Test of finite temperature RPA on a Lipkin model

TL;DR

This paper assesses the effectiveness of finite temperature RPA in modeling a solvable Lipkin model, demonstrating its ability to accurately reproduce temperature-dependent strength distributions relevant to astrophysics.

Contribution

It provides a validation of finite temperature RPA against an exactly solvable model, highlighting its accuracy at low temperatures.

Findings

Finite temperature RPA reproduces the temperature dependence of total strength.

The method is effective for both excitation and de-excitation parts.

Results are relevant for astrophysical applications.

Abstract

We investigate the applicability of finite temperature random phase approximation (RPA) using a solvable Lipkin model. We show that the finite temperature RPA reproduces reasonably well the temperature dependence of total strength, both for the positive energy (i.e., the excitation) and the negative energy (i.e., the de-excitation) parts. This is the case even at very low temperatures, which may be relevant to astrophysical purposes.