论文标题
淬灭陷阱模型的瞬态情况
The Transient Case of The Quenched Trap Model
论文作者
论文摘要
在这项工作中，检查了与平均等待时间不同的淬灭陷阱模型中的扩散。为了获得平均位置概率密度函数的渐近确切表示，随机停止时间的方法被广泛应用。我们确定晶格的维度和几何特性（最上面是该疾病）决定了仅包括退火疾病的平均拟近近似值的合理性。具体而言，对于任何情况下，返回原点的可能性（$ q_0 $）小于$ 1 $，即瞬态案例，可以将淬灭的陷阱模型映射到连续的时间随机步行中。提供了映射的明确形式。在淬灭陷阱模型描述的介质中将外力应用于示踪剂粒子上时，计算了对这种力的响应，并观察到对足够低维度的非线性响应。
In this work the diffusion in the quenched trap model with diverging mean waiting times is examined. The approach of randomly stopped time is extensively applied in order to obtain asymptotically exact representation of the disorder averaged positional probability density function. We establish that the dimensionality and the geometric properties of the lattice, on top of which the disorder is imposed, dictate the plausibility of a mean-filed approximation that will only include annealed disorder. Specifically, for any case when the probability to return to the origin ($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.
