensional ring interacting via a pairwise \ensuremathδ-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.