Low-density limit of dynamical correlations in the Lieb-Liniger model

Abstract

We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb-Liniger model, within an arbitrary eigenstate with a small particle density $\mathcal{D}$. They are valid for all space and time and any interaction strength $c>0$, and are the leading order of an expansion in $\mathcal{D}$. This expansion is obtained by writing the correlation functions as sums over form factors when formally decomposed into partial fractions.

30 pages