MODE-COUPLING THEORY FOR RELAXATION OF COUPLED 2-LEVEL SYSTEMS

A Mori approach to the dynamics of coupled tunnelling units in defect crystals is presented. Transverse and longitudinal correlation functio ns of a two-level system are given as continued fractions; the memory kernels are evaluated in a usual decoupling approximation. Due to the random configuration of the defects on the host lattice both two-level splitting and relaxation rates show a broad distribution; the corresp onding distribution function is derived for the case of a dipolar inte raction of the defects. The theory covers both weak and strong couplin g; the average interaction energy turns out to be the essential parame ter. Dependence on frequency, temperature and concentration of the dyn amical susceptibility is discussed. When passing from weak to strong c oupling, the zero-temperature susceptibility shows a crossover from a constant value to a decrease with the third power of inverse defect co ncentration; there is quite a strong relaxational peak in the suscepti bility. The theory accounts for several features observed in a recent low-frequency experiment on KCl:Li.