A. R. Its, N. A. Slavnov, “On the Riemann–Hilbert approach to asymptotic analysis of the correlation functions of the quantum nonlinear Schrödinger equation: Interacting fermion case”, TMF, 119:2 (1999), 179–248; Theoret. and Math. Phys., 119:2 (1999), 541

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Teoreticheskaya i Matematicheskaya Fizika, 1999, Volume 119, Number 2, Pages 179–248
DOI: https://doi.org/10.4213/tmf736 (Mi tmf736)

This article is cited in 15 scientific papers (total in 15 papers)

On the Riemann–Hilbert approach to asymptotic analysis of the correlation functions of the quantum nonlinear Schrödinger equation: Interacting fermion case

A. R. Its^a, N. A. Slavnov^b

^a IUPUI, Department of Mathematical Sciences
^b Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (585 kB) Citations (15)

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DOI: https://doi.org/10.4213/tmf736

Abstract: We consider the local field dynamic temperature correlation function of the quantum nonlinear Schrödinger equation with a finite coupling constant. This correlation function admits a Fredholm determinant representation. The related operator-valued Riemann–Hilbert problem is used to analyze the leading term of the large time and distance asymptotic expansion of the correlation function.

Received: 28.10.1998

English version:
Theoretical and Mathematical Physics, 1999, Volume 119, Issue 2, Pages 541–593
DOI: https://doi.org/10.1007/BF02557351

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. R. Its, N. A. Slavnov, “On the Riemann–Hilbert approach to asymptotic analysis of the correlation functions of the quantum nonlinear Schrödinger equation: Interacting fermion case”, TMF, 119:2 (1999), 179–248; Theoret. and Math. Phys., 119:2 (1999), 541–593

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf736

https://doi.org/10.4213/tmf736

https://www.mathnet.ru/eng/tmf/v119/i2/p179

This publication is cited in the following 15 articles:

Zhi-Xuan Meng, Shuai-Xia Xu, Yu-Qiu Zhao, “Large time and distance asymptotics of the one-dimensional impenetrable Bose gas and Painlevé IV transition”, Physica D: Nonlinear Phenomena, 475 (2025), 134589
Bothner T., “On the Origins of Riemann-Hilbert Problems in Mathematics”, Nonlinearity, 34:4 (2021), R1–R73
Zhi-Qiang Li, Shou-Fu Tian, Wei-Qi Peng, Jin-Jie Yang, “Inverse scattering transform and soliton classification of higher-order nonlinear Schrödinger–Maxwell–Bloch equations”, Theoret. and Math. Phys., 203:3 (2020), 709–725
Gharakhloo R., Its A.R., Kozlowski K.K., “Riemann-Hilbert Approach to a Generalized Sine Kernel”, Lett. Math. Phys., 110:2 (2020), 297–325
Kozlowski K.K., “On the Thermodynamic Limit of Form Factor Expansions of Dynamical Correlation Functions in the Massless Regime of the Xxz Spin 1/2 Chain”, J. Math. Phys., 59:9, SI (2018), 091408
Brun Ya., Dubail J., “One-Particle Density Matrix of Trapped One-Dimensional Impenetrable Bosons From Conformal Invariance”, SciPost Phys., 2:2 (2017), UNSP 012
Its A.R., Kozlowski K.K., “Large- x Analysis of an Operator-Valued Riemann?Hilbert Problem”, Int. Math. Res. Notices, 2016, no. 6, 1776–1806
Its A.R., Kozlowski K.K., “On Determinants of Integrable Operators With Shifts”, Int. Math. Res. Notices, 2014, no. 24, 6826–6838
Patu O.I. Kluemper A., “Correlation Lengths of the Repulsive One-Dimensional Bose Gas”, Phys. Rev. A, 88:3 (2013), 033623
Kitanine N. Kozlowski K.K. Maillet J.M. Slavnov N.A. Terras V., “Form Factor Approach to Dynamical Correlation Functions in Critical Models”, J. Stat. Mech.-Theory Exp., 2012, P09001
Kozlowski K.K., Terras V., “Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schrodinger model”, J Stat Mech Theory Exp, 2011, P09013
Kozlowski K.K., Maillet J.M., Slavnov N.A., “Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas”, J Stat Mech Theory Exp, 2011, P03018
Caux, JS, “One-particle dynamical correlations in the one-dimensional Bose gas”, Journal of Statistical Mechanics-Theory and Experiment, 2007, P01008
R. K. Bullough, N. M. Bogolyubov, V. S. Kapitonov, K. L. Malyshev, I. Timonen, A. V. Rybin, G. G. Varzugin, M. Lindberg, “Quantum Integrable and Nonintegrable Nonlinear Schrödinger Models for Realizable Bose–Einstein Condensation in $d+1$ Dimensions $(d=1,2,3)$ ”, Theoret. and Math. Phys., 134:1 (2003), 47–61
N. A. Slavnov, “Integral equations for correlation functions of a quantum one-dimensional Bose gas”, Theoret. and Math. Phys., 121:1 (1999), 1358–1376

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

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