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 ⁎ , where 0 < a 2 ⁎ < + ∞ 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 ↗ a 2 ⁎. [ABSTRACT FROM AUTHOR]