Behavior of quasi-particles on hybrid spaces. Relations to the geometry of geodesics and to the problems of analytic number theory

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• 作者：Vsevolod L. Chernyshev ; Anton A. Tolchennikov…
• 关键词：hybrid spaces ; propagation of quasi ; particles ; properties of geodesic flows ; integral points in polyhedra ; theory of abstract primes
• 刊名：Regular and Chaotic Dynamics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：21
• 期：5
• 页码：531-537
• 全文大小：428 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Dynamical Systems and Ergodic Theory
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1468-4845
• 卷排序：21

文摘

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.