LANGEVIN DYNAMICS OF A POLYMER WITH INTERNAL DISTANCE CONSTRAINTS

We present a rigorous approach to the Langevin dynamics of ideal polym er chains subject to internal distance constraints. The permanent cons traints are modeled by harmonic potentials in the limit when the stren gth of the potential approaches infinity (hard cross-links). The cross -links are assumed to exist between arbitrary pairs of monomers. Forma lly exact expressions for the resolvent and spectral density matrix of the system are derived. To illustrate the method we study the diffusi onal behavior of monomers in the vicinity of a single cross-link withi n the framework of the Rouse model. The same problem has been studied previously by Warner [J. Phys. C 14, 4985 (1981)] on the basis of Lagr angian multipliers. Here we derive the full, hence exact, solution to the problem.