Topological Localization in Trivial Random Braids
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Salle 1180, bâtiment E2
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In 2015, P. Serna et al. numerically investigated fluctuations of directed polymers forming unlinked braids and showed that the fluctuations of an individual strand in such braids are qualitatively different from those of a strand in a medium of fixed parallel lines. P. Serna et al. found a logarithmic growth of the transverse spread with polymer length. This suggests that collective topological interactions are collective: each polymer simultaneously fluctuates and constrains the motion of the others. We propose a slightly different interpretation: the logarithmic regime is an intermediate one, and sufficiently long polymers demonstrate topological localization: the transverse spread of strand fluctuations tends to a finite limit. Unlike localization induced by quenched external disorder, in this case localization arises solely from collective topological constraints and leads to topological microphase separation.