TY - JOUR

T1 - Anomalous diffusion, superlocalization and hopping conductivity on fractal media

AU - Harris, A. Brooks

AU - Aharony, A.

PY - 1987/12/15

Y1 - 1987/12/15

N2 - We obtain simple, but rigorous bounds for impurity quantum states, for a tight-z binding model on random fractal structures. From these we conclude that a “typical„ state on a percolation cluster decays with Euclidean distance r as exp [- cra], with 1Š≤ŠaŠ≤Šςc, where rςcis the average chemical distance. Averaging over all random configurations yields regular exponential decay, aŠ=Š1. Our bounds indicate that the probability of a classical random walker to reach distance r at time t decays as exp [- (rd/w/t)α], tŠ< Šrdw, with 1/(dw - 1)Š≤ŠαŠ≤Šςc/(dw - ςc). For the fully averaged probability we expect αŠ=Š1/(dw - 1). The thermally activated hopping conductivity between impurities on a random structure with fractal dimensionality D is found to behave as exp [- (T0/T)β], with βŠ=Šςc/(D + ςc).

AB - We obtain simple, but rigorous bounds for impurity quantum states, for a tight-z binding model on random fractal structures. From these we conclude that a “typical„ state on a percolation cluster decays with Euclidean distance r as exp [- cra], with 1Š≤ŠaŠ≤Šςc, where rςcis the average chemical distance. Averaging over all random configurations yields regular exponential decay, aŠ=Š1. Our bounds indicate that the probability of a classical random walker to reach distance r at time t decays as exp [- (rd/w/t)α], tŠ< Šrdw, with 1/(dw - 1)Š≤ŠαŠ≤Šςc/(dw - ςc). For the fully averaged probability we expect αŠ=Š1/(dw - 1). The thermally activated hopping conductivity between impurities on a random structure with fractal dimensionality D is found to behave as exp [- (T0/T)β], with βŠ=Šςc/(D + ςc).

UR - http://www.scopus.com/inward/record.url?scp=84956135982&partnerID=8YFLogxK

U2 - 10.1209/0295-5075/4/12/003

DO - 10.1209/0295-5075/4/12/003

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AN - SCOPUS:84956135982

SN - 0295-5075

VL - 4

SP - 1355

EP - 1360

JO - Journal de Physique (Paris), Lettres

JF - Journal de Physique (Paris), Lettres

IS - 12

ER -