Low-temperature1/fnoise in microwave dielectric constant of amorphous dielectrics in Josephson qubits

The accurate analytical solution for the low temperature $1/f$ noise in a microwave dielectric constant of amorphous films containing tunneling two-level systems (TLSs) is derived within the standard tunneling model including the weak dipolar or elastic TLS-TLS interactions. The results are consistent with the recent experimental investigations of $1/f$ noise in Josephson junction qubits including the power law increase of the noise amplitude with decreasing temperature at low temperatures $T 0.1$K and its possible sensitivity to quasi-particle excitations are discussed.