Related papers: Zero Energy Bound States in Three--Particle System…
It is proved that the eigenvalues in the N--particle system are absorbed at zero energy threshold, if none of the subsystems has a bound state with $E \leq 0$ and none of the particle pairs has a zero energy resonance. The pair potentials…
We consider a three-particle system in $\mathbb{R}^3$ with non-positive pair-potentials and non-negative essential spectrum. Under certain restrictions on potentials it is proved that the eigenvalues are absorbed at zero energy threshold…
We consider a 3--body system in $\mathbb{R}^3$ with non--positive potentials and non--negative essential spectrum. Under certain requirements on the fall off of pair potentials it is proved that if at least one pair of particles has a zero…
The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non--relativistic quantum mechanics. The long--range part of pair potentials is assumed to be pure Coulomb and no restriction…
We consider the phenomenon of eigenvalue absorption for a many body Hamiltonian, which depends on a parameter. The conditions on pair potentials, which guarantee that the eigenvalues approaching the bottom of the continuous spectrum become…
We have studied the general properties of the energy thresholds of stability for a three-particle system with short-range interaction. A wide region of the interaction constants and various ratios of the masses of particles are considered.…
The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non-relativistic quantum mechanics. The long-range part of pair potentials is assumed to be pure Coulomb and no restriction…
We consider a pairwise interacting quantum 3-body system in 3-dimensional space with finite masses and the interaction term $V_{12} + \lambda(V_{13} + V_{23})$, where all pair potentials are assumed to be nonpositive. The pair interaction…
Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher…
In this note we discuss the Efimov effect emerging in a three-particle quantum system with zero-range interactions. In particular, we consider two non-interacting identical bosons plus a different lighter particle such that the interaction…
We investigate one-dimensional three-body systems composed of two identical bosons and one imbalanced atom (impurity) with two-body and three-body zero-range interactions. For the case in the absence of three-body interaction, we give a…
Universal properties of mass-imbalanced three-body systems in 2D are studied using zero-range interactions in momentum space. The dependence of the three-particle binding energy on the parameters (masses and two-body energies) is highly…
We study bound states of a 3--particle system in $\mathbb{R}^3$ described by the Hamiltonian $H(\lambda_n) = H_0 + v_{12} + \lambda_n (v_{13} + v_{23})$, where the particle pair $\{1,2\}$ has a zero energy resonance and no bound states,…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, i.e., below the essential spectrum, is well understood, the situation of zero energy bound states at the edge…
We consider the bound states of a system consisting of a light particle and two heavy bosonic ones, which are restricted in their quantum mechanical motion to two space dimensions. A $p$-wave resonance in the heavy-light short-range…
We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a…
Universal low-energy properties are studied for three identical bosons confined in two dimensions. The short-range pair-wise interaction in the low-energy limit is described by means of the boundary condition model. The wave function is…
We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in…
We provide an analytical proof of universality for bound states in one-dimensional systems of two and three particles, valid for short-range interactions with negative or vanishing integral over space. The proof is performed in the limit of…