Virial theorem for confined universal Fermi gases

Details Virial theorem for confined universal Fermi gases Virial theorem for confined universal Fermi gases

2008-03-11

arxiv.org/abs/0803.1647v1

Physics

Condensed Matter

Statistical Mechanics

3 pages

Scientific paper

Optically-trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We present a global proof that such a universal gas obeys the virial theorem for {\it any} trapping potential $U$ and any spin mixture, without assuming either the local density approximation or harmonic confinement. The total energy of the gas is given in scale invariant form by $E=<\epsilon\partial U/\partial\epsilon>$, where $\epsilon$ is an {\it arbitrary} energy scale in terms of which all length and energy scales that appear in the confining potential are written. This result enables model-independent energy measurement in traps that are anharmonic as well as anisotropic by observing only the cloud profile, and provides a consistency check for many-body calculations in the universal regime.

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