Viscous Fingering and the Shape of an Electronic Droplet in the Quantum Hall Regime

We show that the semiclassical dynamics of an electronic droplet, confined in a plane in a quantizing inhomogeneous magnetic field in the regime where the electrostatic interaction is negligible, is similar to viscous (Saffman-Taylor) fingering on the interface between two fluids with different viscosities confined in a Hele-Shaw cell. Both phenomena are described by the same equations with scales differing by a factor of up to ${10}^{-9\mathrm{}}$. We also report the quasiclassical wave function of the droplet in an inhomogeneous magnetic field.