Vsevolod L. Chernyshev, Anton A. Tolchennikov, Andrei I. Shafarevich, “Behavior of Quasi-particles on Hybrid Spaces. Relations to the Geometry of Geodesics and to the Problems of Analytic Number Theory”, Regul. Chaotic Dyn., 21:5 (2016), 531

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Regular and Chaotic Dynamics, 2016, Volume 21, Issue 5, Pages 531–537
DOI: https://doi.org/10.1134/S156035471605004X (Mi rcd202)

This article is cited in 8 scientific papers (total in 8 papers)

Behavior of Quasi-particles on Hybrid Spaces. Relations to the Geometry of Geodesics and to the Problems of Analytic Number Theory

Vsevolod L. Chernyshev^a, Anton A. Tolchennikov^bcd, Andrei I. Shafarevich^dceb

^a National Research University “Higher School of Economics”, ul. Myasnitskaya 20, Moscow, 101978 Russia
^b Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
^c Institute for Problems in Mechanics, pr. Vernadskogo 101-1, Moscow, 119526 Russia
^d M. V. Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia
^e National Research Center “Kurchatov Institute”, pl. Akademika Kurchatova 1, Moscow, 123182 Russia

Citations (8)

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DOI: https://doi.org/10.1134/S156035471605004X

Abstract: We review our recent results concerning the propagation of “quasi-particles” in hybrid spaces — topological spaces obtained from graphs via replacing their vertices by Riemannian manifolds. Although the problem is purely classical, it is initiated by the quantum one, namely, by the Cauchy problem for the time-dependent Schrödinger equation with localized initial data.We describe connections between the behavior of quasi-particles with the properties of the corresponding geodesic flows. We also describe connections of our problem with various problems in analytic number theory.

Keywords: hybrid spaces, propagation of quasi-particles, properties of geodesic flows, integral points in polyhedra, theory of abstract primes.

Funding agency	Grant number
Russian Science Foundation	16-11-10069
This work was supported by the Russian Scientific Foundation (grant 16–11–10069).

Received: 26.08.2016
Accepted: 08.09.2016

Bibliographic databases:

Document Type: Article

MSC: 37K25, 53C22, 57R45, 11P21, 11P21

Language: English

Citation: Vsevolod L. Chernyshev, Anton A. Tolchennikov, Andrei I. Shafarevich, “Behavior of Quasi-particles on Hybrid Spaces. Relations to the Geometry of Geodesics and to the Problems of Analytic Number Theory”, Regul. Chaotic Dyn., 21:5 (2016), 531–537

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https://www.mathnet.ru/eng/rcd/v21/i5/p531

This publication is cited in the following 8 articles:

Andrew Eliseev, Vsevolod L. Chernyshev, “Upper bound on saturation time of metric graphs by intervals moving on them”, Journal of Mathematical Analysis and Applications, 531:2 (2024), 127873
Murat V. Vakhitov, Dmitrii S. Minenkov, “On logarithmic asymptotics for the number of restricted partitions in the exponential case”, Moscow J. Comb. Number Th., 12:4 (2023), 297
V. L. Chernyshev, A. A. Tolchennikov, “A Metric Graph for Which the Number of Possible End Positions of a Random Walk Grows Minimally”, Russ. J. Math. Phys., 29:4 (2022), 426
A. A. Izmaylov, L. W. Dworzanski, “Automated analysis of DP-systems using timed-arc Petri nets via TAPAAL tool”, Trudy ISP RAN, 32:6 (2020), 155–166
Andrei Shafarevich, Springer Proceedings in Mathematics & Statistics, 273, Recent Developments in Integrable Systems and Related Topics of Mathematical Physics, 2018, 183
V. L. Chernyshev, A. A. Tolchennikov, “Correction to the Leading Term of Asymptotics in the Problem of Counting the Number of Points Moving on a Metric Tree”, Russ. J. Math. Phys., 24:3 (2017), 290–298
D. S. Minenkov, V. E. Nazaikinskii, V. L. Chernyshev, “On the Limit Shape of Elements of An Arithmetic Semigroup With An Exponentially Growing Counting Function of Basis Elements”, Dokl. Math., 95:3 (2017), 226–229
V. Zh. Sakbaev, I. V. Volovich, “Self-Adjoint Approximations of the Degenerate Schrodinger Operator”, P-Adic Numbers Ultrametric Anal. Appl., 9:1 (2017), 39–52

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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