This paper aims to investigate particle dynamics in a random environment, subjected to power-law time-dependent temperature. To this end, the scaled Brownian motion (SBM), a stochastic process described by a diffusion equation with time-dependent diffusivity, has been studied numerically in quenched disordered systems (QDLs). Here, QDLs have been modeled by spatial correlated Gaussian random potential with an exponential normalized correlation function. Results show nonergodic non-Gaussian subdiffusion for subdiffusive SBM. While a crossover from non-Gaussian Brownian diffusion to long-time Gaussian superdiffusion has been observed for the superdiffusive SBM scenario. Furthermore, the first passage time to an object significantly depends on the governing SBM regime and its scale parameter, where the first passage time becomes faster with the increasing scale parameter. The mechanism underlying these behaviors has been uncovered numerically.

中文翻译：

---

淬灭无序环境中缩放布朗运动的异常非高斯扩散

本文旨在研究随机环境中的粒子动力学，并受到幂律时间相关温度的影响。为此，我们在淬火无序系统（QDL）中对缩放布朗运动（SBM）进行了数值研究，这是一种由具有随时间扩散率的扩散方程描述的随机过程。此处，QDL 通过具有指数归一化相关函数的空间相关高斯随机势进行建模。结果显示次扩散 SBM 的非遍历非高斯次扩散。虽然在超扩散 SBM 场景中观察到从非高斯布朗扩散到长时间高斯超扩散的交叉。此外，到达物体的首次通过时间显着取决于控制 SBM 体系及其尺度参数，其中随着尺度参数的增加，首次通过时间变得更快。这些行为背后的机制已经通过数字揭示。