Semilinear response

Wilkinson, M.; Mehlig, B. and Cohen, D. (2006). Semilinear response. Europhysics Letters, 75(5) pp. 709–715.



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 not extend to the function space of intensities, so that if intensities Phi(i)(omega) yield diffusion constants D-i, then the intensity Sigma(i)Phi(i)(omega) does not result in a diffusion constant Sigma D-i(i). This "semilinear" response can occur in the absorption of radiation by small metal particles.

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