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

Sylvain Prolhac; Herbert Spohn

doi:10.1063/1.3663431

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

Sylvain Prolhac
, Herbert Spohn

TUM Emeriti of Excellence

Technical University of Munich

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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.

Original language	English
Article number	122106
Journal	Journal of Mathematical Physics
Volume	52
Issue number	12
DOIs	https://doi.org/10.1063/1.3663431
State	Published - 20 Dec 2011

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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.",

author = "Sylvain Prolhac and Herbert Spohn",

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AU - Spohn, Herbert

N1 - Funding Information: We thank Tomohiro Sasamoto for most instructive discussions. S.P. acknowledges the support through a Deutsche Forschungsgemeinschaft (DFG) research project (SP181-24).

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N2 - 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.

AB - 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.

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

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