Upper bounds on wavepacket spreading for random Jacobi matrices

Details Upper bounds on wavepacket spreading for random Jacobi matrices Upper bounds on wavepacket spreading for random Jacobi matrices

2006-07-12

arxiv.org/abs/math-ph/0607029v2

Physics

Mathematical Physics

final version, to appear in CMP

Scientific paper

10.1007/s00220-007-0252-0

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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