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ABSTRACT: Directed Feynman paths in 1+1 dimensions that acquire random phases are
examined numerically and analytically. This problem is relevant for
the behavior of the conductance in two-dimensional amorphous insulators in the variable-range-hopping
regime. Large -scale numerical simulations were performed on a model with short-range
correlations. For the scaling of the transverse fluctutations (~tn), we obtain
n=0.68+/-0.025; and for the r.m.s. free-energy fluctuations (~tw), we obtain
w=0.335+/-0.01. Up to 100000 random
samples were used for times as large as 2000. These results seem to exclude a recent
conjecture that n=3/4 and
w=1/2. Two versions of a model with long-range correlations are solved
and shown to yield n=1/2; a physical explanation
is given.
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