An Improved Method of Relaxation Rate Calculation in Double-Well Potential Systems

Abstract

The relaxation behavior of double-well potential systems is considered on the basis of numerical calculation of eigenvalue spectrum of the Schrödinger equation. Depending on the temperature, the relaxation behavior of these systems is either quantum-mechanical or classical. The quantum-mechanical behavior is quite similar to that of two-level systems for which the tunneling model has been developed. On the other hand, the reaction rate method has been adapted for calculation of the relaxation rates of non-radiative transitions. We propose an improvement to this method, which makes it applicable to any double-well potential system. A ‘tunneling degree’ parameter is introduced in order to describe the specific relaxation behavior of these systems in the framework of both the conventional tunneling model and the classical Debye relaxation. A comparative analysis is conducted for α-quartz (E’ defect renters, H^– ion at E’₄ centers) and high-temperature superconducting cuprates (apical O(A) atoms). The calculations presented allow one to give a theoretical description of the relaxation response in these materials under the action of an external field.