Abstract
Phase diagram based on the mean square displacement (MSD) and the distribution of diffusion coefficients of the time-averaged MSD for the stored-energy-driven L\'evy flight (SEDLF) is presented. In the SEDLF, a random walker cannot move while storing energy, and it jumps by the stored energy. The SEDLF shows a whole spectrum of anomalous diffusions including subdiffusion and superdiffusion, depending on the coupling parameter between storing time (trapping time) and stored energy. This stochastic process can be investigated analytically with the aid of renewal theory. Here, we consider two different renewal processes, i.e., ordinary renewal process and equilibrium renewal process, when the mean trapping time does not diverge. We analytically show the phase diagram according to the coupling parameter and the power exponent in the trapping-time distribution. In particular, we find that distributional behavior of time-averaged MSD intrinsically appears in superdiffusive as well as normal diffusive regime even when the mean trapping time does not diverge.
Highlights
In normal diffusion processes, the diffusivity can be characterized by the diffusion coefficient in the mean square displacement (MSD)
We have shown the phase diagram based on the power-law exponent of anomalous diffusion and the distribution of TAMSDs in stored-energy-driven Lévy flight (SEDLF)
While the visit points in SEDLF are the same as the turning points of a random walker in Lévy walk [38], a random walker cannot move while it is trapped in SEDLF, which is completely different from Lévy walk
Summary
The diffusivity can be characterized by the diffusion coefficient in the mean square displacement (MSD). We note that such coupling effects become physically important in turbulent diffusion [38], diffusion of cold atoms [10], and nonthermal systems such as cells [13,43] In such enhanced diffusions, it has been known that the coupling between jump lengths and waiting times follows a power-law fashion like SEDLF [10,38], a particle is always moving, which is different from SEDLF. In terms of an ensemble average, SEDLF exhibits a whole spectrum of diffusion: sub-, normal-, and super-diffusion, depending on the coupling parameter [6,24,26,28].Because distributional behavior of the time-averaged observables such as the diffusion coefficients in SEDLF is different from that in CTRW, it is important to construct a phase diagram in terms of the power-law exponent of the MSD as well as the form of the distribution function of the TAMSD. For α ≤ 1, we only consider an ordinary renewal process because there is no equilibrium ensemble due to divergent mean trapping time which causes aging [7,9,36]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
