Random heteropolymer dynamics - art. no. 051910

We study the Langevin dynamics of the standard random heteropolymer model b y mapping the problem to a supersymmetric field theory using the Martin-Sig gia-Rose formalism. The resulting model is solved nonperturbatively employi ng 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 of mass coordinate. In this way we derive equations of motion for th e correlation and response functions C(t.t') and R(t,t'). The order paramet ers 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 agi ng of the type found in p-spin glasses. Within the approximations used in t his study, the random heteropolymer model can be mapped to the problem of a manifold in a random potential with power law correlations.