  We study the Langevin dynamics of a heteropolymer by means of a mode-coupling
approximation scheme, giving rise to a set of coupled integro-differential
equations relating the response and correlation functions. The analysis shows
that there is a regime at low temperature characterized by out-of-equilibrium
dynamics, with violation of time-translational invariance and of the
fluctuation-dissipation theorem. The onset of ageing dynamics at low
temperatures gives new insight into the nature of the slow dynamics of a
disordered polymer. We also introduce a renormalization-group treatment of our
mode-coupling equations, which supports our analysis, and might be applicable
to other systems.
