Interacting Fermions, Boundaries, and Finite Size Effects

Understand

In this work we analyze how effects of finite size may modify the thermodynamics of a system of strongly interacting fermions that we model using an effective field theory with four-point interactions at finite temperature and density and look in detail at the case of a confining two-layer system.

• We compute the thermodynamic potential in the large-$N$ and mean-field approximations and adopt a zeta-function regularization scheme to regulate the divergences.
• Explicit expansions are obtained in different regimes of temperature and separation.
• The analytic structure of the potential is carefully analyzed and relevant integral and series representations for the various expressions involved are obtained.