Non-linear response in percolation systems

H. Harder, A. Bunde, S. Havlin

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The authors study diffusion in d=2 percolation clusters at criticality under the influence of an external time-dependent field E(t)=E0sin( omega t). They find that the mean displacement (x(t)) of a random walker is a periodic function with a phase shift phi approximately= pi /3 independent of omega and E0. The amplitude A(E0, omega ) of (x(t)) is linear in E0 below a crossover field E*0( omega ). Above E*0( omega ), A(E0, omega ) is strongly non-linear, showing a maximum as a function of E0. They find that both the linear and the non-linear regime can be described by a single scaling function: A(E0, omega ) approximately E0 omega -2d/F(E0/E*0( omega )) where d approximately=2.87 is the diffusion exponent and E*0( omega ) approximately omega beta with beta approximately=0.3. The linear response regime is reached for E0/ omega beta<<1.

Original languageEnglish
Article number012
Pages (from-to)L927-L932
JournalJournal of Physics A: General Physics
Issue number15
StatePublished - 1986
Externally publishedYes


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