Diffusive Decay of Collective Quantum Excitations in Electron Gas

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.