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

摘要

The relaxation behavior of double-well potential systems is considered on the basis of numerical calculation of eigenvalue spectrum of the Schro1 dinger equation. Depending on the tem-perature, 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 calcula-tion 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 a-quartz (E' defect renters, H~ ion at E4 centers) and high-temperature supercon-ducting 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.