TY  - JOUR
A1  - Akimoto, Takuma
A1  - Cherstvy, Andrey G.
A1  - Metzler, Ralf
T1  - Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we report on an interesting phenomenon for the enhancement of diffusion by the start of the measurement in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case, the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. Moreover, the diffusivity can be increased by the aging time when the initial ensemble is not in equilibrium. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance; i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay unexpectedly slowly. Our findings provide a rejuvenation phenomenon in the superdiffusive regime, that is, the diffusivity for a nonequilibrium initial ensemble gradually increases to that for an equilibrium ensemble when the start of the measurement is delayed.
Y1  - 2018
U6  - https://doi.org/10.1103/PhysRevE.98.022105
SN  - 2470-0045
SN  - 2470-0053
VL  - 98
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  -