Viscous fingering and the shape of an electronic droplet in the quantum Hall regime.

@article{Agam2001ViscousFA,
  title={Viscous fingering and the shape of an electronic droplet in the quantum Hall regime.},
  author={Oded Agam and Eldad Bettelheim and Paul B. Wiegmann and Anton Zabrodin},
  journal={Physical review letters},
  year={2001},
  volume={88 23},
  pages={
          236801
        }
}
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). We also report the quasiclassical wave function of the… 
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