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    Vsevolod Chernyshev

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


    Tolchennikov A. A., Chernyshev V. L., Shafarevich A. I.
    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

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