Garbaczewski Piotr, Stephanovich Vladimir
Institute of Physics, Opole University, Opole 45-052, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031113. doi: 10.1103/PhysRevE.80.031113. Epub 2009 Sep 10.
We analyze confining mechanisms for Lévy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump-type processes are considered: those driven by Langevin equation with Lévy noise and those, named topological Lévy processes (occurring in systems with topological complexity such as folded polymers or complex networks), whose Langevin representation is unknown and possibly nonexistent. Our major finding is that both above classes of processes stay in affinity and may share common stationary probability density, even if their detailed dynamical behavior look different. This near-equilibrium observation seems to be generic to a broad class of Lévy noise-driven processes, such as e.g., superdiffusion on folded polymers, geophysical flows, and even climatic changes.
我们分析了 Lévy 飞行的限制机制。当它们在合适的外部势场中演化时，其方差可能存在并表现出超扩散输运的特征。我们考虑了两类随机跳跃型过程：一类由具有 Lévy 噪声的朗之万方程驱动，另一类称为拓扑 Lévy 过程（出现在具有拓扑复杂性的系统中，如折叠聚合物或复杂网络），其朗之万表示未知且可能不存在。我们的主要发现是，上述两类过程具有相似性，并且可能共享共同的平稳概率密度，即使它们的详细动力学行为看起来不同。这种近平衡观测结果似乎对于一大类由 Lévy 噪声驱动的过程具有普遍性，例如折叠聚合物上的超扩散、地球物理流动甚至气候变化。
