Physics – Mathematical Physics
Scientific paper
2006-07-12
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.
Jitomirskaya Svetlana
Schulz-Baldes Hermann
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