S Mukherjee et al 1995 J. Phys. A: Math. Gen. 28 291 doi:10.1088/0305-4470/28/2/007
S Mukherjee, D J Jacobs and H Nakanishi
Show affiliationsIn this paper, we calculate the dynamical exponents of diffusion, dw/df and ds, on a percolation cluster at pc with no loops, for the square and simple cubic lattices by the method of spectral analysis of the transition probability matrix. Results show that ds varies significantly with the spatial dimension, unlike in conventional percolation, but the Alexander-Orbach scaling relation ds=2df/dw still holds. Thus it rules out the possibility that this scaling relation fails for all loopless fractals because of trapping.
82B43 Percolation (See also 60K35)
28A80 Fractals (See also 37Fxx)
60J60 Diffusion processes (See also 58J65)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Issue 2 (21 January 1995)
S Mukherjee et al 1995 J. Phys. A: Math. Gen. 28 291
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