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Universal low-energy properties of three two-dimensional particles

O. I. Kartavtsev·A. V. Malykh
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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 $ρ$ is studied and the universal logarithmic dependence $\sim \ln^3 ρ$ in the vicinity of the triple-collision point is derived. Precise three-body binding energies and the $2 + 1$ scattering length are calculated.

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O. I. Kartavtsev, A. V. Malykh. 2006-06-01. Universal low-energy properties of three two-dimensional particles. https://doi.org/10.1103/physreva.74.042506

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