Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2002-01-09
Physics Reports 367 (2002) 249-385
Nonlinear Sciences
Chaotic Dynamics
170 pages, 48 figures (high quality version available at http://www.klaus-hornberger.de)
Scientific paper
10.1016/S0370-1573(02)00141-2
Magnetic edge states are responsible for various phenomena of magneto-transport. Their importance is due to the fact that, unlike the bulk of the eigenstates in a magnetic system, they carry electric current along the boundary of a confined domain. Edge states can exist both as interior (quantum dot) and exterior (anti-dot) states. In the present report we develop a consistent and practical spectral theory for the edge states encountered in magnetic billiards. It provides an objective definition for the notion of edge states, is applicable for interior and exterior problems, facilitates efficient quantization schemes, and forms a convenient starting point for both the semiclassical description and the statistical analysis. After elaborating these topics we use the semiclassical spectral theory to uncover nontrivial spectral correlations between the interior and the exterior edge states. We show that they are the quantum manifestation of a classical duality between the trajectories in an interior and an exterior magnetic billiard.
Hornberger Klaus
Smilansky Uzy
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