Stochastic model for a vortex depinning in random media

We present a self-organized stochastic model for the dynamics of a single flux line in random media. The dynamics of the flux line in the longitudinal and the transverse direction to average velocity direction are coupled to each other. The roughness exponents of the flux line are measured for each direction, which are α_≈0.63 for the longitudinal and α_⊥≈0.5 for the transverse direction, respectively. The dynamic exponents are obtained as z≈1 for both directions. We also examine the avalanche size distribution, which exhibits a power-law behavior with the exponent consistent with the one for the Sneppen model in 1+1 dimensions.