Spectral analysis of the 2+1 fermionic trimer with contact interactions

Abstract

We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise the discrete spectrum and prove its finiteness, qualify the angular symmetry of the eigenfunctions, and prove the increasing monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence or absence of bound states in the physically relevant regimes of masses.

References in corpus (3)

• Low-energy three-body dynamics in binary quantum gases
• On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians
• Universal description of three two-component fermions

Cited by in corpus (8)

• Self-adjoint extension schemes and modern applications to quantum Hamiltonians
• Models of zero-range interaction for the bosonic trimer at unitarity
• Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three
• Spectral Theory of the Fermi Polaron
• Impurity-induced pairing in two-dimensional Fermi gases
• Energy contribution of a point interacting impurity in a Fermi gas
• Mass-ratio condition for non-binding of three two-component particles with contact interactions
• Efimov spectrum in the Born--Oppenheimer picture of 2+1 system with zero-range heavy-light interactions