On the Effective Quasi-Bosonic Hamiltonian of the Electron Gas: Collective Excitations and Plasmon Modes

TL;DR

This paper rigorously analyzes an effective quasi-bosonic Hamiltonian derived from the electron gas, elucidating how plasmon modes emerge as approximate eigenstates and characterizing collective excitations.

Contribution

It provides a rigorous foundation for the quasi-bosonic Hamiltonian approach and clarifies the nature of plasmon modes as approximate eigenstates.

Findings

Plasmon modes are identified as a special class of approximate eigenstates.

The effective Hamiltonian accurately describes collective excitations.

The approach bridges the random phase approximation with rigorous spectral analysis.

Abstract

We consider an effective quasi-bosonic Hamiltonian of the electron gas which emerges naturally from the random phase approximation and describes the collective excitations of the gas. By a rigorous argument, we explain how the plasmon modes can be interpreted as a special class of approximate eigenstates of this model.