2008/10/10 by Kozlov, G. G.
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences
paper · doi:10.48550/arxiv.0810.1846
For a one dimensional half-infinite chain with diagonal disorder we calculated the ultimate at t→∞ value of the average excitation density at the edge site D if at t=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 D which is exact in the limit of low concentration of defects and is valid for an arbitrary energy of defects ε. In this case D demonstrated the non analytical dependence on ε. ii) The close expression for D is obtained for the case of an arbitrary small disorder. iii) The relative contribution of states with specified energy to D is calculated. All the results obtained are in complete agreement with computer simulation.