2003/12/31 by Murray T. Batchelor, M. T. Batchelor, Xi-Wen Guan +3 · 3 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum, superfluid, helium dynamics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/37/42/l01
published as J. Phys. A 37 (2004) L497-L504 (final version) · 9 pages, 1 figure. This revised version makes contact with earlier work of Gaudin and clarifies the link to the BCS pairing model
arxiv created 2004/08/03 · openalex publication_date 2004/10/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The Bethe roots describing the ground-state energy of the integrable one-dimensional (1D) model of interacting bosons with weakly repulsive two-body delta interactions are seen to satisfy the set of Richardson equations appearing in the strong coupling limit of an integrable BCS pairing model. The BCS model describes boson–boson interactions with zero centre of mass momentum of pairs. It follows that the Bethe roots of the weakly interacting boson model are given by the zeros of Laguerre polynomials. The ground-state energy and the lowest excitation are obtained explicitly via the Bethe roots. A direct link has thus been established, in the context of integrable 1D models, between bosons interacting via weakly repulsive two-body delta interactions and strongly interacting BCS boson pairs.