Localization of random walks to competing manifolds of distinct dimensions
Name
PhysRevE.98.022108.pdf
Size
1.55 MB
Format
Adobe PDF
Checksum (MD5)
7106dd3c6e219d85cdd00ea836a97374
Author(s)
Levi, Raz Halifa
Kantor, Yacov
Kardar, Mehran
Date Issued
August 2018
Journal
Physical Review E
Publisher
American Physical Society
Citation
Levi, Raz Halifa et al. "Localization of random walks to competing manifolds of distinct dimensions." Physical Review E 98, 2 (August 2018): 022108 © 2018 American Physical Society
Version
Final published version
Abstract
We consider localization of a random walk (RW) when attracted or repelled by multiple extended manifolds of different dimensionalities. In particular, we consider a RW near a rectangular wedge in two dimensions, where the (zero-dimensional) corner and the (one-dimensional) wall have competing localization properties. This model applies also (as cross section) to an ideal polymer attracted to the surface or edge of a rectangular wedge in three dimensions. More generally, we consider (d−1)- and (d−2)-dimensional manifolds in d-dimensional space, where attractive interactions are (fully or marginally) relevant. The RW can then be in one of four phases where it is localized to neither, one, or both manifolds. The four phases merge at a special multicritical point where (away from the manifolds) the RW spreads diffusively. Extensive numerical analyses on two-dimensional RWs confined inside or outside a rectangular wedge confirm general features expected from a continuum theory, but also exhibit unexpected attributes, such as a reentrant localization to the corner while repelled by it.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.98.022108
