Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime

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