Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model - Erdős, László; Knowles, Antti (Communications in mathematical physics, 2011)
We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H xy , indexed by , are independent, uniformly distributed random variables if 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 . 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 of the matrix.