有偏连续时间随机游动中扩散的增强、慢松弛、遍历性和再生
Enhancement, slow relaxation, ergodicity and rejuvenation of diffusion in biased continuous-time random walks
摘要：
偏压对周期势中扩散的增强起着重要的作用。使用连续时间随机游走的存在下的偏见，我们提供了一种新的机制，在随机能量景观的扩散增强。当等待时间的方差发散时，与无偏置的情况相反，有偏置的动态变得超扩散。在超扩散制度，我们发现一个独特的初始系综依赖的扩散。我们表明，时间平均方差收敛到相应的整体平均方差，即，保持遍历性。然而，时间平均方差的轨迹波动衰减缓慢。我们的研究结果表明，在superdiffusive制度的非平衡初始合奏的扩散率逐渐增加到平衡合奏时，测量的开始被延迟，对应于复兴的扩散。
英文摘要：
Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we provide a novel mechanism for the enhancement of diffusion in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance, i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay slowly. Our finding suggests that in the superdiffusive regime the diffusivity for a non-equilibrium initial ensemble gradually increases to that for an equilibrium ensemble when the start of the measurement is delayed, corresponding to a rejuvenation of diffusivity.
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