Spectral diffusion in random lattices

Heinrichs, J. ; Kumar, N. (1979) Spectral diffusion in random lattices Physical Review B: Condensed Matter and Materials Physics, 20 (4). pp. 1377-1389. ISSN 1098-0121

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Official URL: http://prb.aps.org/abstract/PRB/v20/i4/p1377_1

Related URL: http://dx.doi.org/10.1103/PhysRevB.20.1377


The classical diffusion of localized excitations is studied on random linear chain and Bethe lattices (connectivity K) in which the nearest-neighbor transfer rates, Wnm, take values zero and W0 with probabilities p and 1-p, respectively. First an exact formal solution for the decay in time of the average amplitude <P0(t)> of an initial excitation at a lattice site is discussed, using the analogy between the diffusion problem and the response of a random impedance network to a localized current pulse. Detailed results for <P0(t)> at long and intermediate times are obtained close to the percolation threshold p=pc, for the Bethe lattice. The solution decays as t at intermediate times and shows a long-time decay ~tKexp(-Γ(p)t) towards a constant value associated with the effect of finite clusters of coupled sites. The attentuation rate is faster for p<pc than for p>pc, as expected. The one-dimensional case requires a special treatment which is shown to give results identical to those of a different earlier analysis. The generality of our method suggests its application to various other problems.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:85101
Deposited On:29 Feb 2012 12:21
Last Modified:29 Feb 2012 12:21

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