{"citation":{"mla":"Erdös, László, and Antti Knowles. “Quantum Diffusion and Delocalization for Band Matrices with General Distribution.” Annales Henri Poincare, vol. 12, no. 7, Birkhäuser, 2011, pp. 1227–319, doi:10.1007/s00023-011-0104-5.","short":"L. Erdös, A. Knowles, Annales Henri Poincare 12 (2011) 1227–1319.","ama":"Erdös L, Knowles A. Quantum diffusion and delocalization for band matrices with general distribution. Annales Henri Poincare. 2011;12(7):1227-1319. doi:10.1007/s00023-011-0104-5","ieee":"L. Erdös and A. Knowles, “Quantum diffusion and delocalization for band matrices with general distribution,” Annales Henri Poincare, vol. 12, no. 7. Birkhäuser, pp. 1227–1319, 2011.","chicago":"Erdös, László, and Antti Knowles. “Quantum Diffusion and Delocalization for Band Matrices with General Distribution.” Annales Henri Poincare. Birkhäuser, 2011. https://doi.org/10.1007/s00023-011-0104-5.","apa":"Erdös, L., & Knowles, A. (2011). Quantum diffusion and delocalization for band matrices with general distribution. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-011-0104-5","ista":"Erdös L, Knowles A. 2011. Quantum diffusion and delocalization for band matrices with general distribution. Annales Henri Poincare. 12(7), 1227–1319."},"volume":12,"intvolume":" 12","date_created":"2018-12-11T11:59:29Z","publisher":"Birkhäuser","_id":"2766","publist_id":"4124","status":"public","page":"1227 - 1319","quality_controlled":0,"date_updated":"2021-01-12T06:59:33Z","issue":"7","type":"journal_article","doi":"10.1007/s00023-011-0104-5","day":"01","extern":1,"title":"Quantum diffusion and delocalization for band matrices with general distribution","month":"11","publication_status":"published","abstract":[{"lang":"eng","text":"We consider Hermitian and symmetric random band matrices H in d ≥ dimensions. The matrix elements Hxy, indexed by x,y ∈ Λ ⊂ ℤd are independent and their variances satisfy σ2xy:= E{pipe}Hxy{pipe}2 = W-d f((x-y)/W for some probability density f. We assume that the law of each matrix element Hxy is symmetric and exhibits subexponential decay. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales ≪ Wd/3. We also show that the localization length of the eigenvectors of H is larger than a factor Wd/6 times the band width W. All results are uniform in the size {pipe}Λ{pipe} of the matrix. This extends our recent result (Erdo{double acute}s and Knowles in Commun. Math. Phys., 2011) to general band matrices. As another consequence of our proof we show that, for a larger class of random matrices satisfying Σx σ2xy for all y, the largest eigenvalue of H is bounded with high probability by 2+M-2/3+e{open} for any e{open} > 0, where M:= 1/(maxx,y σ2xy)."}],"year":"2011","date_published":"2011-11-01T00:00:00Z","publication":"Annales Henri Poincare","author":[{"full_name":"László Erdös","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"last_name":"Knowles","full_name":"Knowles, Antti","first_name":"Antti"}]}