Impurity states in the one-dimensional Bose gas

TL;DR

This paper investigates the low-energy spectrum of a mobile impurity in a one-dimensional Bose gas, focusing on dilute and Tonks-Girardeau regimes using analytical and diagrammatic methods.

Contribution

It provides a detailed analysis of impurity states in 1D Bose gases, applying perturbation and diagrammatic techniques to two analytically accessible limits.

Findings

Characterization of impurity states in dilute Bose gas

Analysis of impurity behavior in Tonks-Girardeau gas

Application of perturbation and diagrammatic methods

Abstract

The detailed study of the low-energy spectrum for a mobile impurity in the one-dimensional bosonic enviroment is performed. Particularly we have considered only two analytically accessible limits, namely, the case of an impurity immersed in a dilute Bose gas, where one can use many-body perturbation techniques for low-dimensional bosonic systemsm and the case of the Tonks-Girardeau gas, for which the usual fermionic diagrammatic expansion up to the second order is applied.