Distribution of activation energies for thermally activated flux motion in high-${\mathrm{T}}_{\mathrm{c}}$ superconductors: An inversion scheme

Within a thermally activated flux-motion model we derive an exact inversion scheme which makes it possible to calculate the distribution m(${\mathrm{E}}^{\mathrm{*}}$) of activation energies ${\mathrm{E}}^{\mathrm{*}}$ for flux motion from experimental magnetic relaxation data M(t,T). The distributions determined from relaxation data for polycrystalline and single-crystalline ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ strongly resemble a log-normal distribution function. The results show that within this model existing data imply that structural disorder is present in both ceramic and single-crystalline samples.