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

2001/11/30 by Oded Agam, Eldad Bettelheim, P. Wiegmann +1 · 3 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics #Theoretical and Computational Physics #cond-mat #hep-th #nlin.SI

paper · pdf · doi:10.1103/physrevlett.88.236801

published as Phys.Rev.Lett. 88 (2002) 236801 · 4 pages, 1 eps figure included

arxiv created 2002/02/14 · openalex publication_date 2002/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 droplet in an inhomogeneous magnetic field.

Citations

• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid

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