Weakly coupled tunneling systems in mixed crystals

The low-temperature behavior of imperfect crystals like KCl with a few ppm of substitutional defects like OH- or Li+ is dominated by the dynamics of these defects. At low concentrations the defects are usually described as isolated systems. We find that in typical experimental situations even at concentrations of only one ppm the defects are not independent of each other. Instead they form pairs. For weak coupling, bulk quantities like the dielectric constant are hardly affected, but the total moments (electric and elastic) of the pairs of tunneling systems depend on the relative angles between the tunneling systems. Since these angles take several discrete values, there is a set of Rabi frequencies, relaxation rates, and phase coherence times, affecting echo experiments.