The conformation of a semiflexible filament in a quenched random potential

Motivated by the observation of the storage of excess elastic free energy - (prestress) -- in cross linked semiflexible networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random potential. The random potential, which represents the effect of cross linking to other filaments is assumed to have a finite correlation length $\xi$ and mean strength $V_{0}$. We examine statistical distribution of curvature in filament with thermal persistence length $\ell_{P}$ and length $L_0$ in the limit that $\ell_{P} \gg L_0$. We compare our theoretical predictions to finite element Brownian dynamics simulations. Lastly we comment on the validity of replica field techniques in addressing these questions.