  Motivated by recent experiments with Josephson qubits we propose a new
phenomenological model for 1/f noise due to collective excitations of
interacting defects in the qubit's environment. At very low temperatures the
effective dynamics of these collective modes are very slow leading to
pronounced non-Gaussian features and nonstationarity of the noise. We analyze
the influence of this noise on the dynamics of a qubit in various regimes and
at different operation points. Remarkable predictions are absolute time
dependences of a critical coupling and of dephasing in the strong coupling
regime.
