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