Browsing by Author "Cardenas, Esteban"

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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.
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    Spectral properties of Landau Hamiltonians with non-local potentials
    (2020) Cardenas, Esteban; Raikov, Georgi; Tejeda, Ignacio
    We consider the Landau Hamiltonian H-0, self-adjoint in L-2 (R-2), whose spectrum consists of an arithmetic progression of infinitely degenerate positive eigenvalues Lambda(q), q is an element of Z(+). We perturb H-0 by a non-local potential written as a bounded pseudo-differential operator Op(w)(V) with real-valued Weyl symbol V, such that Op(w)(V)H-0(-1) is compact. We study the spectral properties of the perturbed operator H-V = H-0 Op(w)(V). First, we construct symbols V, possessing a suitable symmetry, such that the operator H-V admits an explicit eigenbasis in L-2 (R-2), and calculate the corresponding eigenvalues. Moreover, for V which are not supposed to have this symmetry, we study the asymptotic distribution of the eigenvalues of H-V adjoining any given Lambda(q). We find that the effective Hamiltonian in this context is the Toeplitz operator T-q(V) = p(q)Op(w)(V)p(q), where p(q) is the orthogonal projection onto Ker(H-0 - Lambda I-q), and investigate its spectral asymptotics.
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    Tunneling Estimates for Two-Dimensional Perturbed Magnetic Dirac Systems
    (2024) Cardenas, Esteban; Pavez, Benjamin; Stockmeyer, Edgardo
    We prove tunneling estimates for two-dimensional Dirac systems which are localized in space due to the presence of a magnetic field. The Hamiltonian driving the motion admits the decomposition H=H0+W\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ H = H_0 + W$$\end{document}, where H0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_0 $$\end{document} is a rotationally symmetric magnetic Dirac operator and W is a position-dependent matrix-valued potential satisfying certain smoothness condition in the angular variable. A consequence of our results are upper bounds for the growth in time of the expected size of the system and its total angular momentum.