Relationship between Population Dynamics and the Self-Energy in Driven Non-Equilibrium Systems

TL;DR

This paper investigates the relationship between population decay rates and self-energy in driven non-equilibrium systems, emphasizing the importance of accurate Green's function and self-energy treatment in theoretical models.

Contribution

It clarifies the connection between population decay calculations via Keldysh formalism and equations of motion, highlighting the need for careful handling of cancellations and time dependencies.

Findings

Proper treatment of Green's functions affects decay rate calculations.

Naive assumptions can lead to incorrect decay interpretations.

Careful analysis ensures consistency between different theoretical approaches.

Abstract

We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, it is common to make a number of simplifying assumptions within the differential equation for the populations that allows one to interpret the decay in terms of hot electrons interacting with a phonon bath. Here we show how care must be taken to ensure an accurate treatment of the equation of motion for the populations due to the fact that there are identities that require cancellations of terms that naively look like they contribute to the decay rates. In particular, the average time dependence of the Green's functions and self-energies plays a pivotal role in determining these decay rates.