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Communications in Mathematical Physics

, Volume 273, Issue 3, pp 601–618 | Cite as

Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices

  • Svetlana Jitomirskaya
  • Hermann Schulz-BaldesEmail author
Article

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.

Keywords

Lyapunov Exponent Critical Energy Dynamical Localization Jacobi Matrice Anomalous Diffusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at IrvineIrvineUSA
  2. 2.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenGermany

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