caa a22 4500 475738462 CHVBK 20180406123453.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/s002220000076 doi (NATIONALLICENCE)springer-10.1007/s002220000076 Spectral structure of Anderson type Hamiltonians [Elektronische Daten] [Vojkan Jakšić, Yoram Last] Abstract. : We study self adjoint operators of the form¶H ω = H 0 + ∑λω(n) <δ n ,·>δ n ,¶where the δ n 's are a family of orthonormal vectors and the λω(n)'s are independently distributed random variables with absolutely continuous probability distributions. We prove a general structural theorem saying that for each pair (n,m), if the cyclic subspaces corresponding to the vectors δ n and δ m are not completely orthogonal, then the restrictions of H ω to these subspaces are unitarily equivalent (with probability one). This has some consequences for the spectral theory of such operators. In particular, we show that "well behaved” absolutely continuous spectrum of Anderson type Hamiltonians must be pure, and use this to prove the purity of absolutely continuous spectrum in some concrete cases. Springer-Verlag Berlin Heidelberg, 2000 Jakšić Vojkan Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada, CA aut Last Yoram Institute of Mathematics, The Hebrew University, 91904 Jerusalem, Israel, IL aut https://doi.org/10.1007/s002220000076 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002220000076 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jakšić Vojkan Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada, CA aut NATIONALLICENCE 700 1- Last Yoram Institute of Mathematics, The Hebrew University, 91904 Jerusalem, Israel, IL aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer