论文标题
从随机行驶的随机行走中从本地化到离域轨迹的过渡
Transition from localized to delocalized trajectories in random walk subject to random drives
论文作者
论文摘要
随机驱动的随机行走已被广泛用作物理和生物过程的模型。尽管平衡统计物理学对该系统的动态固定点的分布产生了重要的见解，但其非平衡性能仍然在很大程度上没有探索。相反，大多数现实世界应用涉及该模型的动态方面。特别是，诸如散热和吸收量之类的动态量在预测和控制物质的非平衡阶段中起着核心作用。非平衡统计物理学的最新进展使得对随机驱动器下随机行走的动力学方面进行了更精致的研究。我们对该模型进行了数值研究，并证明它表现出两个不同的阶段：一个局部阶段，典型的随机行走轨迹不扩张，并且局限于固定点的邻域，以及一个典型的随机步行轨迹是广泛的，可以在固定点之间进行过渡。我们提出了散热的不同汇总统计数据，并表明这两个阶段截然不同。我们对这些独特阶段的表征加深了对该模型非平衡阶段的新颖策略。
Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of such a system, its non-equilibrium properties remain largely unexplored. In contrast, most real-world applications concern the dynamical aspects of this model. In particular, dynamical quantities like heat dissipation and work absorption play a central role in predicting and controlling non-equilibrium phases of matter. Recent advances in non-equilibrium statistical physics enable a more refined study of the dynamical aspects of random walk under random drives. We perform a numerical study on this model and demonstrate that it exhibits two distinct phases: a localized phase where typical random walk trajectories are non-extensive and confined to the neighborhood of fixed points, and a delocalized phase where typical random walk trajectories are extensive and can transition between fixed points. We propose different summary statistics for the heat dissipation and show that these two phases are distinctly different. Our characterization of these distinctive phases deepens the understanding of and provides novel strategies for the non-equilibrium phase of this model.
