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Concepts of polymer statistical topology

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Topology and Condensed Matter Physics

Part of the book series: Texts and Readings in Physical Sciences ((TRiPS,volume 19))

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Abstract

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.

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Authors and Affiliations

  1. Université Paris-Sud/CNRS, LPTMS, 91405, Orsay, France

    Sergei Nechaev

  2. Poncelet Laboratory, CNRS/Independent University of Moscow, Moscow, Russia

    Sergei Nechaev

  3. P.N. Lebedev Physical Institute RAS, 119991, Moscow, Russia

    Sergei Nechaev

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  1. Sergei Nechaev
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Editors and Affiliations

  1. Institute of Physics , Bhubaneswar, Odisha, India

    Somendra Mohan Bhattacharjee

  2. School of Mathematics, Tata Institute of Fundamental Research, Mumbai, Maharashtra, India

    Mahan Mj

  3. Department of Physics, Ramakrishna Mission Vivekananda University, Howrah, West Bengal, India

    Abhijit Bandyopadhyay

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Nechaev, S. (2017). Concepts of polymer statistical topology. In: Bhattacharjee, S., Mj, M., Bandyopadhyay, A. (eds) Topology and Condensed Matter Physics. Texts and Readings in Physical Sciences, vol 19. Springer, Singapore. https://doi.org/10.1007/978-981-10-6841-6_15

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