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 (4)

• Three-boson problem near a narrow Feshbach resonance
• Two-dimensional Bose-Einstein condensate in an optical surface trap
• Universal Properties of Two-Dimensional Boson Droplets
• Three-body problem for ultracold atoms in quasi-one-dimensional traps

Cited by in corpus (4)

• Low-energy three-body dynamics in binary quantum gases
• Exact few-body results for strongly correlated quantum gases in two dimensions
• Three-Body Recombination in One Dimension
• Efimov states embedded in the three-body continuum