Application of a simple density-functional approximation to non-identical fermions in one-dimensional confinement

The confinement of particles, both, bosons and fermions, has been a fruitful branch of physics. In the last years, many possibilities of experimental realization have been accomplished, with different theoretical approaches to describe them and to propose new arrangements. In this context, density-functional theory (DFT) has emerged as one of the used tools, in combination with its thermal version (thDFT), for which temperatures T>0 K can be explicitly considered. In this paper we investigate the particular case of one-dimensional confinements involving a two-flavor mixture of fermions, non-identical by the difference in their masses. As a consequence of the mass imbalance, it is known the mixture can be spatially separated as a function of the external potential, fermion-fermion interaction and temperature. In order to describe this scenario by means of a two-component thDFT formalism, we propose a simple ground-state density-functional approximation. Specifically, (I) we reproduce accurate results based on exact diagonalization (not DFT) for T≥0 K; (II) by considering a hybrid confinement, with different shapes of external potential for each fermion flavor, we analyze the escaping probabilities as a function of temperature; and (III) we obtain the expected Perdew, Parr, Levy, and Balduz (PPLB) derivative discontinuity when dealing with fractional numbers of fermions. (author)