Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1999-05-04
Phys. Rev. B 60, 10971 (1999)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
15 pages, 12 embedded figures, submitted to Phys. Rev. B
Scientific paper
10.1103/PhysRevB.60.10971
We present a theoretical study of the excitations on the edge of a two-dimensional electron system in a perpendicular magnetic field in terms of a contour dynamics formalism. In particular, we focus on edge excitations in the quantum Hall effect. Beyond the usual linear approximation, a non-linear analysis of the shape deformations of an incompressible droplet yields soliton solutions which correspond to shapes that propagate without distortion. A perturbative analysis is used and the results are compared to analogous systems, like vortex patches in ideal hydrodynamics. Under a local induction approximation we find that the contour dynamics is described by a non-linear partial differential equation for the curvature: the modified Korteweg-de Vries equation. PACS number(s): 73.40.Hm, 02.40.Ma, 03.40.Gc, 11.10.Lm
Dorsey Alan T.
Wexler Carlos
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