Pérez-Espigares Carlos, Hurtado Pablo I
Departamento de Electromagnetismo y Física de la Materia, and Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, Granada 18071, Spain.
Chaos. 2019 Aug;29(8):083106. doi: 10.1063/1.5091669.
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. In some cases, this leads to symmetry-broken space-time trajectories which enhance the probability of such events due to the emergence of ordered structures. Despite their conceptual and practical importance, these dynamical phase transitions (DPTs) at the trajectory level are difficult to characterize due to the low probability of their occurrence. However, during the last decade, advanced computational techniques have been developed to measure rare events in simulations of many-particle systems that allow the direct observation and characterization of these DPTs. Here we review the application of a particular rare-event simulation technique, based on cloning Monte Carlo methods, to characterize DPTs in paradigmatic stochastic lattice gases. In particular, we describe in detail some tricks and tips of the trade, paying special attention to the measurement of order parameters capturing the physics of the different DPTs, as well as to the finite-size effects (both in the system size and in the number of clones) that affect the measurements. Overall, we provide a consistent picture of the phenomenology associated with DPTs and their measurement.
具有多个自由度的相互作用粒子系统可能会经历相变，以维持诸如电流或活性等动力学可观测量的非典型涨落。在某些情况下，这会导致对称性破缺的时空轨迹，由于有序结构的出现，此类事件的概率会增加。尽管它们在概念和实际应用中都很重要，但由于轨迹层面的这些动力学相变（DPT）发生概率较低，因此难以进行表征。然而，在过去十年中，已经开发出先进的计算技术来测量多粒子系统模拟中的罕见事件，从而能够直接观察和表征这些DPT。在此，我们回顾一种基于克隆蒙特卡罗方法的特定罕见事件模拟技术在典型随机晶格气体中表征DPT的应用。特别是，我们详细描述了一些实用技巧，特别关注捕捉不同DPT物理特性的序参量的测量，以及影响测量结果的有限尺寸效应（包括系统尺寸和克隆数量方面）。总体而言，我们提供了一幅与DPT及其测量相关的现象学的连贯图景。
