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arXiv · 2410.21820

Optimization of quantum graph eigenvalues with preferred orientation vertex conditions

Pavel Exner·Jonathan Rohleder
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Abstract

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 of a fixed total edge length, the configurations for which the ground state eigenvalue is maximized. Furthermore, for general finite metric graphs we provide upper bounds for all eigenvalues.

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Pavel Exner, Jonathan Rohleder. 2024-10-29. Optimization of quantum graph eigenvalues with preferred orientation vertex conditions. https://arxiv.org/abs/2410.21820

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