The distribution function of a semiflexible polymer and random walks with constraints

Abstract

In studying the end-to-end distribution function G(r, N ) of a worm like chain by using the propagator method we have established that the combinatorial problem of counting the paths contributing to G(r, N ) can be mapped onto the problem of random walks with constraints, which is closely related to the representation theory of the Temperley-Lieb algebra. By using this mapping we derive an exact expression of the Fourier-Laplace transform of the distribution function, G(k, p), as a matrix element of an inverse of an infinite rank matrix. Using this result we also derived a recursion relation permitting to compute G(k, p) directly. We present the results of the computation of G(k, N ) and its moments. The moments < r 2n > of G(r, N ) can be calculated exactly by calculating the (1,1) matrix element of 2n-th power of a truncated matrix of rank n + 1.