Browsing by Author "Vugalter, Semjon"

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    Infinite mass boundary conditions for Dirac operators
    (2019) Stockmeyer, Edgardo; Vugalter, Semjon
    We study a self-adjoint realization of a massless Dirac operator on a bounded connected domain Omega subset of R-2 which is frequently used to model graphene. In particular, we show that this operator is the limit, as M -> infinity, of a Dirac operator defined on the whole plane, with a mass term of size M supported outside Omega.
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    On the Asymptotic Dynamics of 2-D Magnetic Quantum Systems
    (2021) Cardenas, Esteban; Hundertmark, Dirk; Stockmeyer, Edgardo; Vugalter, Semjon
    In this work, we provide results on the long-time localization in space (dynamical localization) of certain two-dimensional magnetic quantum systems. The underlying Hamiltonian may have the form H=H-0+W, where H-0 is rotationally symmetric and has dense point spectrum and W is a perturbation that breaks the rotational symmetry. In the latter case, we also give estimates for the growth of the angular momentum operator in time.