We study the time dependence of the local persistence probability during a nonstationary time evolution in the disordered contact process in $d=1$, 2, and 3 dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply at the critical point analytically for $d=1$ and numerically for $d=2,3$. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal dimension-dependent generalized exponent. For $d=1$, the distribution of sample-dependent local persistence is shown to be characterized by a universal limit distribution of effective persistence exponents. Using a phenomenological approach of rare-region effects in the active phase, we obtain a nonuniversal algebraic decay of the average persistence for $d=1$ and enhanced power laws for $d>1$. As an exception, for randomly diluted lattices, the algebraic decay remains valid for $d>1$, which is explained by the contribution of dangling ends. Results on the time dependence of average persistence are confirmed by Monte Carlo simulations. We also prove the equivalence of the persistence with a return probability, a valuable tool for the argumentations.

中文翻译：

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在无序接触过程中扩展局部持久性。

我们研究了无序接触过程中非平稳时间演化过程中局部持续概率的时间依赖性。 $d=\mathrm{1个}$，2和3维。我们提出了一种使用强无序重归一化组（SDRG）技术计算持久性的方法，然后将其应用于分析的临界点，$d=\mathrm{1个}$ 和数字上 $d=2，3$。根据结果​​，平均余辉随着时间的对数的倒数而在晚些时候衰减，并具有与维数相关的通用指数。对于$d=\mathrm{1个}$，样本依赖的局部持久性分布的特征在于有效持久性指数的通用极限分布。使用现象学的方法，在活动阶段的稀有区域效应，我们获得了平均持久性的非通用代数衰减$d=\mathrm{1个}$ 并针对 $d>\mathrm{1个}$。作为例外，对于随机稀释的晶格，代数衰减对于$d>\mathrm{1个}$，这可以通过悬空末端的贡献来解释。平均持续时间与时间的关系的结果通过蒙特卡洛模拟得到了证实。我们还用返回概率证明了持久性的等价性，这是论证的宝贵工具。