Semilinear responseM. 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 . 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 by a constant changes the diffusion constant to . However, we discuss circumstances where this linearity does not extend to the function space of intensities, so that if intensities yield diffusion constants Di, then the intensity does not result in a diffusion constant . 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