{"abstract":[{"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} &gt; 0, where M:= 1/(maxx,y σ2xy).","lang":"eng"}],"publication_status":"published","issue":"7","publication":"Annales Henri Poincare","title":"Quantum diffusion and delocalization for band matrices with general distribution","quality_controlled":0,"doi":"10.1007/s00023-011-0104-5","author":[{"first_name":"László","full_name":"László Erdös","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Antti","full_name":"Knowles, Antti","last_name":"Knowles"}],"_id":"2766","intvolume":"        12","type":"journal_article","extern":1,"volume":12,"publist_id":"4124","date_updated":"2021-01-12T06:59:33Z","date_published":"2011-11-01T00:00:00Z","day":"01","page":"1227 - 1319","status":"public","publisher":"Birkhäuser","year":"2011","date_created":"2018-12-11T11:59:29Z","month":"11","citation":{"short":"L. Erdös, A. Knowles, Annales Henri Poincare 12 (2011) 1227–1319.","mla":"Erdös, László, and Antti Knowles. “Quantum Diffusion and Delocalization for Band Matrices with General Distribution.” <i>Annales Henri Poincare</i>, vol. 12, no. 7, Birkhäuser, 2011, pp. 1227–319, doi:<a href=\"https://doi.org/10.1007/s00023-011-0104-5\">10.1007/s00023-011-0104-5</a>.","ama":"Erdös L, Knowles A. Quantum diffusion and delocalization for band matrices with general distribution. <i>Annales Henri Poincare</i>. 2011;12(7):1227-1319. doi:<a href=\"https://doi.org/10.1007/s00023-011-0104-5\">10.1007/s00023-011-0104-5</a>","ieee":"L. Erdös and A. Knowles, “Quantum diffusion and delocalization for band matrices with general distribution,” <i>Annales Henri Poincare</i>, 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.” <i>Annales Henri Poincare</i>. Birkhäuser, 2011. <a href=\"https://doi.org/10.1007/s00023-011-0104-5\">https://doi.org/10.1007/s00023-011-0104-5</a>.","ista":"Erdös L, Knowles A. 2011. Quantum diffusion and delocalization for band matrices with general distribution. Annales Henri Poincare. 12(7), 1227–1319.","apa":"Erdös, L., &#38; Knowles, A. (2011). Quantum diffusion and delocalization for band matrices with general distribution. <i>Annales Henri Poincare</i>. Birkhäuser. <a href=\"https://doi.org/10.1007/s00023-011-0104-5\">https://doi.org/10.1007/s00023-011-0104-5</a>"}}