# Pair correlation function for a inhomogeneous Laughlin droplet

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?

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## 1 Answer

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.

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Any paper on that I can read about? – huyichen Feb 2 '12 at 18:08

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I'll look for some others, but for the case applied to metallic glasses try: prl.aps.org/abstract/PRL/v105/i20/e205502, or prb.aps.org/abstract/PRB/v35/i5/p2162_1 Also, "Underneath the Bragg Peaks" by Egami has a section on the anisotropic pair distribution function. – Jen Feb 2 '12 at 20:20
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