Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices |
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Authors: | Svetlana Jitomirskaya Hermann Schulz-Baldes |
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Institution: | 1.Department of Mathematics,University of California at Irvine,Irvine,USA;2.Mathematisches Institut,Universit?t Erlangen-Nürnberg,Erlangen,Germany |
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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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Keywords: | |
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