Semilinear Response

TL;DR

This paper explores the concept of semilinear response in quantum systems, highlighting how the diffusion rate of occupation probabilities under time-dependent perturbations can deviate from linearity in the spectrum's intensity, especially in small metal particles.

Contribution

It introduces the concept of semilinear response, showing that diffusion constants do not always sum linearly with spectral intensities in quantum systems.

Findings

Diffusion constants can be non-linear functions of spectral intensities.

Semilinear response occurs in the absorption of radiation by small metal particles.

First-order perturbation theory calculates transition rates in the studied systems.

Abstract

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.