Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.
Phys Rev E. 2018 Jul;98(1-1):012107. doi: 10.1103/PhysRevE.98.012107.
An active network is a prototype model in nonequilibrium statistical mechanics. It can represent, for example, a system with particles that have a self-propulsion mechanism. Each node of the network specifies a possible location of a particle and its orientation. The orientation (which is formally like a spin degree of freedom) determines the self-propulsion direction. The bonds represent the possibility to make transitions: to hop between locations or to switch the orientation. In systems of experimental interest (Janus particles), the self-propulsion is induced by illumination. An emergent aspect is the topological stochastic disorder (TSD). It is implied by the nonuniformity of the illumination. In technical terms the TSD reflects the local nonzero circulations (affinities) of the stochastic transitions. This type of disorder, unlike a nonhomogeneous magnetic field, is non-Hermitian and can lead to the emergence of a complex relaxation spectrum. It is therefore dramatically distinct from the conservative Anderson-type or Sinai-type disorder. We discuss the consequences of having TSD. In particular we illuminate three different routes to underdamped relaxation and show that localization plays a major role in the analysis. Implications of the bulk-edge correspondence principle are addressed too.
主动网络是一种非平衡统计力学的原型模型。它可以表示具有自推进机制的粒子系统。网络的每个节点指定一个粒子的可能位置及其方向。方向（形式上类似于自旋自由度）决定了自推进方向。键表示进行跃迁的可能性：在位置之间跳跃或切换方向。在实验感兴趣的系统（Janus 粒子）中，自推进是由照明引起的。一个新兴的方面是拓扑随机无序（TSD）。它由照明的不均匀性所暗示。从技术上讲，TSD 反映了随机跃迁的局部非零环流（亲和力）。与非均匀磁场不同，这种无序是非厄米的，并且可以导致出现复杂的弛豫谱。因此，它与保守的安德森型或西奈型无序有很大的不同。我们讨论了具有 TSD 的后果。特别是，我们阐明了三种不同的欠阻尼弛豫途径，并表明局域化在分析中起着主要作用。还涉及到体边对应原理的含义。
