Quantum phase transition for the BEC – BCS crossover in condensed matter physics and CPT violation in elementary particle physics

We discuss the quantum phase transition which separates a vacuum state with fully-gapped fermion spectrum from a vacuum state with topologically-protected Fermi points (gap nodes). In the context of condensed-matter physics, such a quantum phase transition with Fermi point splitting may occur for a system of ultracold fermionic atoms in the region of the BEC – BCS crossover, provided the Cooper pairing occurs in the non-$s$-wave channel. For elementary particle physics, the splitting of Fermi points may lead to CPT violation, neutrino oscillations, and other phenomena.