Unitary gas in an isotropic harmonic trap: Symmetry properties and applications

Unitary gas in an isotropic harmonic trap: Symmetry properties and applications

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 coor...

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Veröffentlicht in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2006-11, Vol.74 (5), Article 053604
Hauptverfasser: Werner, Félix, Castin, Yvan
Format: Artikel
Sprache:eng
Schlagworte:
ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOSONS
Condensed Matter
DEGREES OF FREEDOM
FERMIONS
HARMONIC POTENTIAL
INTERACTIONS
Other
Physics
POTENTIAL ENERGY
RADIATION PRESSURE
S WAVES
SCATTERING LENGTHS
SO GROUPS
SYMMETRY
TRAPPING
TRAPS
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Beschreibung
Zusammenfassung: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.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.74.053604