Wednesday, October 10, 2012

1201.1110 (Yves Colin De Verdière)

Magnetic interpretation of the nodal defect on graphs    [PDF]

Yves Colin De Verdière
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.
View original: http://arxiv.org/abs/1201.1110

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