Diffusion and hopping conductivity in disordered one-dimensional lattice systems |
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Authors: | J. Bernasconi W. R. Schneider W. Wyss |
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Affiliation: | (1) Brown Boveri Research Center, CH-5405 Baden, Switzerland;(2) Present address: Department of Physics, University of Colorado, 80309 Boulder, Colorado, USA |
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Abstract: | We investigate one-dimensional lattice systems with (symmetric) nearest neighbor transfer ratesWn, n+1 which are independently distributed according to a probability density(w). For two general classes of(w), we rigorously determine the asymptotic behavior of the relevant single site Green function 0() near=0, and obtain exact results for the long time decay of the initial probability amplitude and for the low energy density of states. A scaling hypothesis, accurately confirmed by computer simulations, is used to relate the low frequency hopping conductivity() uniquely to 0(–i), and we conjecture that the resulting asymptotic behavior for() is also exact. The critical exponents associated with the various asymptotic laws depend on(w) and show a crossover from universal to non-universal behavior. Comparison is made with the results of several approximate treatments. |
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