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

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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 165, Number 1, Pages 32–47
DOI: https://doi.org/10.4213/tmf6562 (Mi tmf6562)

This article is cited in 10 scientific papers (total in 10 papers)

Integral operators with the generalized sine kernel on the real axis

N. A. Slavnov

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

Full-text PDF (571 kB) Citations (10)

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

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

$x$ limit and consider some applications of the obtained results to the theory of integrable models.

Keywords: Fredholm determinant, resolvent, asymptotic expansion.

Received: 27.04.2010

English version:
Theoretical and Mathematical Physics, 2010, Volume 165, Issue 1, Pages 1262–1274
DOI: https://doi.org/10.1007/s11232-010-0108-1

Bibliographic databases:

Document Type: Article

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/tmf6562

https://doi.org/10.4213/tmf6562

https://www.mathnet.ru/eng/tmf/v165/i1/p32

This publication is cited in the following 10 articles:

Jordan Hristov, “A non-linear diffusion problem with power-law diffusivity: An approximate solution experimenting with a modified sinc function”, MMNSA, 4:5-Special Issue: ICAME'24 (2024), 6
O Gamayun, Yu Zhuravlev, N Iorgov, “On Landauer–Büttiker formalism from a quantum quench”, J. Phys. A: Math. Theor., 56:20 (2023), 205203
Daniel Chernowitz, Oleksandr Gamayun, “On the dynamics of free-fermionic tau-functions at finite temperature”, SciPost Phys. Core, 5:1 (2022)
Oleksandr Gamayun, Miłosz Panfil, Felipe Taha Sant'Ana, “Mobile impurity in a one-dimensional gas at finite temperatures”, Phys. Rev. A, 106:2 (2022)
Gamayun O. Iorgov N. Zhuravlev Yu., “Effective Free-Fermionic Form Factors and the Xy Spin Chain”, SciPost Phys., 10:3 (2021), 070
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
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
Ossipov A., “Entanglement Entropy in Fermi Gases and Anderson's Orthogonality Catastrophe”, Phys. Rev. Lett., 113:13 (2014), 130402
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
K K Kozlowski, J M Maillet, N A Slavnov, “Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas”, J. Stat. Mech., 2011:03 (2011), P03018

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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