The scaling limit of polymer dynamics in the pinned phase

Details The scaling limit of polymer dynamics in the pinned phase The scaling limit of polymer dynamics in the pinned phase

2012-04-05

arxiv.org/abs/1204.1253v1

Physics

Mathematical Physics

19 pages, 3 figures

Scientific paper

We consider the stochastic evolution of a $(1+1)$ dimensional interface (or polymer) in presence of an attractive substrate. We start from a configuration far from equilibrium: an interface with a non-trivial macroscopic profile, and look at the evolution of the space rescaled interface. In the case of infinite pinning force we are able to prove that on the diffusive scale (space rescaled by $L$ in both dimensions and time rescaled by $L^2$ where $L$ denotes the length of the interface), the scaling limit of the evolution is given by a free-boundary problem with contracting boundaries which belongs to the family of Stefan problems. This is in contrast with what happens for interface dynamics with no constraint or with repelling substrate. We complement our result by giving a conjecture for the whole pinned phase.

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