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

We study the dynamics of a polymer or a D-dimensional elastic manifold diff using and convected in a non-potential static random flow (the "randomly dr iven polymer model"). We find that short-range (SR) disorder is relevant fo r d less than or equal to 4 for directed polymers teach monomer sees a diff erent flow) and for d less than or equal to 6 for isotropic polymers teach 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 usi ng field theoretical methods. We show that all divergences can be absorbed in multilocal counter-terms which we compute to one loop order. We obtain t he non-trivial roughness zeta, dynamical z and transport exponents rp in a dimensional expansion. For directed polymers we find zeta approximate to 0. 63 (d = 3), zeta approximate to 0.8 (d = 2) and for isotropic polymers zeta approximate to 0.8 (d = 3). In all cases z > 2 and the velocity versus app lied force characteristics is sublinear, i.e. at small forces v(f) similar to f(phi) With phi > 1. It indicates that this new state is glassy, with dy namically 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 g(L)/g(T) Of potential t o transversal disorder, and interesting crossover phenomena between LR and SR behavior. For isotropic polymers new effects (e.g. a sign change of zeta - zeta(o)) 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, makin g it easily accessible by simulations. The phenomenon of pinning by transve rsal disorder is further demonstrated using a two monomer "dumbbell" toy mo del. (C) 1999 Elsevier Science B.V. All rights reserved.