论文标题
一维Mott可变范围跳跃的异常缩放制度
Anomalous scaling regime for one-dimensional Mott variable-range hopping
论文作者
论文摘要
我们为莫特随机步行的一维版本提供了一个异常的，缩放的缩放限制。限制过程可以启发视为具有绝对连续的速度度量和不连续尺度函数的一维扩散，这是由双面稳定的下属给出的。对应于离散模型中低电导的间隔，比例功能中的不连续性作为障碍物，限制过程在越过之前反映了一段时间。我们还讨论如何通过将Bouchaud陷阱模型元素纳入设置，可以将此“阻止”机制与“陷阱”之一结合起来。我们的证明依赖于最近开发的理论，该理论将过程的收敛性与相关的电阻度量度量空间相关联。
We derive an anomalous, sub-diffusive scaling limit for a one-dimensional version of the Mott random walk. The limiting process can be viewed heuristically as a one-dimensional diffusion with an absolutely continuous speed measure and a discontinuous scale function, as given by a two-sided stable subordinator. Corresponding to intervals of low conductance in the discrete model, the discontinuities in the scale function act as barriers off which the limiting process reflects for some time before crossing. We also discuss how, by incorporating a Bouchaud trap model element into the setting, it is possible to combine this 'blocking' mechanism with one of 'trapping'. Our proof relies on a recently developed theory that relates the convergence of processes to that of associated resistance metric measure spaces.
