Quasiparticle approach to collective quantum dielectric response

Abstract

In current research, we use a generalized quantum multistream model to develop an effective quasiparticle theory for quantum many-body effects. The N-electron Schrödinger–Poisson stream model is reduced to a system of coupled differential equations with new wavefunction representation for collective quantum excitations in the many electron system. The current theory is then applied to the collective quantum statistical behavior of homogenous electron gas. Moreover, the generalized energy dispersion relation, which incorporates the quasiparticle band structure, is used to calculate the linear dielectric response of collective quantum excitations in the electron gas with arbitrary degree of degeneracy beyond many-body theories, limiting assumptions such as the independent electron and the random phase approximations. Important parameters of electron gas such as the dynamic structure factor, the loss function, the static charge screening, optical reflectivity, and the electronic stopping power are investigated as applications of current theory. The quasiparticle theory incorporates effects both due to single-electron excitations as well as the electrostatic interaction among electrons in a single picture. Existence of Van-Hove-like singularity at the plasmon wavenumber leads to distinct features of quasiparticle response to electromagnetic perturbations in the electron gas. It is shown that collective quantum excitations in high density electron gas below a given critical electron temperature are blocked due to existence of a large quasiparticle energy bandgap above the Fermi level. A new equation of states is given for the quasiparticle excitation in the electron gas, based on the transition probability of electrons to the quasiparticle level. It is found that, the screening potential of a static charge in quasiparticle model has an oscillatory Lennard–Jones-type attractive form.