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Symmetries of certain double integrals related to Hall effect devices

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Abstract

One encounters iterated elliptic integrals in the study of Hall effect devices, as a result of conformal mappings of Schwarz–Christoffel type. Some of these double elliptic integrals possess amazing symmetries with regard to the physical parameters of the underlying Hall effect devices. We give a unified mathematical treatment of such symmetric double integrals, in the context of Hall effect devices with three and four contacts.

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Authors and Affiliations

  1. Infineon Technologies Austria AG, Siemensstrasse 2, 9500, Villach, Austria

    Udo Ausserlechner

  2. Dpto. de Física Teórica, Facultad de Ciencias, Universidad de Valladolid, Paseo Belén 9, 47011, Valladolid, Spain

    M. Lawrence Glasser

  3. Department of Physics, Clarkson University, Potsdam, NY, 13699, USA

    M. Lawrence Glasser

  4. Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, NJ, 08544, USA

    Yajun Zhou

  5. Academy of Advanced Interdisciplinary Studies (AAIS), Peking University, Beijing, 100871, People’s Republic of China

    Yajun Zhou

Authors
  1. Udo Ausserlechner
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  2. M. Lawrence Glasser
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  3. Yajun Zhou
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Correspondence to M. Lawrence Glasser.

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Partial financial support is acknowledged to the Spanish Junta de Castilla y León (VA057U16) and MINECO (Project MTM2014-57129-C2-1-P).

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Ausserlechner, U., Glasser, M.L. & Zhou, Y. Symmetries of certain double integrals related to Hall effect devices. Ramanujan J 53, 39–48 (2020). https://doi.org/10.1007/s11139-019-00212-6

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  • DOI: https://doi.org/10.1007/s11139-019-00212-6

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