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TMF, 2010, Volume 165, Number 1, Pages 32–47 (Mi tmf6562)  

This article is cited in 4 scientific papers (total in 4 papers)

Integral operators with the generalized sine kernel on the real axis

N. A. Slavnov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: We study the asymptotic properties of integral operators with the generalized sine kernel acting on the real axis. We obtain the formulas for the Fredholm determinant and the resolvent in the large-$x$ limit and consider some applications of the obtained results to the theory of integrable models.

Keywords: Fredholm determinant, resolvent, asymptotic expansion

DOI: https://doi.org/10.4213/tmf6562

Full text: PDF file (571 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 165:1, 1262–1274

Bibliographic databases:

Received: 27.04.2010

Citation: N. A. Slavnov, “Integral operators with the generalized sine kernel on the real axis”, TMF, 165:1 (2010), 32–47; Theoret. and Math. Phys., 165:1 (2010), 1262–1274

Citation in format AMSBIB
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\paper Integral operators with the~generalized sine kernel on the~real axis
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\pages 1262--1274
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kozlowski K.K., Maillet J.M., Slavnov N.A., “Correlation functions for one-dimensional bosons at low temperature”, J Stat Mech Theory Exp, 2011, P03019  crossref  isi  scopus
    2. Ossipov A., “Entanglement Entropy in Fermi Gases and Anderson's Orthogonality Catastrophe”, Phys. Rev. Lett., 113:13 (2014), 130402  crossref  adsnasa  isi  scopus
    3. Gamayun O. Pronko A.G. Zvonarev M.B., “Impurity Green's Function of a One-Dimensional Fermi Gas”, Nucl. Phys. B, 892 (2015), 83–104  crossref  mathscinet  zmath  isi  scopus
    4. Gamayun O., Pronko A.G., Zvonarev M.B., “Time and temperature-dependent correlation function of an impurity in one-dimensional Fermi and Tonks?Girardeau gases as a Fredholm determinant”, New J. Phys., 18 (2016), 045005  crossref  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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