The dynamics of a discrete-time quantum walk subject to time-correlated noise is studied in this paper. The noise, which goes beyond the usual telegraph noise with random variables 1 and $-1$, is modeled as a unitary coin-type operator and it is generated by a sample path of the Ornstein-Uhlenbeck process. Up to the first order in the amplitude of noise, a master equation to describe the walk is derived. The dynamics governed by the master equation is in good agreement with those given by numerical simulations within a certain number of steps, depending on the parameters of noise. Two remarkable features of long-time dynamics are observed in the numerical simulations. (1) In the slow noise regime, with the increase of the noise amplitude, the quantum coherence is suppressed, and the dynamics of noisy discrete-time quantum walk gradually transits to that of classical random walk. (2) In the fast noise regime, the walker is confined into a few lattice sites, and the width of the wave packet is much narrower compared with that in the slow noise regime.

中文翻译：

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具有时间相关噪声的离散时间量子行走

研究了具有时间相关噪声的离散时间量子行走的动力学。噪声超出了通常的电报噪声，具有随机变量1和$-\mathrm{1个}$，被建模为单一硬币型算子，它是由Ornstein-Uhlenbeck过程的样本路径生成的。直至噪声幅度的第一阶，得出描述行走的主方程。主方程控制的动力学与数值模拟在一定数量的步骤内给出的动力学非常吻合，具体取决于噪声的参数。在数值模拟中观察到长期动力学的两个显着特征。（1）在慢噪声环境中，随着噪声幅度的增加，量子相干性受到抑制，有噪声的离散时间量子行走的动力学逐渐过渡到经典随机行走的动力学。（2）在快速噪声状态下，助步器被限制在几个格子位置，