A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Leninsky Prosp. 31, 119071 Moscow, Russia and National Research University Higher School of Economics, Myasnitskaya Ulitsa 20, Moscow 101000, Russia.
J Chem Phys. 2018 Jan 14;148(2):024505. doi: 10.1063/1.5001279.
Diffusive transport of a particle in a spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime for the 1D transport model and found that for slow decaying correlation functions the diffusivity becomes singular at some particular temperature higher than the temperature of the transition to the true non-equilibrium dispersive transport regime. It means that the diffusion becomes anomalous and does not follow the usual ∝ t law. In such situation, the fully developed non-equilibrium regime emerges in two stages: first, at some temperature there is the transition from the normal to anomalous diffusion, and then at lower temperature the average velocity for the infinite medium goes to zero, thus indicating the development of the true dispersive regime. Validity of the Einstein relation is discussed for the situation where the diffusivity does exist. We provide also some arguments in favor of conservation of the major features of the new transition scenario in higher dimensions.
我们考虑了在具有指数态密度的空间相关随机能量景观中粒子的扩散输运。对于 1D 输运模型，我们精确地计算了无弥散准平衡输运状态下的扩散系数，并发现对于缓慢衰减的相关函数，在高于向真正非平衡弥散输运状态转变的温度的某个特定温度下，扩散系数会变得奇异。这意味着扩散变得异常，不再遵循通常的∝t 定律。在这种情况下，完全发展的非平衡状态分两个阶段出现：首先，在某个温度下，从正常扩散到异常扩散的转变，然后在更低的温度下，无限介质的平均速度趋于零，从而表明真正弥散状态的出现。对于存在扩散系数的情况，我们还讨论了爱因斯坦关系的有效性。我们还提供了一些论据，以支持在更高维度上，新的转变情景的主要特征的守恒性。
