Short Range Scaling Laws of Quantum Gases With Contact Interactions

Details Short Range Scaling Laws of Quantum Gases With Contact Interactions Short Range Scaling Laws of Quantum Gases With Contact Interactions

2004-12-31

arxiv.org/abs/cond-mat/0412764v2

Physics

Condensed Matter

Statistical Mechanics

4 pages, 1 figure. 2nd version: the last sentence of the abstract changed; acknowledgements completed

Scientific paper

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 $r^\gamma$. It is shown that $\gamma$ 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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