Reply to arXiv:1002.4366, "Comment on `Motion of an impurity in an ultracold quasi-one-dimensional gas of hard-core bosons`", by S. Giraud and R. Combescot

TL;DR

This paper acknowledges a correction to a previous work regarding impurity-boson distribution functions in a 1D gas, confirming that their results remain accurate for large impurity mass ratios despite the correction.

Contribution

The authors revise their earlier findings by including a previously neglected term, improving the accuracy of impurity-boson distribution predictions in 1D gases.

Findings

Results are highly accurate for large impurity-boson mass ratios.

Qualitative correctness maintained across all mass ratios and coupling constants.

Acknowledgment of the non-negligible contribution of the previously dropped term.

Abstract

In their Comment [1] Giraud and Combescot point out that the contribution to the impurity-boson distribution function $\rho_{bi}(x-y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but nevertheless our results for $\rho_{bi}$ are highly accurate for large impurity-boson mass ratio $m_i/m$ and remain qualitatively correct for all values of $m_i/m$ and all values of the boson-impurity coupling constant.