R. R. NIQMATULLIN zyxwvut : zyxwvu Theoretical Explanation of the “Universal Response” 739 phys. stat. sol. (b) 123, 739 (1984) Subject classification: 14.4 zyxwvut Department zyxwvut of Physics, Kazan State University1) To the Theoretical Explanation of the 66Universa1 Response” z BY R. R. NIGMATULLIN The observation of a universal response of electromagnetic, acoustic, and mechanical influences shows the existence of some tranafer processes in a medium, which are not described by a usual diffusion equation. It is shown that these processes can be explained by making use of the diffusion equation taking into account the ‘non-Marcovian’ character of the excitation transfer process. In accordance with the experimental data a memory function is found which in one limiting case describes pure diffusion (absence of memory) and in another case turns into the wave equation (full memory). A local field frequency distribution function is suggested which confirms the supposi- tions made. The conditions of the realisation of the transfer process with ‘remnant’ memory are found and described by a generalized linear transfer equations in fractional derivations. Die Beobachtung ekes universellen ,,Response“ auf elektromagnetischen, akustischen und me- chanischen Einfliisse zeigt die Existenz von Transferprozessen in einem Medium, die sich nicht durch eine gewohnliche Diffusionsgleichung beschreiben lassen. Es wird gezeigt, daB dieser ProzeB durch die Benutzung der Diffusiongleichung unter Beriicksichtigung des “Nicht-Markoff- schen”-Charakters der Anregungstransferprozesse erklart werden konnen. I n Ubereinstimmung mit den experimentellen Daten wird eine Gediichtnisfunktion gefunden, die in einem Grenzfall die reine Diffusion (Abwesenheit von Gedachtnis) beschreibt und in einem anderen Fall in did Wellengleichung (volles Gedachtnis) iibergeht. Eine Lokalfeld-Frequenzverteilungsfunktion wire vorgeschlagen, die diese Annahmen bestatigt. Die Bedingungen fur die Realisierung eines Transfer- prozesses mit ,,remanentern‘‘ Gedachtnis werden gefunden und durch verallgemeinertelineare Trans- fergleichungen in partiellen Ableitungen beschrieben. 1. Introduction In recent years intensive investigations of dielectric loss in solids have been carried out and are described in [I to 31 containing the most recent achievements in this field. zyxwvut As the detailed analysis of the experimental data for real dielectrics shows the so-called universal response is observed which can be expressed in the form [3] : For the polarization current For the susceptibility zyxwvu f(0) = f(0) - a,wm , (1 c) zy a2/a1 = tg (mm 9 f(w) = bpn-1 , x”(w) = b,wn-l , (1 d) b2/4 = ctg (nz/2) , f’(w) = a@” , w < Up 9 w > wp . In (1 a) to (1 d) 0 < m, n < 1, wp is the characteristic frequency of the loss. The relationships (1 &) to (1 d) are observed in a wide class of materials (dielectrics, semi- conductors) irrespective of their physical nature, type of chemical bond, and polariza- l) ul. Lenina 18,420008 Kazan, USSR.