caa a22 4500 445320281 CHVBK 20180317142701.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00023-011-0104-5 doi (NATIONALLICENCE)springer-10.1007/s00023-011-0104-5 Quantum Diffusion and Delocalization for Band Matrices with General Distribution [Elektronische Daten] [László Erdős, Antti Knowles] We consider Hermitian and symmetric random band matrices H in $${d \geqslant 1}$$ dimensions. The matrix elements H xy , indexed by $${x,y \in \Lambda \subset \mathbb{Z}^d}$$ , are independent and their variances satisfy $${\sigma_{xy}^2:=\mathbb{E} |{H_{xy}}|^2 = W^{-d} f((x - y)/W)}$$ for some probability density f. We assume that the law of each matrix element H xy 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 $${t\ll W^{d/3}}$$ . We also show that the localization length of the eigenvectors of H is larger than a factor $${W^{d/6}}$$ times the band width W. All results are uniform in the size |Λ| of the matrix. This extends our recent result (Erdős 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 $${\sum_x\sigma_{xy}^2=1}$$ for all y, the largest eigenvalue of H is bounded with high probability by $${2 + M^{-2/3 + \varepsilon}}$$ for any $${\varepsilon > 0}$$ , where $${M := 1 / (\max_{x,y}\sigma_{xy}^2)}$$ . Springer Basel AG, 2011 Erdős László Institute of Mathematics, University of Munich, Theresienstr. 39, 80333, Munich, Germany aut Knowles Antti Department of Mathematics, Harvard University, 02138, Cambridge, MA, USA aut Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/7(2011-11-01), 1227-1319 1424-0637 12:7<1227 2011 12 23 https://doi.org/10.1007/s00023-011-0104-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-011-0104-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Erdős László Institute of Mathematics, University of Munich, Theresienstr. 39, 80333, Munich, Germany aut NATIONALLICENCE 700 1- Knowles Antti Department of Mathematics, Harvard University, 02138, Cambridge, MA, USA aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/7(2011-11-01), 1227-1319 1424-0637 12:7<1227 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer