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Localized Solutions of the Schrödinger Equation on Hybrid Spaces. Relation to the Behavior of Geodesics and to Analytic Number Theory

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Recent Developments in Integrable Systems and Related Topics of Mathematical Physics (MP 2016)

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Abstract

In this chapter, we review our results concerning localized asymptotic solutions of time-dependent Schrödinger equation on hybrid spaces. We describe the connections of this problem to the problem of global behavior of geodesics on Riemannian manifolds and to certain problems of the analytic number theory.

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Acknowledgments

The work was supported by the Russian Scientific Foundation (grant 16-11-10069).

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Authors and Affiliations

  1. M.V. Lomonosov Moscow State University, Leninskie Gory, 1, 119992, Moscow, Russia

    Andrei Shafarevich

Authors
  1. Andrei Shafarevich
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Correspondence to Andrei Shafarevich .

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Editors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    Victor M. Buchstaber

  2. Centre of Integrable Systems, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia

    Sotiris Konstantinou-Rizos

  3. School of Mathematics, University of Leeds, Leeds, UK

    Alexander V. Mikhailov

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Shafarevich, A. (2018). Localized Solutions of the Schrödinger Equation on Hybrid Spaces. Relation to the Behavior of Geodesics and to Analytic Number Theory. In: Buchstaber, V., Konstantinou-Rizos, S., Mikhailov, A. (eds) Recent Developments in Integrable Systems and Related Topics of Mathematical Physics. MP 2016. Springer Proceedings in Mathematics & Statistics, vol 273. Springer, Cham. https://doi.org/10.1007/978-3-030-04807-5_10

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