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

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 β parameter are obtained. For β = 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 < β < 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 β represents the memory, aging, and coupling effects of stochastic dynamics in complex materials.