Universal low-energy properties of three two-dimensional particles

Abstract

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 expanded in a set of eigenfunctions on the hypersphere and the system of hyper-radial equations is used to obtain analytical and numerical results. Within the framework of this method, exact analytical expressions are derived for the eigenpotentials and the coupling terms of hyper-radial equations. The derivation of the coupling terms is generally applicable to a variety of three-body problems provided the interaction is described by the boundary condition model. The asymptotic form of the total wave function at a small and a large hyper-radius $\rho$ is studied and the universal logarithmic dependence $\sim {\ln }^3\rho$ in the vicinity of the triple-collision point is derived. Precise three-body binding energies and the $2+1$ scattering length are calculated.

30 pages with 13 figures

References in corpus (16)

• Realization of Bose-Einstein condensates in lower dimensions
• Bose-Einstein condensation in quasi2D trapped gases
• Three-body problem in Fermi gases with short-range interparticle interaction
• Three-body recombination of ultra-cold atoms to a weakly bound $s$ level
• Three-boson problem near a narrow Feshbach resonance
• Two-dimensional Bose-Einstein condensate in an optical surface trap
• Pseudopotential method for higher partial wave scattering
• Universal Properties of Two-Dimensional Boson Droplets
• Two atoms in an anisotropic harmonic trap
• Universality in the Three-Body Problem for 4He Atoms
• Three-body problem for ultracold atoms in quasi-one-dimensional traps
• Three-Body Halos in Two Dimensions
• Coupled-channel pseudo-potential description of the Feshbach resonance in two dimensions
• Threshold behavior of bosonic two-dimensional few-body systems
• Feshbach resonances in a quasi-2D atomic gas
• One-dimensional Bose chemistry: effects of non-integrability

Cited by in corpus (33)

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• Comparing and contrasting nuclei and cold atomic gases
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• Exact few-body results for strongly correlated quantum gases in two dimensions
• Universal 1+2-body bound states in planar atomic wave guides
• Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement
• Three-Body Recombination in One Dimension
• Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap
• Few-body bound states of two-dimensional bosons
• Resonant three-body physics in two spatial dimensions
• Squeezing the Efimov effect
• Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures
• Universal Two-Body Spectra of Ultracold Harmonically Trapped Atoms in Two and Three Dimensions
• Efimov states embedded in the three-body continuum
• Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions
• A supercircle description of universal three-body states in two dimensions
• Energy of N two-dimensional bosons with zero-range interactions
• Universal description of three two-component fermions
• Adiabatic Hyperspherical Representation for the Three-body Problem in Two Dimensions
• Field-induced long-lived supermolecules
• Gas-to-soliton transition of attractive bosons on a spherical surface
• Occurrence conditions for two-dimensional Borromean systems
• Efimov states of three unequal bosons in non-integer dimensions
• Ultracold heteronuclear three-body systems: How diabaticity limits the universality of recombination into shallow dimers
• Fermionic properties of two interacting bosons in a two-dimensional harmonic trap
• Hyperspherical approach to the three-bosons problem in 2D with a magnetic field
• Dynamical excitation processes and correlations of three-body two-dimensional mixtures
• Three-Boson Bound States in Two Dimensions
• Asymmetric lineshapes of Efimov resonances in mass-imbalanced ultracold gases
• Minlos-Faddeev regularization of zero-range interactions in the three-body problem
• Efimov Effect in Long-range Quantum Spin Chains
• Beyond-mean-field analysis of the Townes soliton and its breathing mode
• Quantum Monte Carlo study of few- and many-body Bose systems in one and two dimensions