DNA unzipping and the unbinding of directed polymers in a random media

TL;DR

This paper demonstrates the equivalence between DNA unzipping and directed polymer unbinding in a random medium, revealing a universal relation that simplifies analysis and connects to broader stochastic processes.

Contribution

It establishes a formal equivalence between DNA unzipping and directed polymer unbinding, extending the stochastic matrix form decomposition to disordered systems.

Findings

Derived the probability distribution for polymer distance from the wall.

Showed the equivalence allows reduction of problem dimensionality.

Connected results to KPZ equation and exclusion processes.

Abstract

We consider the unbinding of a directed polymer in a random media from a wall in $d=1+1$ dimensions and a simple one-dimensional model for DNA unzipping. Using the replica trick we show that the restricted partition functions of these problems are {\em identical} up to an overall normalization factor. Our finding gives an example of a generalization of the stochastic matrix form decomposition to disordered systems; a method which effectively allows to reduce dimensionality of the problem. The equivalence between the two problems, for example, allows us to derive the probability distribution for finding the directed polymer a distance $z$ from the wall. We discuss implications of these results for the related Kardar-Parisi-Zhang equation and the asymmetric exclusion process.