Stability of the 2+2 fermionic system with point interactions

Abstract

We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m_c \approx 0.58 such that the system is stable, i.e., the energy is bounded from below, for m \in [m_c, m_c^{-1}]. So far it was not known whether this 2+2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N+M system.

LaTeX, 12 pages; typos corrected, references and 2 figures added; to appear in Math. Phys. Anal. Geom

References in corpus (2)

• Stability of a fermionic $N+1$ particle system with point interactions
• Stability of the two-dimensional Fermi polaron

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• Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity
• Energy contribution of a point interacting impurity in a Fermi gas
• Three-body contact for fermions. I. General relations
• Hamiltonians for Quantum Systems with Contact Interactions