Brownian Motion and Polymer Statistics on Certain Curved Manifolds

Details Brownian Motion and Polymer Statistics on Certain Curved Manifolds Brownian Motion and Polymer Statistics on Certain Curved Manifolds

1998-04-05

arxiv.org/abs/cond-mat/9804050v1

Physics

Condensed Matter

Soft Condensed Matter

9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to appear in Phys. Rev E

Scientific paper

10.1103/PhysRevE.57.4411

We have calculated the probability distribution function G(R,L|R',0) of the end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a cylinder, a cone and a curved torus in 3-D. We showed that: surface curvature induces a geometrical localization area; at short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at large scales, (R-R')^2 is constant for the sphere, it is linear in L for the cylinder and reaches different constant values for the torus. The cone vertex induces (function of opening angle and R') contraction of the chain for all lengths. Explicit crossover formulas are derived.

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