Memory regeneration phenomenon in dielectrics: the fractional derivative approach

Abstract

Classical theory predicts that a capacitor's charging current obeys the first-order differential equation and hence follows the exponential Debye law. However, there are many experimental results confirming the inverse-power Curie–von Schweidler law of the charging current. The principal difference between the Curie–von Schweidler law and the Debye law is the presence of memory: the process depends not only on initial conditions but also on the whole prehistory. We constructed and investigated the capacitor model that extends the fractional Westerlund model by accounting for the resistance of the capacitor. To follow the transition to classical Debye theory, we investigated the solution of the fractional equation for the order α close to 1. The calculations show that the solution obeys the exponential law up to some point of time independently of the prehistory and then changes its behavior to the inverse power law depending on the prehistory. Comparison with experimental data confirmed the existence of this effect. We named it the regenerated memory effect.