Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions. Academic Article uri icon


  • We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros of the nth eigenfunction of the Schrdinger operator on a quantum graph is related to the stability of the nth eigenvalue of the perturbation of the operator by magnetic potential. More precisely, we consider the nth eigenvalue as a function of the magnetic perturbation and show that its Morse index at zero magnetic field is equal to - (n-1).

published proceedings

  • Philos Trans A Math Phys Eng Sci

author list (cited authors)

  • Berkolaiko, G., & Weyand, T.

citation count

  • 11

complete list of authors

  • Berkolaiko, Gregory||Weyand, Tracy

publication date

  • January 2014