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Communications in Mathematical Physics

, Volume 303, Issue 2, pp 509–554 | Cite as

Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model

  • László Erdős
  • Antti Knowles
Article

Abstract

We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H xy , indexed by \({x,y \in \Lambda \subset \mathbb{Z}^d}\), are independent, uniformly distributed random variables if \({\lvert{x-y}\rvert}\) is less than the band width W, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales \({t\ll W^{d/3}}\). We also show that the localization length of the eigenvectors of H is larger than a factor W d/6 times the band width. All results are uniform in the size \({\lvert{\Lambda}\rvert}\) of the matrix.

Keywords

Heat Kernel Chebyshev Polynomial Anderson Model Band Matrice Quantum 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 2011

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of MunichMunichGermany
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA

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