JMP Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Journal of Mathematical Physics / Volume 52 / Issue 12 / ARTICLES / Quantum Mechanics (General and Nonrelativistic)

J. Math. Phys. 52, 122106 (2011); http://dx.doi.org/10.1063/1.3663431 (17 pages)

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

Sylvain Prolhac and Herbert Spohn

Zentrum Mathematik and Physik Department, Technische Universität München, D-85747 Garching, Germany

View MapView Map

(Received 23 September 2011; accepted 2 November 2011; published online 30 December 2011)

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.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. δ-BOSE GAS WITH REPULSIVE INTERACTION (κ < 0)
  3. δ-BOSE GAS WITH ATTRACTIVE INTERACTION (κ > 0)
  4. ANALYTIC CONTINUATION FROM κ < 0 To κ > 0
    1. Contribution of the residues
    2. Partitions and permutations
    3. Pole structure of the integrand and summation over Bethe eigenstates
  5. THE SPECIAL CASE x = y = 0
  6. CONCLUSIONS

RELATED DATABASES

To view database links for this article, you need to log in.

KEYWORDS and PACS

Keywords

boson systems, eigenvalues and eigenfunctions

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3663431

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    E. H. Lieb, “Exact analysis of an interacting Bose gas. II. The excitation spectrum,” Phys. Rev. 130, 1616–1624 (1963).

    C. N. Yang and C. P. Yang, “Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction,” J. Math. Phys. 10, 1115–1122 (1969)JMAPAQ000010000007001115000001.

    M. Gaudin, “Bose gas in one dimension. I. The closure property of the scattering wavefunctions,” J. Math. Phys. 12, 1674–1676 (1971)JMAPAQ000012000008001674000001.

    M. Gaudin, “Bose gas in one dimension. II. Orthogonality of the scattering states,” J. Math. Phys. 12, 1677–1680 (1971)JMAPAQ000012000008001677000001.

    M. Gaudin, “Boundary energy of a Bose gas in one dimension,” Phys. Rev. A 4, 386–394 (1971).

    J. B. McGuire, “Study of exactly soluble one-dimensional N-body problems,” J. Math. Phys. 5, 622–636 (1964)JMAPAQ000005000005000622000001.

    P. Calabrese and J. S. Caux, “Correlation functions of the one-dimensional attractive Bose gas,” Phys. Rev. Lett. 98, 150403 (2007).

    V. B. Priezzhev, “Exact nonstationary probabilities in the asymmetric exclusion process on a ring,” Phys. Rev. Lett, 91, 050601 (2003).


For access to citing articles, you need to log in.



Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. The propagator of the attractive delta-Bose gas in one dimension
  2. An alternative approach to Schrödinger equations with a spatially varying mass
  3. On the supremum and infimum of bounded quantum observables
  4. The stochastisation hypothesis and the spacing of planetary systems
  5. When do measures on the space of connections support the triad operators of loop quantum gravity?
Go to AIP Home
Copyright © American Institute of Physics
close