One-Particle Reduced Density Matrix of Impenetrable Bosons in One Dimension at Zero Temperature

We report the large-$\mathcal{r}$ and small-$\mathcal{r}$ expansions of the one-particle reduced density $\stackrel{\mathrm{`}}{\mathrm{m}}$atrix $\rho \left(\mathcal{r}\right)$ of a system of impenetrable bosons in one dimension at zero temperature. These expansions were derived from an exact calculation of $\rho \left(\mathcal{r}\right)$ to be reported elsewhere. We find that the large-$\mathcal{r}$ expansion of $\rho \left(\mathcal{r}\right)$ contains oscillatory terms which we relate to the analytic structure of the momentum density function $n\left(k\right)\mathrm{}$.