Semilinear Response

Details Semilinear Response Semilinear Response

2005-12-04

arxiv.org/abs/cond-mat/0512070v2

Europhysics Letters 75, 709 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 1 figure

Scientific paper

10.1209/epl/i2006-10182-9

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.

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