The unitary gas in an isotropic harmonic trap: symmetry properties and applications
F\'elix Werner (LKB - Lhomond), Yvan Castin (LKB - Lhomond)
TL;DR
This paper explores the properties of a unitary gas in an isotropic harmonic trap, revealing exact analytical results including symmetry relations and mappings to free-space problems, advancing understanding of strongly interacting quantum gases.
Contribution
It provides new exact analytical solutions and symmetry insights for the unitary gas in a harmonic trap, connecting trapped and free-space problems.
Findings
Mapping between trapped and free-space zero-energy problems
Separability in hyperspherical coordinates
Identification of SO(2,1) hidden symmetry
Abstract
We consider N atoms trapped in an isotropic harmonic potential, with s-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the free-space zero-energy problem, separability in hyperspherical coordinates, SO(2,1) hidden symmetry, and relations between the moments of the trapping potential energy and the moments of the total energy.
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