Completely Integrable Equation for the Quantum Correlation Function of Nonlinear Schr\"odinger Eqaution

TL;DR

This paper derives an integro-differential equation generalizing the nonlinear Schrödinger equation to describe time and temperature-dependent correlation functions in a penetrable Bose gas, extending integrable models beyond free fermions.

Contribution

It introduces a novel integro-differential equation for correlation functions in non free fermionic models, generalizing classical integrable equations.

Findings

Derived an integro-differential equation for correlation functions

Generalized the nonlinear Schrödinger equation to continuum models

Applicable to penetrable Bose gas at finite temperature

Abstract

Correlation functions of exactly solvable models can be described by differential equation [Barough, McCoy, Wu]. In this paper we show that for non free fermionic case differential equations should be replaced by integro-differential equations. We derive an integro-differential equation, which describes time and temperature dependent correlation function $<\psi(0,0)\psi^\dagger(x,t)>_T$ of penetrable Bose gas. The integro-differential equation turns out be the continuum generalization of classical nonlinear Schr\"odinger equation.