Fingering of Electron Droplets in Nonuniform Magnetic Fields

A semiclassical analysis of a two-dimensional electron droplet in a high, nonuniform magnetic field predicts that the droplet will form ``fingered'' patterns upon increasing the number of electrons. We construct explicit examples of these patterns using methods first developed for the flow of two-dimensional viscous fluids. We complement our analytical results with Monte Carlo simulations of the droplet wavefunction, and find that at the point where the semiclassical analysis predicts a cusp on the interface, the droplet fissions--a type of ``quantum breakup'' phenomenon.