PATH-INTEGRAL DESCRIPTION OF POLYMERS USING FRACTIONAL BROWNIAN WALKS

The statistical properties of fractional Brownian walks are used to co nstruct a path integral representation of the conformations of polymer s with different degrees of bond correlation. We specifically derive a n expression for the distribution function of the chains' end-to-end d istance, and evaluate it by several independent methods, including dir ect evaluation of the discrete limit of the path integral, decompositi on into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coor dinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of t he monomer along the chain backbone, now depend on an index h, the deg ree of correlation of the fractional Brownian walk. The special case o f h = 1/2 corresponds to the random walk. In constructing the normal m ode picture of the chain, we conjecture the existence of a theorem reg arding the zeros of the Bessel function.