We study random walks with finite jump distance l in continuum percolation systems (random void model). Using scaling arguments and numerical simulations we show that the mean-square displacement at criticality is characterized by r2(t) t2k with an exponent k depending sensitively on the time regime considered. For times below tx(1)l-a1 (a14 in d=2 and a15 in d=3), we recover the results of Halperin et al., k13 in d=2 and k0.18 in d=3, which apply in the limit l0. In a wide intermediate time regime tx(1)tx(2) we predict the exponents k from the overlapping Lorentz gas. © 1989 The American Physical Society.
Petersen, J., Roman, H., Bunde, A., Dieterich, W. (1989). Nonuniversality of transport exponents in continuum percolation systems: Effects of finite jump distance. PHYSICAL REVIEW. B, CONDENSED MATTER, 39(1), 893-896 [10.1103/PhysRevB.39.893].
Nonuniversality of transport exponents in continuum percolation systems: Effects of finite jump distance
Roman H. E.;
1989
Abstract
We study random walks with finite jump distance l in continuum percolation systems (random void model). Using scaling arguments and numerical simulations we show that the mean-square displacement at criticality is characterized by r2(t) t2k with an exponent k depending sensitively on the time regime considered. For times below tx(1)l-a1 (a14 in d=2 and a15 in d=3), we recover the results of Halperin et al., k13 in d=2 and k0.18 in d=3, which apply in the limit l0. In a wide intermediate time regime tx(1)tx(2) we predict the exponents k from the overlapping Lorentz gas. © 1989 The American Physical Society.
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