The James Franck Institute, The University of Chicago, Chicago, IL 60637.
Department of Physics, University of California, Merced, CA 95343.
Proc Natl Acad Sci U S A. 2018 Sep 25;115(39):E9031-E9040. doi: 10.1073/pnas.1721096115. Epub 2018 Sep 11.
In this paper, we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We consider two physically disparate systems: stochastic networks governed by microscopic single-particle dynamics, and collections of driven interacting particles described by coarse-grained hydrodynamic theory. We derive our results by mapping to well-known electronic models and exploiting the resulting correspondence between a bulk topological number and the spectrum of dissipative modes localized at the boundary. For the Markov networks, we report a general procedure to uncover the topological properties in terms of the transition rates. For the active fluid on a substrate, we introduce a topological interpretation of fluid dissipative modes at the edge. In both cases, the presence of dissipative couplings to the environment that break time-reversal symmetry are crucial to ensuring topological protection. These examples constitute proof of principle that notions of topological protection do indeed extend to dissipative processes operating out of equilibrium. Such topologically robust boundary modes have implications for both biological and synthetic systems.
本文报道了拓扑保护的概念可以应用于由主动耗散过程驱动远离平衡的稳定构型。我们考虑了两个物理上截然不同的系统：由微观单粒子动力学控制的随机网络，以及由粗粒化流体力学理论描述的受驱动相互作用粒子的集合。我们通过映射到著名的电子模型并利用由此产生的体拓扑数与边界局域耗散模式的谱之间的对应关系来得出我们的结果。对于马尔可夫网络，我们报告了一种根据跃迁率揭示拓扑性质的一般方法。对于基底上的主动流体，我们引入了一种对边缘流体耗散模式的拓扑解释。在这两种情况下，与破坏时间反演对称性的环境的耗散耦合对于确保拓扑保护至关重要。这些例子构成了拓扑保护的概念确实扩展到远离平衡的耗散过程的原理证明。这种拓扑鲁棒边界模式对于生物和合成系统都有影响。
