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The Aharonov–Bohm
effect in spectral asymptotics of the magnetic Schrödinger
operator
Gregory Eskin and James Ralston |
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Vol. 7 (2014), No. 1, 245–266
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Abstract |
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We show that in the absence of a magnetic field the spectrum of the magnetic Schrödinger operator in an annulus depends on the cosine of the flux associated with the magnetic potential. This result follows from an analysis of a singularity in the “wave trace” for this Schrödinger operator, and hence shows that even in the absence of a magnetic field the magnetic potential can change the asymptotics of the Schrödinger spectrum; that is, the Aharonov–Bohm effect takes place. We also study the Aharonov–Bohm effect for the magnetic Schrödinger operator on a torus. |
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In memory of Hans Duistermaat |
Keywords
Aharonov–Bohm effect, magnetic Schrödinger operator, wave
trace
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Mathematical Subject Classification 2010
Primary: 35P20, 35S30, 81S99
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Milestones
Received: 25 February 2013
Revised: 30 October 2013
Accepted: 27 November 2013
Published: 7 May 2014
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Authors |
| Gregory Eskin | |
| Mathematics Department University of California, Los Angeles Los Angeles, CA 90095-1555 United States |
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| James Ralston | |
| Mathematics Department University of California, Los Angeles Los Angeles, CA 90095-1555 United States |
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