Polymers and manifolds in static random flows: a renormalization group study

We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for directed polymers (each monomer sees a different flow) and for d < 6 for isotropic polymers (each monomer sees the same flow) and more generally for d<d_c(D) in the case of a manifold. This leads to new large scale behavior, which we analyze using field theoretical methods. We show that all divergences can be absorbed in multilocal counter-terms which we compute to one loop order. We obtain the non trivial roughness zeta, dynamical z and transport exponents phi in a dimensional expansion. For directed polymers we find zeta about 0.63 (d=3), zeta about 0.8 (d=2) and for isotropic polymers zeta about 0.8 (d=3). In all cases z>2 and the velocity versus applied force characteristics is sublinear, i.e. at small forces v(f) f^phi with phi > 1. It indicates that this new state is glassy, with dynamically generated barriers leading to trapping, even by a divergenceless (transversal) flow. For random flows with long-range (LR) correlations, we find continuously varying exponents with the ratio gL/gT of potential to transversal disorder, and interesting crossover phenomena between LR and SR behavior. For isotropic polymers new effects (e.g. a sign change of zeta - zeta_0) result from the competition between localization and stretching by the flow. In contrast to purely potential disorder, where the dynamics gets frozen, here the dynamical exponent z is not much larger than 2, making it easily accessible by simulations. The phenomenon of pinning by transversal disorder is further demonstrated using a two monomer ``dumbbell'' toy model.Comment: Final version, some explications added and misprints corrected (69 pages latex, 40 eps-figures included

Diffusion of polymer chains in disordered media

The diffusion of a polymer chain in a random environment is studied by means of the RG method. Below the critical dimension of the disorder considered ($d_{\rm c}=2$) the anomalous diffusion takes place and the results for polymer chain follows from that of the Brownian particle by an appropriate rescaling of the strength of the disorder and the bare diffusion coefficient. The results of the RG study of the anomalous diffusion below the critical dimension are used to compute the renormalized diffusion coefficient above the critical dimension