Abstract
We show that in the absence of a magnetic field the spectrum of the magnetic Schr\"odinger 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 Schr\"odinger operator, and hence shows that even in the absence of a magnetic field the magnetic potential can change the asymptotics of the Schr\"odinger spectrum, i.e. the Aharonov-Bohm effect takes place. We also study the Aharonov-Bohm effect for the magnetic Schr\"odinger operator on a torus.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
