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

DOI10.1007/BF02557351zbMath0991.81016arXivmath-ph/9811009OpenAlexW3101102896MaRDI QIDQ1567772

Alexander R. Its, Nikita A. Slavnov

Publication date: 9 September 2002

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/9811009

zbMATH Keywords

parabolic cylinder functionsFredholm determinant representationquantum nonlinear Schrödinger equationmatrix Riemann-Hilbert problemfinite coupling constantlarge time and distance asymptotic expansionlocal field dynamic temperature correlation functionlocalized Riemann-Hilbert problemnegative chemical potentialoperator-valued Riemann-Hilbert problempositive chemical potentialregularized integral operatorshifted saddle point

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) NLS equations (nonlinear Schrödinger equations) (35Q55) Boundary value problems in the complex plane (30E25)

Related Items (6)

Inverse scattering transform and soliton classification of higher-order nonlinear Schrödinger-Maxwell-Bloch equations ⋮ Form factor approach to dynamical correlation functions in critical models ⋮ Integral equations for correlation functions of a quantum one-dimensional Bose gas ⋮ On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin 1/2 chain ⋮ Riemann-Hilbert approach to a generalized sine kernel ⋮ On the origins of Riemann–Hilbert problems in mathematics*

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