TY - JOUR

T1 - Fluctuations of the probability density of diffusing particles for different realizations of a random medium

AU - Eisenberg, E.

AU - Havlin, S.

AU - Weiss, G. H.

PY - 1994

Y1 - 1994

N2 - We study the fluctuations of the probability density P(r,t) of diffusing particles to be at distance r at time t in the presence of random potentials, represented by random transition rates. We find an exact relation which expresses all the moments of P(r,t) in terms of its first moment, for both quenched and annealed disorder and for any dimension. From this relation follows that anomalous diffusion implies nontrivial behavior of the moments of P(r,t), such as an exponential divergence of the relative fluctuations for large r.

AB - We study the fluctuations of the probability density P(r,t) of diffusing particles to be at distance r at time t in the presence of random potentials, represented by random transition rates. We find an exact relation which expresses all the moments of P(r,t) in terms of its first moment, for both quenched and annealed disorder and for any dimension. From this relation follows that anomalous diffusion implies nontrivial behavior of the moments of P(r,t), such as an exponential divergence of the relative fluctuations for large r.

UR - http://www.scopus.com/inward/record.url?scp=0000824186&partnerID=8YFLogxK

U2 - 10.1103/physrevlett.72.2827

DO - 10.1103/physrevlett.72.2827

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AN - SCOPUS:0000824186

SN - 0031-9007

VL - 72

SP - 2827

EP - 2830

JO - Physical Review Letters

JF - Physical Review Letters

IS - 18

ER -