We study the Langevin dynamics of the standard random heteropolymer model by
mapping the problem to a supersymmetric field theory using the
Martin-Siggia-Rose formalism. The resulting model is solved non-perturbatively
employing a Gaussian variational approach. In constructing the solution, we
assume that the chain is very long and impose the translational invariance
which is expected to be present in the bulk of the globule by averaging over
the center the of mass coordinate. In this way we derive equations of motion
for the correlation and response functions C(t,t') and R(t,t'). The order
parameters are extracted from the asymptotic behavior of these functions. We
find a dynamical phase diagram with frozen (glassy) and melted (ergodic)
phases. In the glassy phase the system fails to reach equilibrium and exhibits
aging of the type found in p-spin glasses. Within the approximations used in
this study, the random heteropolymer model can be mapped to the problem of a
manifold in a random potential with power law correlations.Comment: 16 pages, 2 figures, submitted to Phys. Rev. E, references added, few
typos correcte
