On the Riemann-Hilbert approach to the asymptotic analysis of the correlation functions of the Quantum Nonlinear Schrodinger equation. Non-free fermionic case

TL;DR

This paper employs a Riemann-Hilbert approach to analyze the asymptotic behavior of correlation functions in the Quantum Nonlinear Schrödinger equation with finite coupling, revealing leading order dynamics in large time and distance regimes.

Contribution

It introduces a novel application of the Riemann-Hilbert method to the non-free fermionic case of the Quantum Nonlinear Schrödinger equation for asymptotic analysis.

Findings

Derivation of the leading asymptotic term for the correlation function.

Representation of the correlation function as a Fredholm determinant.

Application of the Riemann-Hilbert problem to analyze asymptotics.

Abstract

We consider the local field dynamical temperature correlation function of the Quantum Nonlinear Schrodinger equation with the finite coupling constant. This correlation function admits a Fredholm determinant representation. The related operator-valued Riemann--Hilbert problem is used for analysing the leading term of the large time and long distance asymptotics of the correlation function.