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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2002-36
November 2002

Spiraling attractors and quantum dynamics for a class of long-range magnetic fields


Horia D. Cornean, Ira Herbst, Erik Skibsted


We consider the long time behavior of a quantum particle in a 2-D magnetic field which is homogeneous of degree -1. If the field never vanishes, above a certain energy the associated classical dynamical system has a globally attracting periodic orbit in a reduced phase space. For that energy regime, we construct a simple approximate evolution based on this attractor, and prove that it completely describes the quantum dynamics of our system.

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