Localization of random walks to competing manifolds of distinct dimensions
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 locali...
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| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/117339 https://orcid.org/0000-0002-1112-5912 |
| _version_ | 1826189090132852736 |
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| author | Levi, Raz Halifa Kantor, Yacov Kardar, Mehran |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Levi, Raz Halifa Kantor, Yacov Kardar, Mehran |
| author_sort | Levi, Raz Halifa |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:09:42Z |
| format | Article |
| id | mit-1721.1/117339 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:09:42Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1173392022-09-30T07:59:38Z Localization of random walks to competing manifolds of distinct dimensions Levi, Raz Halifa Kantor, Yacov Kardar, Mehran Massachusetts Institute of Technology. Department of Physics Kardar, Mehran 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. National Science Foundation (U.S.) (Grant DMR-1708280) National Science Foundation (U.S.) (Grant PHY 1748958) 2018-08-13T18:53:28Z 2018-08-13T18:53:28Z 2018-08 2018-07 2018-08-08T18:00:28Z Article http://purl.org/eprint/type/JournalArticle 2470-0045 2470-0053 http://hdl.handle.net/1721.1/117339 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 https://orcid.org/0000-0002-1112-5912 en http://dx.doi.org/10.1103/PhysRevE.98.022108 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Levi, Raz Halifa Kantor, Yacov Kardar, Mehran Localization of random walks to competing manifolds of distinct dimensions |
| title | Localization of random walks to competing manifolds of distinct dimensions |
| title_full | Localization of random walks to competing manifolds of distinct dimensions |
| title_fullStr | Localization of random walks to competing manifolds of distinct dimensions |
| title_full_unstemmed | Localization of random walks to competing manifolds of distinct dimensions |
| title_short | Localization of random walks to competing manifolds of distinct dimensions |
| title_sort | localization of random walks to competing manifolds of distinct dimensions |
| url | http://hdl.handle.net/1721.1/117339 https://orcid.org/0000-0002-1112-5912 |
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