The distribution function of a semiflexible polymer and random walks with constraints
Abstract
In studying the endtoend distribution function G(r,N) of a wormlike 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 TemperleyLieb algebra. By using this mapping we derive an exact expression of the FourierLaplace transform of the distribution function, G(k,p), as a matrix element of the 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 langler^{2n}rangle of G(r,N) can be calculated exactly by calculating the (1, 1) matrix element of 2nth power of a truncated matrix of rank n + 1.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 November 2002
 DOI:
 10.1209/epl/i2002002535
 arXiv:
 arXiv:condmat/0206338
 Bibcode:
 2002EL.....60..546S
 Keywords:

 36.20.r;
 05.40.a;
 03.65.Fd;
 Macromolecules and polymer molecules;
 Fluctuation phenomena random processes noise and Brownian motion;
 Algebraic methods;
 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics
 EPrint:
 6 pages, 2 figures, added a reference