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Published in:
2017 | OriginalPaper | Chapter
Concepts of polymer statistical topology
Author : Sergei Nechaev
Published in: Topology and Condensed Matter Physics
Publisher: Springer Singapore
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This chapter reviews a few conceptual steps in an analytic description of topological interactions involving topology and statistical physics of fluctuating non-phantom rope-like objects. The main ingredient here is the statistics of Brownian bridges in a non-Euclidean space of constant negative curvature. After an introduction to the role of knots and topological constraints in polymeric systems, following topics are discussed, (i) the conformal methods for entangled random walks, (ii) conditional Brownian bridges in hyperbolic spaces, and (iii) the crumpled globule phase of polymers.