Unstable quasiparticles as a source of thermodynamic instabilities in the thermal nonlocal Nambu-Jona-Lasinio model

It has already been shown that in thermal nonlocal Nambu-Jona-Lasinio models some unphysical behavior, such as a negative pressure, may arise. In this article, it is shown how this behavior can be related to the pressence of highly unstable poles of the propagator of the model, for both the Gaussian and Lorentzian regulators cases. Computations are carried out within the real time formalism, which allows to isolate the contributions from different poles and identify the source of these instabilities. It has also been shown in recent articles how these instabilities are softened by the inclusion of the Polyakov loop when a Gaussian regulator is considered. This article shows how the softening of instabilities can be understood by studying the effect of the Polyakov loop on the poles of the propagator for the Gaussian regulator.