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Short Range Scaling Laws of Quantum Gases With Contact Interactions

Shina Tan
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Abstract

The probability amplitude for $N$ particles in a quantum gas with negligible range of interparticle interaction potentials to come to a small region of size $r$ scales like $r^γ$. It is shown that $γ$ is quantitatively related to the ground state energy of these $N$ fermions in the unitarity limit, confined by an isotropic harmonic potential. For large $N$, the short range density distribution of these $N$ particles is predominantly the same as the Thomas-Fermi profile of the gas in the unitarity limit confined by such a harmonic potential. These results may shed light on strongly interacting ultracold atomic Fermi gases, in a trap or on an optical lattice.

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Shina Tan. 2005-02-18. Short Range Scaling Laws of Quantum Gases With Contact Interactions. https://arxiv.org/abs/cond-mat/0412764

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