Physics on the edge: contour dynamics, waves and solitons in the quantum Hall effect

摘要

We present a theoretical study of the excitations on the edge of atwo-dimensional electron system in a perpendicular magnetic field in terms of acontour dynamics formalism. In particular, we focus on edge excitations in thequantum Hall effect. Beyond the usual linear approximation, a non-linearanalysis of the shape deformations of an incompressible droplet yields solitonsolutions which correspond to shapes that propagate without distortion. Aperturbative analysis is used and the results are compared to analogoussystems, like vortex patches in ideal hydrodynamics. Under a local inductionapproximation we find that the contour dynamics is described by a non-linearpartial differential equation for the curvature: the modified Korteweg-de Vriesequation. PACS number(s): 73.40.Hm, 02.40.Ma, 03.40.Gc, 11.10.Lm