Related papers: Zero Energy Bound States in Three--Particle System…
We expose the relation between the properties of the three-body continuum states and their two-body subsystems. These properties refer to their bound and virtual states and resonances, all defined as poles of the $S$-matrix. For one…
We study charged particles in three dimensions interacting via a short-range potential in addition to the Coulomb potential. When the Bohr radius and the scattering length are much larger than the potential range, low-energy physics of the…
The Relativistic formulation of the three-boson model interacting via a zero-range two-body force in the null-plane is given in 2+1 and 1+1 space-time dimension. The bound state energy is calculed as function of the two-body boson binding…
A zero range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parametrizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary…
We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting…
In the literature it is conjectured that the ground state energies of three and four bosons are universally related for all pair-interactions given that two bosons have a zero energy resonance and no negative energy bound states. Here it is…
We propose a criterion to determine the existence of zero-energy edge states for a class of particle-hole symmetric systems. A loop is assigned for each system, and its topology and a symmetry play an essential role. Applications to d-wave…
The Bethe-Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body…
We consider a system of $N$ pairwise interacting particles described by the Hamiltonian $H$, where $\sigma_{ess} (H) = [0,\infty)$ and none of the particle pairs has a zero energy resonance. The pair potentials are allowed to take both…
An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of…
In previous work, we have developed a relativistic, model-independent three-particle quantization condition, but only under the assumption that no poles are present in the two-particle K matrices that appear as scattering subprocesses. Here…
We study a three-body system, formed by a light particle and two identical heavy dipoles, in two dimensions in the Born-Oppenheimer approximation. We present the analytic light-particle wave function resulting from an attractive zero-range…
We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…
We generalize in this paper a theorem of Titchmarsh for the positivity of Fourier sine integrals. We apply then the theorem to derive simple conditions for the absence of positive energy bound states (bound states embedded in the continuum)…
The low-energy spectrum of three particles interacting via nearly resonant two-body interactions in the Efimov regime is set by the so-called three-body parameter. We show that the three-body parameter is essentially determined by the…
We study multipoint scatterers with zero-energy bound states in three dimensions. We present examples of such scatterers with multiple zero eigenvalue or with strong multipole localization of zero-energy bound states.
We study a heavy-heavy-light three-body system confined to one space dimension. Both binding energies and corresponding wave functions are obtained for (i) the zero-range, and (ii) two finite-range attractive heavy-light interaction…
Using our recently developed relativistic three-particle quantization condition, we study the finite-volume energy shift of a spin-zero three-particle bound state. We reproduce the result obtained using non-relativistic quantum mechanics by…
Energy levels are investigated for two charged particles possessing an attractive, momentum-independent, zero-range interaction in a uniform magnetic field. A transcendental equation governs the spectrum, which is characterized by a…
Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order $L^{-6}$. Furthermore,…