Exact and Asymptotic Features of the Edge Density Profile for the One Component Plasma in Two Dimensions

Abstract

There is a well known analogy between the Laughlin trial wave function for the fractional quantum Hall effect, and the Boltzmann factor for the two-dimensional one-component plasma. The latter requires continuation beyond the finite geometry used in its derivation. We consider both disk and cylinder geometry, and focus attention on the exact and asymptotic features of the edge density. At the special coupling (Formula presented.) the system is exactly solvable. In particular the k-point correlation can be written as a k × k determinant, allowing the edge density to be computed to first order in Γ - 2. A double layer structure is found, which in turn implies an overshoot of the density as the..