Anomalous two-state model for anomalous diffusion - art. no. 051108

An anomalous two-state model (ATSM) with the anomalous long-tailed kinetics of transitions between states is proposed to describe the specific feature s of anomalous diffusion (AD) and AD-assisted transitions (ADAT) in the dou ble-well potential. In the ATSM the system is assumed to undergo the conven tional diffusion in both states but with different diffusion coefficients. The anomalous features of diffusion result from the modulation of the diffu sion coefficient caused by transitions between ATSM states. The anomalous s pace-time evolution predicted by the ATSM is treated within the Continuous time random walk theory. With the use of the proposed ATSM the transient be havior of the AD and the ADAT is analyzed in detail. We found a large varie ty of different (and sometimes peculiar) types of the space-time behavior o f the free AD and ADAT. The free AD is found to be of subdiffusion or super diffusion type for fairly long time depending on the relation between the p arameters 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.