Directed polymer in random media with a defect

Abstract

We investigate a directed polymer in random media with an attractive defect at the center of the one-dimensional substrate. Without the defect, the end to end distance Deltax of the polymer follows Deltax approximately t;{1/z} , with z=3/2 and t is the polymer length. When the defect strength is weak, its contribution to Deltax is negligible. If > or =_{c} , then Deltax approaches a finite value Deltax_{sat}() in large t limit, and we find Deltax_{sat} approximately (-_{c});{-delta} , with delta approximately 3.0 . Such transition is related to the queuing phenomena of the asymmetric simple exclusion process. The polymer energy fluctuation is also discussed.