A renormalization-group analysis is carried out of the long-time behavior of random walks in a one-dimensional lattice consisting of three kinds of bonds generated by a deterministic inflation rule. The random walker is subject to a local drift force, depending on the kind of bond it traverses. The mean-square displacement after time t is found to scale as t2ν where the exponent ν is nonuniversal and depends continuously on the magnitude of the drift force. The model studied is one of a general class of systems that exhibits similar behavior.
Nonuniversal diffusion in a chain with deterministic local drifts
MARITAN, AMOS;
1993
Abstract
A renormalization-group analysis is carried out of the long-time behavior of random walks in a one-dimensional lattice consisting of three kinds of bonds generated by a deterministic inflation rule. The random walker is subject to a local drift force, depending on the kind of bond it traverses. The mean-square displacement after time t is found to scale as t2ν where the exponent ν is nonuniversal and depends continuously on the magnitude of the drift force. The model studied is one of a general class of systems that exhibits similar behavior.
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