Relaxation and Acoustic Properties of Localized Electron Lowered Symmetry Centers

Abstract
Relaxation behavior of electron lowered symmetry centers is considered on the basis of numerical calculation of the Schrödinger equation. The relaxation behavior of these systems is either quantum-mechanical or classical, depending on the temperature. A "tunneling degree" parameter is introduced in order to describe the specific relaxation behavior of these systems in the framework of the both conventional tunneling mode1 and classical Debye relaxation. A comparative analysis for electron lowered symmetry centers in α-quartz, such as E' defect centers, H^- ion at E₄' centers, and apex O(A) atoms in high-temperature superconducting cuprates is reported.