Anchoring of polymers by traps randomly placed on a line

We study the dynamics of a Rouse polymer chain which diffuses in a three-di mensional space under the constraint that one of its ends, referred to as t he slip-link, may move only along a one-dimensional line containing randoml y placed, immobile, perfect traps. Extensions of this model occur naturally in many fields, ranging from the spreading of polymer liquids on chemicall y active substrates to the binding of biomolecules by ligands. For our mode l we succeed in computing exactly the time evolution of the probability P-s l(t) that the chitin slip-link will not encounter any of the traps until ti me t and, consequently, that until this time the chain will remain mobile.