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 KnowlesEmail author


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.


Heat Kernel Chebyshev Polynomial Anderson Model Band Matrice Quantum Diffusion 
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© Springer-Verlag 2011

Authors and Affiliations

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

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