Figure 6
Neighbor counting statistics for the Laughlin states, N = 200, q = 1, 10, 90. The blue line shows the average numbers of particles n(l), within the chord length l. The green line is a guide to the eye, and shows and approximation of a sharp correlation hole around each particle. The precise form is \({\tilde{n}}(l)=N{l}^{2}/4-1\) (for \(l > \sqrt{4/N}\)) which is the expected average number of particles if the other N − 1 particles are distributed with uniformly over the sphere, but with a region of size \(l=\sqrt{4/N}\) unoccupied. The inset shows \(g(l)=\frac{2{n}^{{\prime} }(l)}{Nl}\) where the derivative is with respect to l. This is identical to the two-point correlation function. It also shows the number variance σ(l) as a function of l.
