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Theoretical and Mathematical Physics

Statistics of the Edge Green's Function for a One-Dimensional Disordered System with Binary or Uniform Diagonal Disorder

G. G. Kozlov

Published Aug 1, 2004• 0 citations
Publisher
DOI
10.1023/b:tamp.0000036548.22172.e4

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arXiv:0810.1846•Oct 10, 2008•0 citations
For a one dimensional half-infinite chain with diagonal disorder we calculated the ultimate at t→∞t\to\inftyt→∞ value of the average excitation density at the edge site DDD if at t=0t=0t=0 the excitation was localised at the edge site (Anderson' s creterium). We obtained the following results: i) for the binary disordered chain we derived the close expression for DDD which is exact in the limit of low concentration of defects and is valid for an arbitrary energy of defects ε\varepsilonε. In this case DDD demonstrated the non analytical dependence on ε\varepsilonε. ii) The close expression for DDD is obtained for the case of an arbitrary small disorder. iii) The relative contribution of states with specified energy to DDD is calculated. All the results obtained are in complete agreement with computer simulation.