Pair correlation function for a inhomogeneous Laughlin droplet

Question

Pair correlation function for the usual Laughlin droplet is defined as $g(\vec{r})$: $$\rho_0 g(\vec{r})=\frac{1}{N}\langle\sum_i^N \sum_{j \neq i}^N \delta(\vec{r}-\vec{r_i}+\vec{r_j})\rangle$$, where $\rho_0=\frac{\nu}{2\pi l_0^2}$. So if now the Laughlin droplet is inhomogeneous, meaning that the density function $\rho(\vec{r})$ is direction dependent, then should the pair correlation function still be defined the same as above, or do we need to change $\rho_0$ to something else?

Answer 1

If the system is anisotropic, you'll need to consider expanding the pair correlation function to accommodate the anisotropy - typically this is done using an expansion in spherical harmonics.