Contact matrices provide a coarse grained description of the configuration ω of a linear chain (polymer or random walk) on ℤn : Cij(ω) = 1 when the distance between the positions of the ith and jth steps are less than or equal to some distance a and C ij(ω) = 0 otherwise. We consider models in which polymers of length N have weights corresponding to simple and self-avoiding random walks, SRW and SAW, with a the minimal permissible distance. We prove that to leading order in N, the number of matrices equals the number of walks for SRW, but not for SAW. The coarse grained Shannon entropies for SRW agree with the fine grained ones for n ≤ 2, but differs for n ≥ 3.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)