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Physical Review A

Effect of hard-core repulsion on the structures of a trapped two-dimensional three-boson system

Bao Cheng-guang, Yuan Zhang He, Gang Huang, T. Y. Shi

Published Jan 11, 2002• 10 citations
Publisher

Abstract

A two-dimensional three-boson system interacting with hard-core repulsion and trapped by parabolic confinement has been investigated. Two density functions associated with breathing motion and deformation, respectively, have been defined. Based on these density functions, the wave functions of low-lying states have been analyzed in detailed. The states are found to have explicit geometric features caused by the hard-core repulsion, these features depend strongly on the constraints imposed by symmetry. Striking similarity exists in the density functions, so that breathing bands can be well defined. A classification scheme is thereby proposed.

DOI
10.1103/physreva.65.022508

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A two-dimensional three-boson system interacting with hard-core repulsion and trapped by parabolic confinement has been investigated. Two density functions associated with breathing motion and deformation, respectively, have been defined. Based on these density functions, the wave functions of low-lying states have been analyzed in detailed. The states are found to have explicit geometric features caused by the hard-core repulsion, these features depend strongly on the constraints imposed by symmetry. Striking similarity exists in the density functions, so that breathing bands can be well defined. A classification scheme is thereby proposed.
A two-dimensional spin 1 three-boson system trapped by a parabolic confinement and interacting with hard-core repulsion has been investigated. The spectrum has been analyzed in detail, in particular, the existence of breathing bands has been confirmed. Two density functions associated with the oscillations of breathing and deformation, respectively, have been defined to study the structure of low-lying states. The inherent nodal structure of wave functions is found to play a decisive role. The effect of rotation on the ground-state property has also been studied. Not only the angular momentum, the permutation symmetry will also transit in accord with the increase of the speed of rotation.
A two-dimensional rotating six-boson system interacting with hard-core repulsion and trapped by parabolic confinement has been investigated. The emphasis is placed on the study of the effect of symmetry. The magic numbers are found to originate from the quantum constraints. The energy of an eigenstate and the spatial distribution of its wave function are found to be strongly affected by its inherent ability to get access to symmetric shapes. Some states with special inherent ability are found to be crystal-like, they have explicit geometric structures.
Four identical spinless bosons with purely attractive two-body short-range interactions and repulsive three-body interactions under external spherically symmetric harmonic confinement are considered. The repulsive three-body potential prevents the formation of deeply bound states with molecular character. The low-energy spectrum with vanishing orbital angular momentum and positive parity for infinitely large two-body sss-wave scattering length is analyzed in detail. Using the three-body contact, states are classified as universal, quasiuniversal, or strongly nonuniversal. Connections with the zero-range interaction model are discussed. The energy spectrum is mapped out as a function of the two-body sss-wave scattering length as,as>0{a}_{s}, {a}_{s}>0as​,as​>0. In the weakly to medium-strongly interacting regime, one of the states approaches the energy obtained for a hard-core interaction model. This state is identified as the energetically lowest-lying ``BEC state.'' Structural properties are also presented.