2007/07/12 by D. T. Son, Son, D. T.
Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Quantum, superfluid, helium dynamics #cond-mat.other
paper · pdf · doi:10.48550/arxiv.0707.1851
6 pages, 1 figure
arxiv created 2007/07/12 · openalex publication_date 2007/07/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we consider three issues related to the unitary Fermi gas in a harmonic trap. We present a short proof of a virial theorem, which states that the average energy of a particle system at unitarity in a harmonic trap is twice larger than the average potential energy. The theorem is valid for all systems with no intrinsic scale, at zero or finite temperature. We discuss the odd-even splitting in a unitarity Fermi gas in a harmonic trap. We show that at large number of particles N the odd-even splitting is proportional to N1/9ℏω, with an undetermined numerical constant. We also show that for odd N the lowest excitation energies are of order N-1/3ℏω.