  We address the dynamics of entanglement and quantum discord for two non
interacting qubits initially prepared in a maximally entangled state and then
subjected to a classical colored noise, i.e. coupled with an external
environment characterized by a noise spectrum of the form $1/f^{\alpha}$. More
specifically, we address systems where the Gaussian approximation fails, i.e.
the sole knowledge of the spectrum is not enough to determine the dynamics of
quantum correlations. We thus investigate the dynamics for two different
configurations of the environment: in the first case the noise spectrum is due
to the interaction of each qubit with a single bistable fluctuator with an
undetermined switching rate, whereas in the second case we consider a
collection of classical fluctuators with fixed switching rates. In both cases
we found analytical expressions for the time dependence of entanglement and
quantum discord, which may be also extended to a collection of flcutuators with
random switching rates. The environmental noise is introduced by means of
stochastic time-dependent terms in the Hamiltonian and this allows us to
describe the effects of both separate and common environments. We show that the
non-Gaussian character of the noise may lead to significant effects, e.g.
environments with the same power spectrum, but different configurations, give
raise to opposite behavior for the quantum correlations. In particular,
depending on the characteristics of the environmental noise considered, both
entanglement and discord display either a monotonic decay or the phenomena of
sudden death and revivals. Our results show that the microscopic structure of
environment, besides its noise spectrum, is relevant for the dynamics of
quantum correlations, and may be a valid starting point for the engineering of
non-Gaussian colored environments.
