An index theorem for Schrödinger operators on metric graphs

2018/09/25 by Latushkin, Yuri, Sukhtaiev, Selim · 1 citation
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1809.09344

Abstract

We show that the spectral flow of a one-parameter family of Schrödinger operators on a metric graph is equal to the Maslov index of a path of Lagrangian subspaces describing the vertex conditions. In addition, we derive an Hadamard-type formula for the derivatives of the eigenvalue curves via the Maslov crossing form.

Cited by

• Index theory for non-compact quantum graphs

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