Brockmann D, Geisel T
Max-Planck-Institut für Strömungsforschung, Bunsenstrasse 10, Göttingen, Germany.
Phys Rev Lett. 2003 May 2;90(17):170601. doi: 10.1103/PhysRevLett.90.170601. Epub 2003 Apr 28.
We investigate the impact of external periodic potentials on superdiffusive random walks known as Lévy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random walks, Lévy flights are surprisingly sensitive to the shape of the potential while their asymptotic behavior ceases to depend on the Lévy index mu. Our analysis is based on a novel generalization of the Fokker-Planck equation suitable for systems in thermal equilibrium. Thus, the results presented are applicable to the large class of situations in which superdiffusion is caused by topological complexity, such as diffusion on folded polymers and scale-free networks.
我们研究了外部周期性势对被称为 Lévy 飞行的超扩散随机游走的影响,并表明即使是强超扩散输运也会受到外场的显著影响。与普通随机游走不同,Lévy 飞行对势的形状出奇地敏感,而它们的渐近行为不再依赖于 Lévy 指数 μ。我们的分析基于适用于热平衡系统的福克 - 普朗克方程的一种新颖推广。因此,所呈现的结果适用于由拓扑复杂性导致超扩散的一大类情况,例如在折叠聚合物和无标度网络上的扩散。