Topological damping of Aharonov-Bohm effect: quantum graphs and vertex conditions
https://doi.org/10.17586/2220-8054-2015-6-3-309-319
Abstract
The magnetic Schr¨ odinger operator was studied on a figure 8-shaped graph. It is shown that for specially chosen vertex conditions, the spectrum of the magnetic operator is independent of the flux through one of the loops, provided the flux through the other loop is zero. Topological reasons for this effect are explained.
Supporting agencies: The work of PK was partially supported by the Swedish Research Council (Grant D0497301) and ZiF-Zentrum f¨ ur interdisziplinre Forschung, Bielefeld (Coopera tion Group Discrete and continuous models in the theory of networks). The authors would like to thank Muhammad Usman for careful reading of the manuscript.
About the Authors
O. Kurasov
Department of Mathematics, Stockholm University
Sweden
Sweden
106 91 Stockholm
A. Serio
Department of Mathematics, Stockholm University
Sweden
Sweden
106 91 Stockholm
Review
For citations:
Kurasov O., Serio A. Topological damping of Aharonov-Bohm effect: quantum graphs and vertex conditions. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(3):309–319. https://doi.org/10.17586/2220-8054-2015-6-3-309-319
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