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Abstract
We present a rigorous approach to the Langevin dynamics of ideal polymer chains subject to internal distance constraints. The permanent constraints are modeled by harmonic potentials in the limit when the strength of the potential approaches infinity (hard cross-links). The cross-links are assumed to exist between arbitrary pairs of monomers. Formally exact expressions for the resolvent and spectral density matrix of the system are derived. To illustrate the method we study the diffusional behavior of monomers in the vicinity of a single cross-link within 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 Lagrangian multipliers. Here we derive the full, hence exact, solution to the problem.
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