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Diffraction of the Aharonov–Bohm Hamiltonian

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Abstract

In this paper, we compute the diffractive wave propagator of the Aharonov–Bohm effect (Aharonov and Bohm, Phys Rev 115(3):485, 1959) on \({\mathbf {R}}^2\) with a single solenoid using a technique of moving solenoid location. In addition, we compute the corresponding diffraction coefficient which is the principal symbol of the diffractive propagator. This paper proves the propagation of singularities of the Aharonov–Bohm Hamiltonian.

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Notes

  1. Note that we use the standard \(L^2\)-weight here rather that the b-weight used in [20]. This gives a one order difference in r comparing to [20].

  2. Although these are only locally well-defined functions on \({\mathbf {R}}^2\) individually, the pairing is well-defined due to the complex conjugation in the sesquilinear pairing.

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Acknowledgements

The author is grateful to Luc Hillairet and Jared Wunsch for proposing this topic, and to Dean Baskin, Luc Hillairet and two anonymous referees for helpful comments on the manuscript. The author is especially very grateful to Jared Wunsch for many helpful discussions as well as valuable comments on this manuscript.

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  1. Department of Mathematics, Northwestern University, Evanston, IL, USA

    Mengxuan Yang

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  1. Mengxuan Yang
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Correspondence to Mengxuan Yang.

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Communicated by Jan Derezinski.

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Yang, M. Diffraction of the Aharonov–Bohm Hamiltonian. Ann. Henri Poincaré 22, 3619–3640 (2021). https://doi.org/10.1007/s00023-021-01069-6

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