Localization of random walks to competing manifolds of distinct dimensions
Localization of random walks to competing manifolds of distinct dimensions
复制标题
随机游走到不同维度的竞争流形的局部化
DOI：
10.1103/physreve.98.022108
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发表时间：
2018
影响因子：
2.4
通讯作者：
Kardar, Mehran
中科院分区：
文献类型：
--
作者：
Levi, Raz Halifa;Kantor, Yacov;Kardar, Mehran
我们考虑本地化的随机游动（RW）时，吸引或排斥的多个扩展流形的不同维度。特别是，我们认为RW附近的矩形楔在两个维度，其中（零维）角落和（一维）墙有竞争本地化属性。该模型也适用于（作为横截面）吸引到三维矩形楔的表面或边缘的理想聚合物。更一般地说，我们考虑维空间中的维和维流形，其中吸引力相互作用（完全或轻微）相关。然后，RW可以处于四个相位中的一个，其中它不局限于任何一个、一个或两个流形。四个阶段合并在一个特殊的多临界点（远离流形）的RW扩散。广泛的数值分析的二维RWs内或外的矩形楔限制确认预期从连续理论的一般功能，但也表现出意想不到的属性，如再入本地化的角落，而排斥它。
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- and-dimensional manifolds in-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.