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.
Collective excitations in graphene in magnetic field
研究了单层石墨烯中的集体激发。得到了描述石墨烯中电子集体性质的方程。推导中运用了多粒子量子流体力学方法的基本思想。作为推导的起点，我们使用无质量电子的狄拉克方程，该方程通常用于描述石墨烯中的电子[D. E. Sheehy和J. Schmalian，Phys.Rev.Lett. 99，226803（2007）]，其中考虑了库仑相互作用。本文通过推导石墨烯量子流体动力学方程（GQHD）研究了集体激发的色散特性。我们考虑了石墨烯在外部磁场中的情况，磁场与石墨烯样品成一定角度。我们在GQHD方程的线性近似中进行。我们观察到，垂直于石墨烯平面的磁场对集体激发的色散没有影响。对于以一定角度指向石墨烯的磁场，我们获得波色散对系统参数的依赖性：磁场的强度、波矢量、相对于磁场的波传播方向。
