| Issue |
Europhys. Lett.
Volume 60, Number 4, November 2002
|
|
|---|---|---|
| Page(s) | 546 - 551 | |
| Section | Atomic and molecular physics | |
| DOI | https://doi.org/10.1209/epl/i2002-00253-5 | |
| Published online | 01 November 2002 | |
The distribution function of a semiflexible polymer and random walks with constraints
1
Martin-Luther-Universität Halle, Fachbereich Physik - D-06099 Halle, Germany
2
Institut für Festkörperforschung, Forschungszentrum Jülich D-52425 Jülich, Germany
Received:
6
May
2002
Accepted:
30
August
2002
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 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 
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.
PACS: 36.20.-r – Macromolecules and polymer molecules / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 03.65.Fd – Algebraic methods
© EDP Sciences, 2002
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