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Title: Vortex equations governing the fractional quantum Hall effect

An existence theory is established for a coupled non-linear elliptic system, known as “vortex equations,” describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the existence and uniqueness of multiple vortices over a doubly periodic domain and the full plane. In the doubly periodic situation, explicit sufficient and necessary conditions are obtained that relate the size of the domain and the vortex numbers. For the full plane case, existence is established for all finite-energy solutions and exponential decay estimates are proved. Quantization phenomena of the magnetic flux are found in both cases.
Authors:
 [1]
  1. Department of Mathematics, Polytechnic School of Engineering, New York University, Brooklyn, New York 11201 (United States)
Publication Date:
OSTI Identifier:
22479592
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ELECTRONS; EQUATIONS; HALL EFFECT; MAGNETIC FLUX; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PERIODICITY; QUANTIZATION; VARIATIONAL METHODS; VORTEX THEORY