TY - JOUR

T1 - Winding angle distribution for planar random walk, polymer ring entangled with an obstacle, and all that

T2 - Spitzer-Edwards-Prager-Frisch model revisited

AU - Grosberg, A.

AU - Frisch, H.

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2003/8/29

Y1 - 2003/8/29

N2 - Using a general Green function formulation, we re-derive, both (i) Spitzer and his followers results for the winding angle distribution of the planar Brownian motion, and (ii) Edwards-Prager-Frisch results on the statistical mechanics of a ring polymer entangled with a straight bar. In the statistical mechanics part, we consider both cases of quenched and annealed topology, Among new results, we compute exactly the (expectation value of) the surface area of the locus of points such that each of them has linking number n with a given closed random walk trajectory (ring polymer). We also consider the generalizations of the problem for the finite diameter (disc-like) obstacle and winding within a cavity.

AB - Using a general Green function formulation, we re-derive, both (i) Spitzer and his followers results for the winding angle distribution of the planar Brownian motion, and (ii) Edwards-Prager-Frisch results on the statistical mechanics of a ring polymer entangled with a straight bar. In the statistical mechanics part, we consider both cases of quenched and annealed topology, Among new results, we compute exactly the (expectation value of) the surface area of the locus of points such that each of them has linking number n with a given closed random walk trajectory (ring polymer). We also consider the generalizations of the problem for the finite diameter (disc-like) obstacle and winding within a cavity.

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U2 - 10.1088/0305-4470/36/34/303

DO - 10.1088/0305-4470/36/34/303

M3 - Article

AN - SCOPUS:0242266383

VL - 36

SP - 8955

EP - 8981

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 34

ER -