  In this work the multistream quasiparticle model of collective electron
excitations is used to study the energy-density distribution of collective
quantum excitations in an interacting electron gas with arbitrary degree of
degeneracy. Generalized relations for the probability current and energy
density distributions is obtained which reveals a new interesting quantum
phenomenon of diffusive decay of pure quasiparticle states at microscopic
level. The effects is studied for various cases of free quasiparticles,
quasiparticle in an infinite square-well potential and half-space collective
excitations. It is shown that plasmon excitations have the intrinsic tendency
to decay into equilibrium state with uniform energy density spacial
distribution. It is found that plasmon levels of quasipaticle in a square-well
potential are unstable decaying into equilibrium state due to the fundamental
property of collective excitations. The decay rates of pure plasmon states are
determined analytically. Moreover, for damped quasiparticle excitations the
non-vanishing probability current divergence leads to imaginary energy density
resulting in damping instability of energy density dynamic. The pronounced
energy density valley close to half-space boundary at low level excitations
predicts attractive force close to the surface. Current research can have
implications with applications in plasmonics and related fields. Current
analysis can be readily generalized to include external potential and magnetic
field effects.
