A polymer in a multi-interface medium

Abstract

We consider a model for a polymer chain interacting with a sequence of equispaced flat interfaces through a pinning potential. The intensity δ∈ℝ of the pinning interaction is constant, while the interface spacing T=T_N is allowed to vary with the size N of the polymer. Our main result is the explicit determination of the scaling behavior of the model in the large N limit, as a function of (T_N)_N and for fixed δ>0. In particular, we show that a transition occurs at T_N=O(log N). Our approach is based on renewal theory.