Aharonov–Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition
Fialova M. 2024. Aharonov–Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition. Annales Henri Poincare.
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Abstract
The Aharonov–Casher theorem is a result on the number of the so-called zero modes of a system described by the magnetic Pauli operator in R2. In this paper we address the same question for the Dirac operator on a flat two-dimensional manifold with boundary and Atiyah–Patodi–Singer boundary condition. More concretely we are interested in the plane and a disc with a finite number of circular holes cut out. We consider a smooth compactly supported magnetic field on the manifold and an arbitrary magnetic field inside the holes.
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2024-09-05
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Annales Henri Poincare
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Springer Nature
Acknowledgement
First and foremost I am grateful to Jan Philip Solovej for fruitful meetings during (and after) my PhD programme, when this work was done. Further I would like to thank Joshua Hunt, Anna Sisak, Jakub Löwit, Błażej Ruba, Volodymir Riabov, Lukas Schimmer and Georgios Koutentakis for valuable discussions. Many thanks belong to Rafael Benguria for hosting my visit, during which some of the work has been done. I am also grateful to Marina Prokhorova who first initiated the discussion of this project topic and to Annemarie Luger for her valuable comments during my PhD defence and in particular pointing out the qualitative difference in our two main results. I would like to acknowledge support for research on this paper from VILLUM FONDEN through the QMATH Centre of Excellence grant. nr. 10059. This project also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. I am grateful to the two reviewers for reading carefully my manuscript and pointing out several issues contributing thus significantly to the readability and clarity of this paper.
Open access funding provided by Institute of Science and Technology (IST Austria).
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Cite this
Fialova M. Aharonov–Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition. Annales Henri Poincare. 2024. doi:10.1007/s00023-024-01482-7
Fialova, M. (2024). Aharonov–Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-024-01482-7
Fialova, Marie. “Aharonov–Casher Theorems for Dirac Operators on Manifolds with Boundary and APS Boundary Condition.” Annales Henri Poincare. Springer Nature, 2024. https://doi.org/10.1007/s00023-024-01482-7.
M. Fialova, “Aharonov–Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition,” Annales Henri Poincare. Springer Nature, 2024.
Fialova M. 2024. Aharonov–Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition. Annales Henri Poincare.
Fialova, Marie. “Aharonov–Casher Theorems for Dirac Operators on Manifolds with Boundary and APS Boundary Condition.” Annales Henri Poincare, Springer Nature, 2024, doi:10.1007/s00023-024-01482-7.
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