Mass Concentration of Two-Spinless Fermi Systems with Attractive Interactions

We study the two-spinless mass-critical Fermi systems with attractive interactions and trapping potentials. We prove that ground states of the system exist, if and only if the strength $a$ of attractive interactions satisfies $0<a<a_2^{\ast }$, where $0<a_2^{\ast }<+\mathrm{\infty }$ is the best constant of a dual finite-rank Lieb-Thirring inequality. By the blow-up analysis of many-fermion systems, we show that ground states of the system concentrate at the flattest minimum points of the trapping potential $V(x)$ as $a\nearrow a_2^{\ast }$.