The Riemann-Hilbert problem associated with the quantum Nonlinear Schrodinger equation

Details The Riemann-Hilbert problem associated with the quantum Nonlinear Schrodinger equation The Riemann-Hilbert problem associated with the quantum Nonlinear Schrodinger equation

1997-06-20

arxiv.org/abs/hep-th/9706147v1

J.Phys.A30:8241-8255,1997

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, Latex, no figures

Scientific paper

10.1088/0305-4470/30/23/021

We consider the dynamical correlation functions of the quantum Nonlinear Schrodinger equation. In a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator-valued Fredholm determinant. In this paper we show that a Riemann-Hilbert problem can be associated with this Fredholm determinant. This Riemann-Hilbert problem formulation permits us to write down completely integrable equations for the Fredholm determinant and to perform an asymptotic analysis for the correlation function.

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