  The electronic environment causes decoherence and dissipation of the
collective surface plasmon excitation in metallic nanoparticles. We show that
the coupling to the electronic environment influences the width and the
position of the surface plasmon resonance. A redshift with respect to the
classical Mie frequency appears in addition to the one caused by the spill-out
of the electronic density outside the nanoparticle. We characterize the
spill-out effect by means of a semiclassical expansion and obtain its
dependence on temperature and the size of the nanoparticle. We demonstrate that
both, the spill-out and the environment-induced shift are necessary to explain
the experimentally observed frequencies and confirm our findings by
time-dependent local density approximation calculations of the resonance
frequency. The size and temperature dependence of the environmental influence
results in a qualitative agreement with pump-probe spectroscopic measurements
of the differential light transmission.
