Hysteresis-Induced Long-Time Tails

It is shown analytically that the output of the standard model for complex, nonlocal hysteresis, the Preisach model, exhibits long-time tails under quite general conditions. For uncorrelated input signals the exponent of the algebraic output correlation decay is determined solely by the tails of the input and the Preisach density. Correspondingly we identify universality classes leading to identical algebraic tails. These results predict the occurrence of $1/f$ noise for a large class of hysteretic systems.