Dynamic Behaviour of Vortex Matter, Memory Effect and Mittag--Leffler Relaxation

Using fractional Fokker--Planck equation and Langevin equation's Monte Carlo simulation, we find that when current density is less than critical current density, at the very beginning the motion for vortices is mainly within the pinning well with the typical relaxation time T_r. When time t is longer than T_r, the vortex glass will distort between two adjacent pining wells and will lead to memory effect which is lacking in the Mott insulator and pancake vortices. The inertial effect is not dominating as compared with the formation and growth of easy-flow channels. The random quenched disorder will lead to Mittag--Leffler relaxation.