- We discuss the response of a quantum system to a time-dependent perturbation with spectrum Φ (ω). 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 Φ (ω) by a constant λ changes the diffusion constant to λD. However, we discuss circumstances where this linearity does not extend to the function space of intensities, so that if intensities Φ i (ω) yield diffusion constants D i, then the intensity∑ i Φ i (ω) does not result in a diffusion constant∑ i D i. This" semilinear" response can occur in the absorption of radiation by small metal particles.