Unitary gas in an isotropic harmonic trap: Symmetry properties and applications
Félix Werner,Yvan Castin +1 more
TLDR
In this paper, the authors consider a set of atoms trapped in an isotropic harmonic potential, with infinite scattering length, and obtain exact analytical results: mapping between the trapped problem and the free-space zero-energy problem, separability in hyperspherical coordinates, SO(2,1) hidden symmetry, existence of a decoupled bosonic degree of freedom, and relations between the moments of the trapping potential energy and the moment of the total energy.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, existence of a decoupled bosonic degree of freedom, and relations between the moments of the trapping potential energy and the moments of the total energy.read more
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Many-Body Physics with Ultracold Gases
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Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry
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Nonrelativistic conformal field theories
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The BCS-BEC crossover and the unitary fermi gas
TL;DR: In this paper, it was shown that the ultracold Fermi gases exhibited behavior that, with the turn of a knob, could be made to span the entire range from BCS to BEC.
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Generalized virial theorem and pressure relation for a strongly correlated Fermi gas
TL;DR: For a two-component Fermi gas in the unitarity limit (i.e., with infinite scattering length), there is a well-known virial theorem, first shown by J.E. Thomas et al..