Maxwell-Bloch equation and Correlation function for penetrable Bose gas

TL;DR

This paper analyzes the static temperature-dependent correlation functions of a one-dimensional quantum nonlinear Schrödinger equation in the small mass limit, linking them to Maxwell-Bloch equations and providing asymptotic behavior insights.

Contribution

It introduces a novel approach to describe correlation functions via Maxwell-Bloch equations in the small mass limit of the Bose gas.

Findings

Correlation functions simplified in the small mass limit.

Asymptotic behavior of correlation functions evaluated.

Determinant representation reduces to vacuum expectation values.

Abstract

We consider the quantum nonlinear Schr\"odinger equation in one space and one time dimension. We are interested in the non-free-fermionic case. We consider static temperature-dependent correlation functions. The determinant representation for correlation functions simplifies in the small mass limit of the Bose particle. In this limit we describe the correlation functions by the vacuum expectation value of a boson-valued solution for Maxwell-Bloch differential equation. We evaluate long-distance asymptotics of correlation functions in the small mass limit.