Effective propagators for quenched disorder in linear polymers

A chain conformation space path integral theory is implemented to study the statistics of inhomogeneous polymers randomly constructed from two different kinds of monomers. A replica approach analogous to that used in spin glass systems is adopted to average over the quenched randomness. A perturbative analysis requires mixed propagators coupling identical replicas of an arbitrary sequence of monomers, Making use of these effective propagators we estimate the effect of the quenched disorder on intra-chain interactions and calculate the asymptotic behavior of the system in the limit of very large chains. This thermodynamic limit is analyzed comparing the effective Gibbs measure determined by the effective Hamiltonian with the Gibbs measure for a homogeneous polymer system where the intra-chain interactions correspond to the averaged interactions of the original system.