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

Expanding Stereochemical and Skeletal Diversity Using Petasis Reactions and 1,3-Dipolar Cycloadditions

A short and modular synthetic pathway using intramolecular 1,3-dipolar cycloaddition reactions and yielding functionalized isoxazoles, isoxazolines, and isoxazolidines is described. The change in shape of previous compounds and those in this study is quantified and compared using principal moment-of-inertia shape analysis.Chemistry and Chemical Biolog