Distribution of flux-pinning energies in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$ from flux noise

The spectral density of the magnetic flux noise measured in high-temperature superconductors in low magnetic fields scales approximately as the inverse of the frequency and increases with temperature. We use the temperature and frequency dependence of the noise to determine the pinning energies of individual flux vortices in thermal equilibrium. The distribution of pinning energies peaks below 0.1 eV in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and near 0.2 eV in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$. The noise power is proportional to the ambient magnetic field, indicating that the vortex motion is uncorrelated.