Europhys. Lett.
Volume 75, Number 5, September 2006
Page(s) 709 - 715
Section General
Published online 04 August 2006
Europhys. Lett., 75 (5), pp. 709-715 (2006)
DOI: 10.1209/epl/i2006-10182-9

Semilinear response

M. Wilkinson1, B. Mehlig2 and D. Cohen3

1  Faculty of Mathematics and Computing, The Open University Walton Hall, Milton Keynes, MK7 6AA, UK
2  Department of Physics, Göteborg University - 41296 Gothenburg, Sweden
3  Department of Physics, Ben-Gurion University - Beer-Sheva, 84105, Israel

received 25 April 2006; accepted in final form 17 July 2006
published online 4 August 2006

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 Di, 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.

05.60.-k - Transport processes.
73.23.-b - Electronic transport in mesoscopic systems.
78.67.-n - Optical properties of low-dimensional, mesoscopic, and nanoscale materials and structures.

© EDP Sciences 2006