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SUMMARY:Topological localization in unentangled random braids
DTSTART:20261113T140000Z
DTEND:20261113T160000Z
DTSTAMP:20261111T123500Z
UID:indico-event-17626@indico.math.cnrs.fr
CONTACT:gaiur@ihes.fr\;+33758543130
DESCRIPTION:Speakers: Sergei Nechaev (LPTMS - CNRS & Universite Paris Sacl
 ay)\n\nIn 2015\, P. Serna\, G. Bunin\, and A. Nahum numerically investigat
 ed fluctuations in a bunch of unentangled random threads. They showed that
  fluctuations of an individual tread in a braid are qualitatively differen
 t from those of a thread embedded in a medium of fixed parallel lines. In 
 particular\, they observed a logarithmic increase in the transverse span\,
  D\, of a thread with its length\, N. Studying this problem both numerical
 ly and analytically\, we propose the following interpretation: the logarit
 hmic regime is an intermediate one\, and sufficiently long threads exhibit
  topological localization\, where span D approaches a finite limit at N >>
  1. Unlike localization induced by quenched external disorder\, this pheno
 menon arises solely from collective topological constraints\, giving rise 
 to topological microphase separation. We study braids within a locally fre
 e approximation and confirm the localization by analytical investigation o
 f Brownian bridges on the asymptotic Cayley graph of a locally free group 
 LF_n which approximates the braid group B_{n+1}. We conjecture that topolo
 gically induced localization emerges as a phase transition: for a small nu
 mber of threads\, n ~ 3 -- 5\, the span\, D\, grows algebraically with N (
 N>>1)\, as D ~ N^{1/4}. By contrast\, for large n\, each thread in a long 
 braid asymptotically localizes\, approaching D ~ const.\n\nhttps://indico.
 math.cnrs.fr/event/17626/
LOCATION:Salle Marie-Louise Dubreil-Jacotin (IHP - Bâtiment Borel)
URL:https://indico.math.cnrs.fr/event/17626/
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