Semiclassical theory for absorption of radiation in particles with diffusive electron motion

We present a semiclassical analysis for the electric dipole absorption of electromagnetic radiation by small metallic particles, in the case where the electron motion is diffusive. We find that there are two contributions to the one-body effective potential: the ‘static’ potential makes a dominant contribution to the absorption coefficient below the frequency ωc = D/a2, and the ‘dynamic’ potential is dominant for frequencies ω ≫ ωc (here D is the diffusion constant, and a the size of the particle). Remarkably, these two contributions sum to give exactly the classical absorption coefficient for all frequencies.