Semilinear Response

Abstract

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 λchanges the diffusion constant to λD. However, we discuss circumstances where this linearity does notextend to the function space of intensities, so that if intensities Φ_i(ω) yield diffusion constants D_i, then the intensity \sum_i Φ_i(ω) 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.