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math-ph2025
First order operators on shrinking graph-like spaces
Pavel Exner, Olaf Post
In this article we discuss the convergence of first order operators on a thickened graph (a graph-like space) towards a similar operator on the underlying metric graph. On the grap…
math-ph2025
The Flea on the Magnetic Elephant
Pavel Exner, Léo Morin
We investigate a two-dimensional magnetic Laplacian with two radially symmetric magnetic wells. Its spectral properties are determined by the tunneling between them. If the tunneli…
math-ph2025
Optimization of quantum graph eigenvalues with preferred orientation vertex conditions
Pavel Exner, Jonathan Rohleder
We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition…