  The present paper theoretically investigates features of quantum dynamics for
localized plasmons in three-particle or four-particle spaser systems consisting
of metal nanoparticles and semiconductor quantum dots. In the framework of the
mean field approximation, the conditions for the observation of stable
stationary regimes for single-particle plasmons in spaser systems are revealed,
and realization of these regimes is discussed. The strong dipole-dipole
interaction between adjacent nanoparticles for the four-particle spaser system
is investigated. We show that this interaction can lead to the decreasing of
the autocorrelation function values for plasmons. The generation of entangled
plasmons in a three-particle spaser system with nonlinear plasmon-exciton
interaction is predicted. For the first time the use of an external magnetic
field is proposed for control of the cross-correlation between plasmons in the
three-particle spaser system.
