  We show that the dynamics of the surface plasmon in metallic nanoparticles
damped by its interaction with particle-hole excitations can be modelled by a
single degree of freedom coupled to an environment. In this approach, the fast
decrease of the dipole matrix elements that couple the plasmon to particle-hole
pairs with the energy of the excitation allows a separation of the Hilbert
space into low- and high-energy subspaces at a characteristic energy that we
estimate. A picture of the spectrum consisting of a collective excitation built
from low-energy excitations which interacts with high-energy particle-hole
states can be formalised. The high-energy excitations yield an approximate
description of a dissipative environment (or "bath") within a finite confined
system. Estimates for the relevant timescales establish the Markovian character
of the bath dynamics with respect to the surface plasmon evolution for
nanoparticles with a radius larger than about 1 nm.
