  It is shown how any Lindbladian evolution with selfadjoint Lindblad
operators, either Markovian or nonMarkovian, can be understood as an averaged
random unitary evolution. Both mathematical and physical consequences are
analyzed. First a simple and fast method to solve this kind of master equations
is suggested and particularly illustrated with the phase-damped master equation
for the multiphoton resonant Jaynes-Cummings model in the rotating-wave
approximation. A generalization to some intrinsic decoherence models present in
the literature is included. Under the same philosophy a proposal to generalize
the Jaynes-Cummings model is suggested whose predictions are in accordance with
experimental results in cavity QED and in ion traps. A comparison with
stochastic dynamical collapse models is also included.
