989 research outputs found
Physics on the edge: contour dynamics, waves and solitons in the quantum Hall effect
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.LmComment: 15 pages, 12 embedded figures, submitted to Phys. Rev.
Solitons on the edge of a two-dimensional electron system
We present a study of the excitations of the edge of a two-dimensional
electron droplet in a magnetic field in terms of a contour dynamics formalism.
We find that, beyond the usual linear approximation, the non-linear analysis
yields soliton solutions which correspond to uniformly rotating shapes. These
modes are found from a perturbative treatment of a non-linear eigenvalue
problem, and as solutions to a modified Korteweg-de Vries equation resulting
from a local induction approximation to the nonlocal contour dynamics. We
discuss applications to the edge modes in the quantum Hall effect.Comment: 4 pages, 2 eps figures (included); to appear in Phys. Rev. Letter
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