  We discuss the response of a quantum system to a time-dependent perturbation
with spectrum \Phi(\omega). This is characterised by a rate constant D
describing the diffusion of occupation probability between levels. We calculate
the transition rates by first-order perturbation theory, so that multiplying
\Phi(\omega) by a constant \lambda changes the diffusion constant to \lambda D.
However, we discuss circumstances where this linearity does notextend to the
function space of intensities, so that if intensities \Phi_i(\omega) yield
diffusion constants D_i, then the intensity \sum_i \Phi_i(\omega) does not
result in a diffusion constant \sum_i D_i. This `semilinear' response can occur
in the absorption of radiation by small metal particles.
