Fingered” Patterns in 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 wave function, 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.