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2013
Impact Factor

Vsevolod Chernyshev

20 Myasnitskaya, 101000, Moscow
National Research University "Higher School of Economics"

Publications:

Chernyshev V. L., Tolchennikov A. A., Shafarevich A. I.
Behavior of Quasi-particles on Hybrid Spaces. Relations to the Geometry of Geodesics and to the Problems of Analytic Number Theory
2016, vol. 21, no. 5, pp.  531-537
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
Citation: Chernyshev V. L., Tolchennikov A. A., Shafarevich A. I.,  Behavior of Quasi-particles on Hybrid Spaces. Relations to the Geometry of Geodesics and to the Problems of Analytic Number Theory, Regular and Chaotic Dynamics, 2016, vol. 21, no. 5, pp. 531-537
DOI:10.1134/S156035471605004X

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