Magnetic interpretation of the nodal defect on graphs

Details Magnetic interpretation of the nodal defect on graphs Magnetic interpretation of the nodal defect on graphs

2012-01-05

arxiv.org/abs/1201.1110v1

Physics

Mathematical Physics

Scientific paper

In this note, we present a natural proof of a recent and surprising result of
Gregory Berkolaiko (arXiv 1110.5373) interpreting the "Courant nodal defect" of
a Schr\"odinger operator on a finite graph as a Morse index associated to the
deformations of the operator by switching on a magnetic field. This proof is
inspired by a nice paper of Miroslav Fiedler published in 1975.

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