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Asymptotic estimate for the number of Gaussian packets on three decorated graphs by Chernyshev, V. L.; Tolchennikov, A. A. is a scholarly article available to read on EtoBox.

What is Asymptotic estimate for the number of Gaussian packets on three decorated graphs about?

We study a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds, i.e. a decorated graph. We construct a semiclassical asymptotics of the solutions of Cauchy problem for a time-dependent Schr\"{o}dinger equation on a decorated graph with a localized initial function. The main term of our asymptotic solution at an arbitrary finite time is the sum of Gaussian packets and generalized Gaussian packets. We study the number of such packets as time goes to infinity. We prove asymptotic estimations for this number for the following decorated graphs: cylinder with a segment, two dimensional torus with a segment, three dimensional torus with a segment. Also we prove general theorem about a manifold with a segment and apply it to the case of a uniformly secure manifold.

Author

Chernyshev, V. L.; Tolchennikov, A. A.

Published

2014

Language

EN