The Riemann-Hilbert problem associated with the quantum Nonlinear Schrodinger equation
High Energy Physics - Theory
2008-11-26 v1 Condensed Matter
Quantum Algebra
Exactly Solvable and Integrable Systems
q-alg
solv-int
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.
Cite
@article{arxiv.hep-th/9706147,
title = {The Riemann-Hilbert problem associated with the quantum Nonlinear Schrodinger equation},
author = {V. E. Korepin and N. A. Slavnov},
journal= {arXiv preprint arXiv:hep-th/9706147},
year = {2008}
}
Comments
21 pages, Latex, no figures