Non-linear diffusion equation and relaxation processes in solids

A non-logarithmic time dependence of the magnetization relaxation in superconductors is modeled by certain solutions of the nonlinear equation for flux diffusion, which can be derived either on the assumption of a logarithmic dependence of the pinning potential on the current density or, equivalently, a power-law current-voltage characteristic. Limiting cases of the spatiotemporal evolution of the flux density profile are identified: at one end of the parameters governing non-linearity the classical, linear processes relevant to the reversible part of the H-T diagram of high-T_c materials are found, whereas at the other end, a true critical-state behaviour emerges. Scaling relations between the sample size, magnetic field and characteristic relaxation times are established, which should characterize the magnetization relaxation process as well as the response to an AC field in susceptibility measurements