Exact solution for flux creep with logarithmicU(j) dependence: Self-organized critical state in high-Tcsuperconductors

An exact solution describing flux creep in high-${\mathit{T}}_{\mathit{c}}$ superconductors is found, assuming the creep activation barrier U grows logarithmically with decreasing current j: U=${\mathit{U}}_0$ ln(${\mathit{j}}_0$/j). For incomplete flux penetration, the flux density B is a function of the single variable ξ=x/${\mathit{t}}^{1/(\mathrm{\sigma }+2)}$, σ=${\mathit{U}}_0$/T, and the system considered exhibits self-organized criticality. In a fully penetrated sample, B depends separately upon x and t. A sharp transition between these regimes occurs when the flux fronts from opposite sides of the sample meet, resulting in a kink in the magnetization relaxation curve.