Sergey Nechaev, Wednesday, September 16th at 6:00 PM.
Title: Topological Localization in Trivial Random Braids
Annotation: In 2015, P. Serna et al. numerically studied the fluctuations of directed polymers forming random unentangled braids and showed that the fluctuations of an individual strand in a random trivial braid are qualitatively different from the fluctuations of a strand in a medium of stationary parallel lines. P. Serna et al. discovered a logarithmic increase in the transverse amplitude with polymer length. This indicates that collective topological interactions are collective in nature: each polymer simultaneously fluctuates and constrains the motion of the others.
We propose a slightly different interpretation: the logarithmic regime is intermediate, and at longer polymer lengths, topological localization arises in the system: the transverse amplitude of the strand fluctuations tends to a finite limit. In contrast to localization caused by frozen external disorder, in this case localization arises solely due to collective topological constraints and leads to topological microphase separation.