Nuclear Physics B Vol. 552 (3) pp. 529-598
Copyright (C) 1999 Elsevier Science B.V. All rights reserved.
a Kay Jörg Wiese
b Pierre Le Doussal
a , Fachbereich Physik, Universität GH Essen, 45117 Essen,, Germany
b , CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond,, 75231 Paris Cedex,, France
Received 29 August 1998; Revised 25 February 1999; Accepted 16 March 1999
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<dc(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 ζ , dynamical z and transport exponents φ in a dimensional expansion. For directed polymers we find ζ≈0.63 ( d=3 ), ζ≈0.8 ( d=2 ) and for isotropic polymers ζ≈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 φ with φ>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 ζ- ζ0 ) 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.
PACS Classification: 74.60.Ge; 05.20.-y