The propagator of the attractive delta-Bose gas in one dimension

2011/09/30 by Sylvain Prolhac, Herbert Spohn · 1 citation
Mathematics · Physics and Astronomy · #Analytic continuation #Ansatz #Bethe ansatz #Cold Atom Physics and Bose-Einstein Condensates #Continuation #Dimension (graph theory) #Propagator #Quantum #Random Matrices and Applications #Spectral Theory in Mathematical Physics #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1063/1.3663431

published as J. Math. Phys. 52, 122106 (2011) · 20 pages

openalex publication_date 2011/12/01 · arxiv created 2012/01/05 · arxiv updated 2012/01/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider the quantum δ-Bose gas on the infinite line. For repulsive interactions, Tracy and Widom have obtained an exact formula for the quantum propagator. In our contribution we explicitly perform its analytic continuation to attractive interactions. We also study the connection to the expansion of the propagator in terms of the Bethe ansatz eigenfunctions. Thereby we provide an independent proof of their completeness.

Citations

• Bethe ansatz solution for one-dimensional directed polymers in random media
• The dynamics of the one-dimensional delta-function Bose gas

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