Nonuniversal transport exponents in quasi-one-dimensional systems with a power-law distribution of conductances

We study transport in quasi-one-dimensional systems consisting of n connected parallel chains of length L with a power-law distribution of bond conductivities P()1/4-± ±<1, 1. When the transverse bonds are perfect conductors, we find that the conventional law for the transport exponents in one-dimensional systems is not universal but depends sensitively on n. For n finite, there exists a critical value of ±, ±c=1-1/n. For ±±c, the resistivity exponent » and the diffusion exponent dw stick at their classical values »=1 and dw=2. For ±>±c, both exponents vary continuously with n: »=1/n(1-±) and dw=1+1/n(1-±). These values represent lower bounds if the transverse bonds have the same power-law distribution. In the case of n=1, the transport exponents accept their well-known one-dimensional values. In the two-dimensional limit n1/4L, we obtain »=0 and dw=2, irrespective of ±.. AE