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Magnetic interpretation of the nodal defect on graphs

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 نشر من قبل Yves Colin de Verdiere
 تاريخ النشر 2012
  مجال البحث فيزياء
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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 Schrodinger 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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