A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales
A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales
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理解介观现象的框架：新兴的不可预测性、对称性破缺和跨尺度的动态
DOI：
10.1016/j.cplett.2016.10.059
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发表时间：
2016-11-16
影响因子：
2.8
通讯作者：
Wang, Jin
中科院分区：
文献类型：
--
作者：
Qian, Hong;Ao, Ping;Wang, Jin
通过整合Anderson最初提出的对称性破缺、非线性动力系统的分叉、Landau的唯象相变理论和Kramers最先研究的突发稀有事件的机制这四条思路，我们引入了一个可能的框架，用于理解介观动力学，其中包括(I)快速微观(低水平)运动，(Ii)每个吸引盆地内的中层运动，以及(Iii)相邻盆地之间的较高水平的罕见转变，这些转变具有随系统大小呈指数指数下降的缓慢速率。在这个介观框架中，快速动力学用快速变化的随机过程来表示，而中层用非线性动力学来表示。多重吸引子是作为非线性系统的涌现性质出现的。Kramers理论的本质是随机元和非线性之间的相互作用，导致了不同盆地之间的连续跳跃式过渡。我们认为，每一次相变都是一种动态的对称性破缺，有可能出现Thom-Zeeman灾难以及具有遍历性破缺的相变(例如，细胞分化)。非线性介观系统的慢时间动力学不是确定性的，而是一个离散的随机跳跃过程。这些离散态的存在以及它们之间的马尔可夫跃迁都是一种浮现现象。这个新出现的随机跳跃动力学然后用作在更大的空间和更慢的时间尺度(例如，演化)上聚集的更高级别的非线性动力学的随机元素。这一描述抓住了安德森概述的层次结构，并说明了介观动力学的两种不同类型的极限：关于时间t->无穷大的长时间系综热力学，以及紧随系统大小N->；无穷大的短时间轨道稳态。在这些限制下，对称性破缺和尖点突变是同一介观系统在不同时间尺度上的两个视角。(C)2016爱思唯尔B.V.保留所有权利。
By integrating four lines of thoughts: symmetry breaking originally advanced by Anderson, bifurcation from nonlinear dynamical systems, Landau's phenomenological theory of phase transition, and the mechanism of emergent rare events first studied by Kramers, we introduce a possible framework for understanding mesoscopic dynamics that links (i) fast microscopic (lower level) motions, (ii) movements within each basin-of-attraction at the mid-level, and (iii) higher-level rare transitions between neighboring basins, which have slow rates that decrease exponentially with the size of the system. In this mesoscopic framework, the fast dynamics is represented by a rapidly varying stochastic process and the mid-level by a nonlinear dynamics. Multiple attractors arise as emergent properties of the nonlinear systems. The interplay between the stochastic element and nonlinearity, the essence of Kramers' theory, leads to successive jump-like transitions among different basins. We argue each transition is a dynamic symmetry breaking, with the potential of exhibiting Thom-Zeeman catastrophe as well as phase transition with the breakdown of ergodicity (e.g., cell differentiation). The slow-time dynamics of the nonlinear mesoscopic system is not deterministic, rather it is a discrete stochastic jump process. The existence of these discrete states and the Markov transitions among them are both emergent phenomena. This emergent stochastic jump dynamics then serves as the stochastic element for the nonlinear dynamics of a higher level aggregates on an even larger spatial and slower time scales (e.g., evolution). This description captures the hierarchical structure outlined by Anderson and illustrates two distinct types of limit of a mesoscopic dynamics: A long-time ensemble thermodynamics in terms of time t -> infinity followed by the size of the system N -> infinity, and a short-time trajectory steady state with N -> infinity followed by t -> infinity. With these limits, symmetry breaking and cusp catastrophe are two perspectives of the same mesoscopic system on different time scales. (C) 2016 Elsevier B.V. All rights reserved.