--- _id: '2717' abstract: - lang: eng text: '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. ' author: - first_name: László full_name: László Erdös id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Antti full_name: Knowles, Antti last_name: Knowles citation: ama: 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 apa: Erdös, L., & Knowles, A. (2011). Quantum diffusion and eigenfunction delocalization in a random band matrix model. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-011-1204-2 chicago: Erdös, László, and Antti Knowles. “Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model.” Communications in Mathematical Physics. Springer, 2011. https://doi.org/10.1007/s00220-011-1204-2. ieee: L. Erdös and A. Knowles, “Quantum diffusion and eigenfunction delocalization in a random band matrix model,” Communications in Mathematical Physics, vol. 303, no. 2. Springer, pp. 509–554, 2011. ista: Erdös L, Knowles A. 2011. Quantum diffusion and eigenfunction delocalization in a random band matrix model. Communications in Mathematical Physics. 303(2), 509–554. mla: 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. short: L. Erdös, A. Knowles, Communications in Mathematical Physics 303 (2011) 509–554. date_created: 2018-12-11T11:59:14Z date_published: 2011-04-01T00:00:00Z date_updated: 2021-01-12T06:59:15Z day: '01' doi: 10.1007/s00220-011-1204-2 extern: 1 intvolume: ' 303' issue: '2' month: '04' page: 509 - 554 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4175' quality_controlled: 0 status: public title: Quantum diffusion and eigenfunction delocalization in a random band matrix model type: journal_article volume: 303 year: '2011' ...