0
2013
Impact Factor

    Andrey Shafarevich

    Leninskie Gory, Moscow, 119991, Russia
    Lomonosov Moscow State University

    Publications:

    Tolchennikov A. A., Chernyshev V. L., Shafarevich A. I.
    Abstract
    In the first part of the article we consider a semiclassical asymptotics for a Cauchy problem for the Schrodinger operator on a metric graph. We discuss the statistical properties of the corresponding classical dynamical system: the behavior of «number of particles» at large times and distribution of «particles» on the graph. We describe the distribution of energy on infinite regular trees. In the second part we describe the asymptotics of the spectrum of the Laplace and Schrodinger operators on a thin torus and on the simplest surfaces with delta-potentials.
    Keywords: dynamical systems, quantum, metric graphs, semiclassical theory, spectral properties, Schrodinger operator
    Citation: Tolchennikov A. A., Chernyshev V. L., Shafarevich A. I.,  Asymptotic properties and classical dynamical systems in quantum problems on singular spaces, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 3, pp.  623-638
    DOI:10.20537/nd1003010

    Back to the list