Time-evolution of excitations in normal Fermi liquids

TL;DR

This paper investigates the time evolution of excitations in Fermi liquids, analyzing short- and long-term behaviors of the electron spectral function, revealing non-analytic decay features and limitations of the GW approximation.

Contribution

It provides a detailed analysis of excitation dynamics in Fermi liquids, highlighting non-analytic decay terms and the need for higher-order diagrams beyond GW for accurate long-term behavior.

Findings

Identifies non-analytic terms in short-time excitation decay.

Shows exponential decay in long-time limit is inconsistent with GW approximation.

Highlights the necessity of higher-order diagrams for Fermi liquid consistency.

Abstract

We inspect the initial and the long time evolution of excitations a Fermi liquids by analyzing the time behavior of the electron spectral function. Focusing on the short-time limit we study the electron-boson model for the homogenous electron gas and apply the first order (in boson propagator) cumulant expansion of the electron Green's function. In addition to a quadratic decay in time upon triggering the excitation, we identify non-analytic terms in the time expansion similar to those found in the Fermi edge singularity phenomenon. We also demonstrate that the exponential decay in time in the long-time limit is inconsistent with the GW approximation for the self-energy. The background for this is the Paley-Wiener theorem of complex analysis. To reconcile with the Fermi liquid behavior an inclusion of higher order diagrams (in the screened Coulomb interaction) is required.