We study analytically and numerically the binding properties, in particular the ground state, of the so-called $(2+1)$ -fermion system, which is a three-dimensional system of two identical fermions interacting with a third particle of different species through a zero-range interaction. We model the system with a specific self-adjoint point interaction Hamiltonian recently constructed in the mathematical literature. First we characterize the internal symmetry of the bound states in the attractive case. Then we show that the system confines in a precise regime of masses and that its ground-state energy stays finite as the mass becomes close to the critical point of the collapse of the system.We study analytically and numerically the binding properties, in particular the ground state, of the so-called $(2+1)$-fermion system, which is a three-dimensional system of two identical fermions interacting with a third particle of different species through a zero-range interaction. We model the system with a specific self-adjoint point interaction Hamiltonian recently constructed in the mathematical literature. First we characterize the internal symmetry of the bound states in the attractive case. Then we show that the system confines in a precise regime of masses and that its ground-state energy stays finite as the mass becomes close to the critical point of the collapse of the system.

Physical Review AMay 6, 201317 citations

On Point-Like Interaction between n Fermions and Another Particle

R. A. Minlos

Moscow Mathematical JournalJan 1, 201138 citations

Spectral Properties of the 2+1 Fermionic Trimer with Contact Interactions

Simon Becker, Alessandro Michelangeli, Andrea Ottolini

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 and prove the finiteness of the discrete spectrum, qualify the angular symmetry of the eigenfunctions, and prove the monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence of bound states in a physically relevant regime of masses.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 and prove the finiteness of the discrete spectrum, qualify the angular symmetry of the eigenfunctions, and prove the monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence of bound states in a physically relevant regime of masses.

arXiv:1712.10209Dec 29, 20173 citations

Interacting Composite Fermions

Chia‐Chen Chang

Jun 22, 20060 citations

Making Contact with Strongly Interacting Fermions

Anonymous

PhysicsMay 23, 20190 citations

Efimov-DNA phase diagram: Three stranded DNA on a cubic lattice

Somendra M. Bhattacharjee, Damien Paul Foster

We define a generalized model for three-stranded DNA consisting of two chains of one type and a third chain of a different type. The DNA strands are modeled by random walks on the three-dimensional cubic lattice with different interactions between two chains of the same type and two chains of different types. This model may be thought of as a classical analog of the quantum three-body problem. In the quantum situation, it is known that three identical quantum particles will form a triplet with an infinite tower of bound states at the point where any pair of particles would have zero binding energy. The phase diagram is mapped out, and the different phase transitions are examined using finite-size scaling. We look particularly at the scaling of the DNA model at the equivalent Efimov point for chains up to 10 000 steps in length. We find clear evidence of several bound states in the finite-size scaling. We compare these states with the expected Efimov behavior.We define a generalized model for three-stranded DNA consisting of two chains of one type and a third chain of a different type. The DNA strands are modeled by random walks on the three-dimensional cubic lattice with different interactions between two chains of the same type and two chains of different types. This model may be thought of as a classical analog of the quantum three-body problem. In the quantum situation, it is known that three identical quantum particles will form a triplet with an infinite tower of bound states at the point where any pair of particles would have zero binding energy. The phase diagram is mapped out, and the different phase transitions are examined using finite-size scaling. We look particularly at the scaling of the DNA model at the equivalent Efimov point for chains up to 10 000 steps in length. We find clear evidence of several bound states in the finite-size scaling. We compare these states with the expected Efimov behavior.

arXiv:2106.01690The Journal of Chemical PhysicsAug 12, 20210 citations

We study analytically and numerically the binding properties, in particular the ground state, of the so-called

(2+1)

-fermion system, which is a three-dimensional system of two identical fermions interacting with a third particle of different species through a zero-range interaction. We model the system with a specific self-adjoint point interaction Hamiltonian recently constructed in the mathematical literature. First we characterize the internal symmetry of the bound states in the attractive case. Then we show that the system confines in a precise regime of masses and that its ground-state energy stays finite as the mass becomes close to the critical point of the collapse of the system.