Excitation Spectra

Abstract

One of the most common ways to analyze the properties of a many-fermion system is to study its excitation spectrum, which can largely be described in terms of small-amplitude oscillations. Such oscillations constitute the response of the system to a small perturbation and thus help to understand linear response dynamics. The small amplitude allows a handling by linearized analysis of motion, a generalization of the harmonic motion around the ground state in any simple system [40]. In a many-fermion system, the harmonic analysis is similar but a bit more complex because of the quantum nature and the large number of degrees of freedom involved [10]. It amounts to exploring the space of one-particle–one-hole (1ph) excitations about the ground state. A particularly interesting feature is that individual perturbations couple to collective (harmonic oscillations) similarly to a set of coupled oscillators. This collective (small-amplitude) motion has been widely studied in self-bound fermion systems such as nuclei, metal clusters, quantum dots, or atomic traps.