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- W2040374761 abstract "We study the motion of a particle or elementary excitation that hops between nearest neighbors in a one-dimensional array of traps. The trap depths and transition probabilities are random, but they may show correlations over short distances. When certain averages of the inverse transition rates exist, the low-lying eigenvalues of the master equation for the system are distributed like those of some equivalent regular chain. However, the nature of this equivalent regular chain depends on the degree of correlation of the random transition rates. Moreover, for a chain with periodic boundary conditions the degeneracy of the eigenvalues in the regular chain is lifted. The amount of this splitting depends on the degree of randomness and on the chain length. The density of low-lying eigenvalues is closely related to the asymptotic form of the probability for finding the particle at some large time at the same place where it started its random walk. Our results are obtained by studying the moments of the reciprocals of the eigenvalues, in which the distribution of low-lying eigenvalues leaves a characteristic fingerprint." @default.
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- W2040374761 date "1981-10-15" @default.
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- W2040374761 title "Effect of correlations on the low-frequency behavior of random one-dimensional systems" @default.
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- W2040374761 doi "https://doi.org/10.1103/physrevb.24.4329" @default.
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