Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle

2006/04/13 by J. F. van Diejen · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #math.SP #msc:81Q05

paper · pdf · doi:10.1007/s00220-006-0076-3

published as Commun. Math. Phys. 267 (2006), 451-476. · 25 pages, LaTeX

arxiv created 2006/04/13 · openalex publication_date 2006/08/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

We introduce an integrable lattice discretization of the quantum system of n bosonic particles on a ring interacting pairwise via repulsive delta potentials. The corresponding (finite-dimensional) spectral problem of the integrable lattice model is solved by means of the Bethe Ansatz method. The resulting eigenfunctions turn out to be given by specializations of the Hall-Littlewood polynomials. In the continuum limit the solution of the repulsive delta Bose gas due to Lieb and Liniger is recovered, including the orthogonality of the Bethe wave functions first proved by Dorlas (extending previous work of C.N. Yang and C.P. Yang).

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