Anomalous two-state model for anomalous diffusion.
An anomalous two-state model (ATSM) with the anomalous long-tailed kinetics of transitions between states is proposed to describe the specific features of anomalous diffusion (AD) and AD-assisted transitions (ADAT) in the double-well potential. In the ATSM the system is assumed to undergo the conventional diffusion in both states but with different diffusion coefficients. The anomalous features of diffusion result from the modulation of the diffusion coefficient caused by transitions between ATSM states. The anomalous space-time evolution predicted by the ATSM is treated within the continuous time random walk theory. With the use of the proposed ATSM the transient behavior of the AD and the ADAT is analyzed in detail. We found a large variety of different (and sometimes peculiar) types of the space-time behavior of the free AD and ADAT. The free AD is found to be of subdiffusion or superdiffusion type for fairly long time depending on the relation between the parameters of the ATSM. The kinetics of the ADAT can be either conventional (exponential) or anomalous (of inverse power type) for different parameters of the model and time.
Shushin
A I
AI
Institute of Chemical Physics, Russian Academy of Sciences, 117977, GSP-1, Kosygin strasse 4, Moscow, Russia.