We consider the non-equilibrium dynamics of disordered systems as defined bya master equation involving transition rates between configurations (detailedbalance is not assumed). To compute the important dynamical time scales infinite-size systems without simulating the actual time evolution which can beextremely slow, we propose to focus on first-passage times that satisfy'backward master equations'. Upon the iterative elimination of configurations,we obtain the exact renormalization rules that can be followed numerically. Totest this approach, we study the statistics of some first-passage times for twodisordered models : (i) for the random walk in a two-dimensional self-affinerandom potential of Hurst exponent $H$, we focus on the first exit time from asquare of size $L \times L$ if one starts at the square center. (ii) for thedynamics of the ferromagnetic Sherrington-Kirkpatrick model of $N$ spins, weconsider the first passage time $t_f$ to zero-magnetization when starting froma fully magnetized configuration. Besides the expected linear growth of theaveraged barrier $\bar{\ln t_{f}} \sim N$, we find that the rescaleddistribution of the barrier $(\ln t_{f})$ decays as $e^{- u^{\eta}}$ for large$u$ with a tail exponent of order $\eta \simeq 1.72$. This value can be simplyinterpreted in terms of rare events if the sample-to-sample fluctuationexponent for the barrier is $\psi_{width}=1/3$.
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机译：我们考虑由一个主方程定义的无序系统的非平衡动力学，该主方程涉及构型之间的过渡速率（不假定详细的平衡）。为了在不模拟可能极其缓慢的实际时间演化的情况下计算重要的动态时标无限系统，我们建议关注满足“后向主方程”的首次通过时间。通过反复消除配置，我们获得了可以在数值上遵循的确切的重新规范化规则。为了测试这种方法，我们研究了两种无序模型的一些首次通过时间的统计数据：（i）对于Hurst指数$ H $的二维自亲和势的随机游走，我们关注方差的第一次退出时间如果从正方形中心开始，则为$ L乘以L $。 （ii）对于$ N $自旋的铁磁Sherrington-Kirkpatrick模型的动力学，我们考虑从完全磁化的配置开始时第一次通过时间$ t_f $到零磁化。除了平均障碍$ \ bar {\ ln t_ {f}} \ sim N $的预期线性增长之外，我们发现障碍$（\ ln t_ {f}）$的重新定标分布随着$ e ^ {-u ^ {\ eta}} $表示大$ u $，尾指数为$ \ eta \ simeq 1.72 $。如果障碍物的样本间波动指数为$ \ psi_ {width} = 1/3 $，则可以根据稀有事件简单地解释该值。
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