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

Abstract

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.

21 pages, Latex, no figures

Cited by in corpus (3)

• Time and Temperature Dependent Correlation Functions of 1D Models of Quantum Statistical Mechanics
• On the Riemann-Hilbert approach to the asymptotic analysis of the correlation functions of the Quantum Nonlinear Schrodinger equation. Non-free fermionic case
• Integral equations for the correlation functions of the quantum one-dimensional Bose gas