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Upper bounds on wavepacket spreading for random Jacobi matrices

Svetlana Jitomirskaya·Hermann Schulz-Baldes
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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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Svetlana Jitomirskaya, Hermann Schulz-Baldes. 2007-02-15. Upper bounds on wavepacket spreading for random Jacobi matrices. https://doi.org/10.1007/s00220-007-0252-0

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