Local spectral density of an interacting one-dimensional Bose gas with an impurity

TL;DR

This paper derives an analytic expression for the local spectral density of a weakly interacting one-dimensional Bose gas with a static impurity, valid across all distances and frequencies, using the Bogoliubov-de Gennes approximation.

Contribution

It provides a comprehensive analytic formula for the local spectral density in a 1D Bose gas with impurity, extending understanding of impurity effects in quantum gases.

Findings

Analytic expression for spectral density obtained

Valid for all distances and frequencies

Applicable for positive impurity coupling strengths

Abstract

A weakly interacting Bose gas with a single static impurity is studied in one dimension. The local spectral density is evaluated and an analytic expression valid for positive strengths of the impurity coupling to the bosons, at all distances and at all frequencies is obtained using the Bogoliubov-de Gennes approximation.