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2014 The Aharonov–Bohm effect in spectral asymptotics of the magnetic Schrödinger operator
Gregory Eskin, James Ralston
Anal. PDE 7(1): 245-266 (2014). DOI: 10.2140/apde.2014.7.245

Abstract

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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Gregory Eskin. James Ralston. "The Aharonov–Bohm effect in spectral asymptotics of the magnetic Schrödinger operator." Anal. PDE 7 (1) 245 - 266, 2014. https://doi.org/10.2140/apde.2014.7.245

Information

Received: 25 February 2013; Revised: 30 October 2013; Accepted: 27 November 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1293.35186
MathSciNet: MR3219506
Digital Object Identifier: 10.2140/apde.2014.7.245

Subjects:
Primary: 35P20 , 35S30 , 81S99

Keywords: Aharonov–Bohm effect , magnetic Schrödinger operator , wave trace

Rights: Copyright © 2014 Mathematical Sciences Publishers

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