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Spiraling attractors and quantum dynamics for a class of long-range magnetic fields |
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| Authors: | Horia D. Cornean |
| Affiliation: | a Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg, Denmark b Department of Mathematics, University of Virginia, Charlottesville, VA 22903, USA c Institut for Matematiske Fag, Aarhus Universitet, Ny Munkegade, 8000 Aarhus C, Denmark |
| Abstract: | We consider the long time behavior of a quantum particle in a 2D 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. |
| Keywords: | Classical and quantum dynamics Long range magnetic fields Asymptotic completeness |
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