Superuniversality of acceleration correlations for random walks on fractals Academic Article uri icon

abstract

  • Abstract The acceleration-acceleration correlation function, K (t)=(a (t). a (0))(a= d 2 r/dt 2, 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.

publication date

  • February 21, 1987