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Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices
Authors:Svetlana Jitomirskaya  Hermann Schulz-Baldes
Institution:1.Department of Mathematics,University of California at Irvine,Irvine,USA;2.Mathematisches Institut,Universit?t Erlangen-Nürnberg,Erlangen,Germany
Abstract:A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.
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