Edge Asymptotics of Planar Electron Densities

The $N\to\infty$ limit of the edges of finite planar electron densities is discussed for higher Landau levels. For full filling, the particle number is correlated with the magnetic flux, and hence with the boundary location, making the $N\to\infty$ limit more subtle at the edges than in the bulk. In the $n^{\rm th}$ Landau level, the density exhibits $n$ distinct steps at the edge, in both circular and rectangular samples. The boundary characteristics for individual Landau levels, and for successively filled Landau levels, are computed in an asymptotic expansion.