Superuniversality of acceleration correlations for random walks on fractals

H. Nakanishi*, Y. Meir, Y. Gefen, A. Aharony, P. Schofield

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The acceleration-acceleration correlation function, K(t)=(a(t).a(0)) (a=d2r/dt2, where r is the displacement), of a random walker on a fractal lattice is studied analytically and numerically on percolation clusters and on diffusion-limited aggregates at dimensions d=2,3. After t(>>1) discrete time steps, the authors find K(t)=A(t)/(r 2(t)), with A(t) approximately (-1)t. At a fixed distance R from the origin they find the superuniversal law K(R) approximately R -2 on all fractals and for all d.

Original languageEnglish
Article number007
Pages (from-to)L153-L158
JournalJournal of Physics A: Mathematical and General
Issue number3
StatePublished - 1987


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