Strong anomalous diffusion in two-state process with L\'evy walk and Brownian motion
Abstract
Strong anomalous diffusion phenomena are often observed in complex physical and biological systems, which are characterized by the nonlinear spectrum of exponents q(q) by measuring the absolute q-th moment |x|q. This paper investigates the strong anomalous diffusion behavior of a two-state process with L\'evy walk and Brownian motion, which usually serves as an intermittent search process. The sojourn times in L\'evy walk and Brownian phases are taken as power law distributions with exponents α+ and α-, respectively. Detailed scaling analyses are performed for the coexistence of three kinds of scalings in this system. Different from the pure L\'evy walk, the phenomenon of strong anomalous diffusion can be observed for this two-state process even when the distribution exponent of L\'evy walk phase satisfies α+<1, provided that α-<α+. When α+<2, the probability density function (PDF) in the central part becomes a combination of stretched L\'evy distribution and Gaussian distribution due to the long sojourn time in Brownian phase, while the PDF in the tail part (in the ballistic scaling) is still dominated by the infinite density of L\'evy walk.
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