A Simple Model for Stretched Exponential Relaxation in Three-Level Jumping Process

Abstract

y In this study, operator formalism is briefly introduced which is used to model Debye-type relaxation with three-level jumping based on Markovian framework. The author generalizes this formalism to the non-Markovian process to model the non-exponential relaxation and internal friction of real bcc metals or systems like Snoek-type. By using this formalism, stretched exponential relaxation and the frequency and temperature dependence of internal friction depending upon beta parameter are obtained. For beta = 1, it is shown that the relaxation is exponential which obeys Debye law, and the frequency and temperature dependence of internal peak are represented by a single Debye peak. However, for 0 < beta < 1 the author shows that relaxation is given by stretched exponential form, and the internal friction deviates from single Debye peak. It is concluded that beta represents the memory, aging, and coupling effects of stochastic dynamics in complex materials.