Behavior of quasi-particles on hybrid spaces. Relations to the geometry of geodesics and to the problems of analytic number theoryстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 17 января 2018 г.
Аннотация: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 Schrodinger 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.