Quantum diffusion and eigenfunction delocalization in a random band matrix model

L. Erdös, A. Knowles, Communications in Mathematical Physics 303 (2011) 509–554.

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Abstract
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 {pipe}x-y{pipe} 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.
Publishing Year
Date Published
2011-04-01
Journal Title
Communications in Mathematical Physics
Volume
303
Issue
2
Page
509 - 554
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Erdös L, Knowles A. Quantum diffusion and eigenfunction delocalization in a random band matrix model. Communications in Mathematical Physics. 2011;303(2):509-554. doi:10.1007/s00220-011-1204-2
Erdös, L., & Knowles, A. (2011). Quantum diffusion and eigenfunction delocalization in a random band matrix model. Communications in Mathematical Physics, 303(2), 509–554. https://doi.org/10.1007/s00220-011-1204-2
Erdös, László, and Antti Knowles. “Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model.” Communications in Mathematical Physics 303, no. 2 (2011): 509–54. https://doi.org/10.1007/s00220-011-1204-2.
L. Erdös and A. Knowles, “Quantum diffusion and eigenfunction delocalization in a random band matrix model,” Communications in Mathematical Physics, vol. 303, no. 2, pp. 509–554, 2011.
Erdös L, Knowles A. 2011. Quantum diffusion and eigenfunction delocalization in a random band matrix model. Communications in Mathematical Physics. 303(2), 509–554.
Erdös, László, and Antti Knowles. “Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model.” Communications in Mathematical Physics, vol. 303, no. 2, Springer, 2011, pp. 509–54, doi:10.1007/s00220-011-1204-2.

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