Causer Luke, Bañuls Mari Carmen, Garrahan Juan P
School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Phys Rev Lett. 2022 Mar 4;128(9):090605. doi: 10.1103/PhysRevLett.128.090605.
Recent work has shown the effectiveness of tensor network methods for computing large deviation functions in constrained stochastic models in the infinite time limit. Here we show that these methods can also be used to study the statistics of dynamical observables at arbitrary finite time. This is a harder problem because, in contrast to the infinite time case, where only the extremal eigenstate of a tilted Markov generator is relevant, for finite time the whole spectrum plays a role. We show that finite time dynamical partition sums can be computed efficiently and accurately in one dimension using matrix product states and describe how to use such results to generate rare event trajectories on demand. We apply our methods to the Fredrickson-Andersen and East kinetically constrained models and to the symmetric simple exclusion process, unveiling dynamical phase diagrams in terms of counting field and trajectory time. We also discuss extensions of this method to higher dimensions.
最近的研究表明，张量网络方法在无限时间极限下计算受约束随机模型中的大偏差函数是有效的。在此我们表明，这些方法也可用于研究任意有限时间下动态可观测量的统计特性。这是一个更具挑战性的问题，因为与无限时间情况不同，在无限时间情况下只有倾斜马尔可夫生成器的极值本征态是相关的，而在有限时间时整个谱都起作用。我们表明，使用矩阵乘积态可以在一维中高效且准确地计算有限时间动态配分函数，并描述如何利用这些结果按需生成罕见事件轨迹。我们将我们的方法应用于弗雷德里克森 - 安德森模型和东动力学约束模型以及对称简单排斥过程，揭示了基于计数场和轨迹时间的动态相图。我们还讨论了该方法向更高维度的扩展。
