Ignatyuk V V
Institute for Condensed Matter Physics, 1 Svientsitskii Street, 79011 Lviv, Ukraine.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041133. doi: 10.1103/PhysRevE.80.041133. Epub 2009 Oct 30.
We consider surface diffusion of a single particle, which performs site-to-site underbarrier hopping, fulfils intrasite motion between the ground and the first-excited states within a quantum well, and interacts with surface phonons. We obtain a chain of quantum-kinetic equations for one-particle distribution functions and nonequilibrium hopping probabilities. The generalized diffusion coefficients are derived, and the generic non-Markovian diffusion equation is written down both for the infinite lattice model and in the continuous media limit. In the latter case, the one-particle distribution function obeys the telegrapher's equation, which could give us a nonmonotonic behavior of the intermediate distribution functions at large spatial gradients. In a weak-coupling limit, if the energy of level splitting is comparable with the temperature, there are also pronounced oscillations of the generalized diffusion coefficients. The recrossing/multiple crossing phenomena, a problem of long tails of the generalized diffusion coefficients, as well as a mapping into the next- to the nearest-neighbors hopping regime, are discussed.
我们考虑单个粒子的表面扩散，该粒子在势垒下进行逐个位点的跳跃，在量子阱内的基态和第一激发态之间实现位点内运动，并与表面声子相互作用。我们得到了关于单粒子分布函数和非平衡跳跃概率的一系列量子动力学方程。推导了广义扩散系数，并针对无限晶格模型和连续介质极限写出了一般的非马尔可夫扩散方程。在后一种情况下，单粒子分布函数服从电报方程，这可能会在大空间梯度下给出中间分布函数的非单调行为。在弱耦合极限下，如果能级分裂的能量与温度相当，广义扩散系数也会有明显的振荡。讨论了再穿越/多次穿越现象、广义扩散系数长尾巴的问题以及映射到次近邻跳跃 regime 的情况。
