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

TL;DR

This paper analyzes the spectral properties of a three-particle quantum system with contact interactions, identifying the spectrum's structure, eigenfunction symmetries, and how bound states depend on mass ratios.

Contribution

It provides a comprehensive spectral analysis of the 2+1 fermionic trimer with contact interactions, including spectrum localization, eigenfunction symmetry, and mass-dependent bound state existence.

Findings

Identified the essential spectrum and localized the discrete spectrum.

Proved the finiteness of the discrete spectrum.

Demonstrated the monotonicity of eigenvalues with respect to mass ratio.

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.