Long-lived states in electrophoresis: Collision of a polymer chain with two or more obstacles

We study the long-lived states which occur when a field-driven polymer chain collides with two or more fixed obstacles. For two obstacles we show that below a critical separation distance there are two catenary states, whereas beyond this there are no such states. We further show that for the two long-lived states one is stable and the other is unstable. We introduce a simple model for the dynamics for which many exact results can be obtained. In particular we show that the long-lived states can have two very different ways of unhooking, depending sensitively on the initial conditions.