Dephasing of interacting tunneling systems

We investigate the phase coherence time of weakly interacting tunneling systems (TSs). We show that all neighbors of a given TS form together with the TS of interest an entangled cluster as long as the linewidth of the excitation of the neighbor is smaller than its interaction energy with the TS of interest. Thus, the relaxation of all neighbors in the cluster contributes to the dephasing of the TS of interest. This mechanism dominates the transversal decay of the TSs and it explains recent two-pulse echo experiments in which the exponential decay rate could not be explained within spectral diffusion consistent with internal friction data. However, since the proposed mechanism predicts only an exponential decay, the Gaussian like decay at short times remains unexplained.