Comment on "Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons [Phys. Rev. A 79, 033610 (2009)]"

TL;DR

This paper critiques a recent study on impurity dynamics in a 1D hard-core boson gas, clarifying that their general results are only valid when the impurity mass is infinite, due to an identified error.

Contribution

It identifies and corrects an error in a recent theoretical analysis of impurity motion in a 1D bosonic system, clarifying the valid conditions for their results.

Findings

The original study's general results are only valid for infinite impurity mass.

An error was found in the initial assumptions of the previous work.

Corrected understanding aligns with physical intuition and known exact results.

Abstract

Very recently Girardeau and Minguzzi [arXiv:0807.3366v2, Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they deal with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial step is erroneous, contradicting both physical intuition and known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.