Dynamical model for gain-assisted localized surface plasmons

We present a dynamical model for a classically treated metal spherical inclusion in a gain assisted medium described using quantum formalism. The model integrates geometry via a proper set of boundary conditions and it is shown to be consistent with the statical formula for polarizability, which can be obtained in the low amplitude linear approximation. This dynamical approach is able to describe transient regimes, to study instabilities and to account the effects of a pulsed pump.