In this work the diffusion in the quenched trap model with diverging mean waiting times is examined. The approach of randomly stopped time is extensively applied in order to obtain asymptotically exact representation of the disorder averaged positional probability density function. We establish that the dimensionality and the geometric properties of the lattice, on top of which the disorder is imposed, dictate the plausibility of a mean-filed approximation that will only include annealed disorder. Specifically, for any case when the probability to return to the origin ($Q_0$) is less than $1$, i.e. the transient case, the quenched trap model can be mapped on to the continuous time random walk. The explicit form of the mapping is provided. In the case when an external force is applied on a tracer particle in a media described by the quenched trap model, the response to such force is calculated and a non-linear response for sufficiently low dimensionality is observed.

中文翻译：

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淬火陷阱模型的瞬态情况

在这项工作中，研究了具有不同平均等待时间的淬火陷阱模型中的扩散。随机停止时间的方法被广泛应用，以获得无序平均位置概率密度函数的渐近精确表示。我们确定晶格的维数和几何特性，在其上强加了无序，决定了仅包括退火无序的均值场近似的合理性。具体而言，对于返回原点的概率（$Q_0$）小于$1$ 的任何情况，即瞬态情况，淬火陷阱模型可以映射到连续时间随机游走。提供了映射的显式形式。