外势中的次扩散：隐藏在正规势背后的反常
Sub-diffusion in External Potential: Anomalous hiding behind Normal
摘要：
我们提出了一个子扩散模型，其中一个外力是在任何时候都作用在一个粒子上，而不仅仅是在跳的时刻。这一假设的含义是随机捕获时间对力的依赖性，与标准的连续时间随机行走模型相比，粒子行为发生了显着变化。常动力导致从非遍历的亚扩散过渡到看似遍历的扩散行为。然而，我们发现它仍然是反常的，在某种意义上说，扩散系数取决于力和反常指数。对于二次势，我们发现反常指数不仅定义了收敛速度，而且定义了不同于标准Boltzmann平衡的平稳分布。
英文摘要：
We propose a model of sub-diffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the dramatic change of particles behavior compared to the standard continuous time random walk model. Constant force leads to the transition from non-ergodic sub-diffusion to seemingly ergodic diffusive behavior. However, we show it remains anomalous in a sense that the diffusion coefficient depends on the force and the anomalous exponent. For the quadratic potential we find that the anomalous exponent defines not only the speed of convergence but also the stationary distribution which is different from standard Boltzmann equilibrium.
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