Quantum gases on a torus

This manuscript is aimed at studying the thermodynamic properties of quantum gases confined to a torus. To do that, we consider $\mathit{\text{noninteracting}}$ gases within the grand canonical ensemble formalism. In this context, fermoins and bosons are taken into account and the calculations are properly provided in both analytical and numerical manners. In particular, the system turns out to be sensitive to the topological parameter under consideration: the winding number. Furthermore, we also derive a model in order to take into account $\mathit{\text{interacting}}$ quantum gases. To corroborate our results, we implement such a method for two different scenarios: a ring and a torus.