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 E. 2018 Aug;98(2-1):022129. doi: 10.1103/PhysRevE.98.022129.
We study the spectral properties of classical and quantum Markovian processes that are reset at random times to a specific configuration or state with a reset rate that is independent of the current state of the system. We demonstrate that this simple reset dynamics causes a uniform shift in the eigenvalues of the Markov generator, excluding the zero mode corresponding to the stationary state, which has the effect of accelerating or even inducing relaxation to a stationary state. Based on this result, we provide expressions for the stationary state and probability current of the reset process in terms of weighted sums over dynamical modes of the reset-free process. We also discuss the effect of resets on processes that display metastability. We illustrate our results with two classical stochastic processes, the totally asymmetric random walk and the one-dimensional Brownian motion, as well as two quantum models: a particle coherently hopping on a chain and the dissipative transverse field Ising model, known to exhibit metastability.
我们研究了经典和量子马尔可夫过程的谱性质，这些过程在随机时间被重置到一个特定的配置或状态，重置率与系统的当前状态无关。我们证明了这种简单的重置动力学导致马科夫生成器的本征值发生均匀移动，排除了与定态对应的零模，这会加速甚至诱导系统达到定态。基于这个结果，我们给出了重置过程的定态和概率流的表达式，这是在重置自由过程的动力学模式上的加权和。我们还讨论了重置对显示亚稳性的过程的影响。我们用两个经典的随机过程，完全非对称随机行走和一维布朗运动，以及两个量子模型：一个粒子在链上相干地跳跃和耗散的横向场伊辛模型，来展示我们的结果，这些模型都表现出亚稳性。
