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Discrete Magnetic Bottles on Quasi-Linear Graphs

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Abstract

We study discrete magnetic Schrödinger operators on graphs that are obtained by adding decorations to the linear graph \(\mathbb {N}\). We construct examples in which the magnetic field destroys the essential spectrum. The methods rely on spectral comparison theorems for quadratic forms and a careful study of an explicit Schrödinger operator on a finite graph.

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Acknowledgements

I would like to express my sincere gratitude to my advisors Professors Nabila Torki-Hamza and Luc Hillairet for the continuous support of my Ph.D. study, for their patience, motivation, and immense knowledge. Without their wisdom this paper would not have been possible. I would like to thank the Laboratory ofMathematics of Orleans (MAPMO) and the research unity (UR/13ES47) of Faculty of Sciences of Bizerte (University of Carthage) for its financial and its continuous support. Finally, this work was financially supported by the “PHC Utique” program of the French Ministry of Foreign Affairs and Ministry of higher education and research and the Tunisian Ministry of higher education and scientific research in the CMCU Project No. 13G1501 “Graphes, Géométrie et théorie Spectrale”.

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  1. Institut Denis Poisson, Université d’Orléans, Orléans, France

    Zied Medini

  2. Faculté des Sciences de Bizerte, Université de Carthage, Zarzouna, Tunisia

    Zied Medini

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  1. Zied Medini
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Correspondence to Zied Medini.

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Communicated by Daniel Aron Alpay.

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Medini, Z. Discrete Magnetic Bottles on Quasi-Linear Graphs. Complex Anal. Oper. Theory 13, 1401–1417 (2019). https://doi.org/10.1007/s11785-018-00883-x

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  • DOI: https://doi.org/10.1007/s11785-018-00883-x

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