  We consider the nonequilibrium work distribution of a quantum oscillator with
modulated angular frequency. We examine the discrete-to-continuous transition
of the distribution as the temperature and the degree of nonadiabaticity of the
frequency transformation are increased. We further develop a perturbative
approach to analyze the effect of weak quartic anharmonicities, as well as of a
random electric field on a charged oscillator. We find in both cases that the
degree of nonadiabaticity is enhanced by the perturbation.
