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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. Chernysheva, Anton A. Tolchennikovbcd, Andrei I. Shafarevichdceb

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
Citation in format AMSBIB
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\paper Behavior of Quasi-particles on Hybrid Spaces. Relations to the Geometry of Geodesics and to the Problems of Analytic Number Theory
\jour Regul. Chaotic Dyn.
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\vol 21
\issue 5
\pages 531--537
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