title: Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions.
abstract: We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros of the nth eigenfunction of the Schrödinger 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 φ - (n-1).
authors.affiliation: Department of Mathematics, Texas A&M University, , College Station, TX 77843-3368, USA.
authors.forename: Gregory
authors.initials: G
authors.lastname: Berkolaiko
authors.forename: Tracy
authors.initials: T
authors.lastname: Weyand
keywords: magnetic Schrödinger operator; magnetic-nodal connection; nodal count; quantum graphs; zeros of eigenfunctions