Test of finite temperature random-phase approximation on a Lipkin model

Hagino, Koichi*; Minato, Futoshi   

We investigate the applicability of the 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.