Thermodynamic properties of the trigonometric Rosen–Morse potential and applications to a quantum gas of mesons

In this study we work out thermodynamic functions for a quantum gas of mesons described as color-electric charge dipoles. They refer to a particular parametrization of the trigonometric Rosen-Morse potential which allows to be transformed to a perturbation of free quantum motion on the three-dimensional hyper-sphere, $S^{3}$, a manifold that can host only charge-neutral systems, the charge dipoles being the configuration of the minimal number of constituents. To the amount charge neutrality manifests itself as an important aspect of the color confinement in the theory of strong interaction, the Quantum Chromodynamics. We expect our findings to be of interest to the evaluation of temperature phenomena in the physics of hadrons and in particular in a quantum gas of color charge dipoles as are the mesons. The results are illustrated for $f_0$ and $J/\psi$ mesons.