Generalized Tunneling Model for TLS in amorphous materials and its predictions for their dephasing and the noise in superconducting microresonators

We formulate the generalized tunneling model for two level systems in insulators that takes into account the interaction between them and a slow power law dependence of their density of states. We show that the predictions of this model are in a perfect agreement with the recent studies of the noise in high quality superconducting resonators. The predictions also agree with the temperature dependence of the TLS dephasing rates observed in phase qubits. Both observations are impossible to explain in the framework of the standard tunneling model of TLS. We discuss the origin of the universal dimensionless parameter that controls the interaction between TLS in glasses and show that it is consistent with the assumptions of the model.