2004/10/24 by Zohar Nussinov, Nussinov, Zohar, S. Nussinov +2
Mathematics · Physics and Astronomy · #Advanced Frequency and Time Standards #Atomic and Molecular Physics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.other #cond-mat.str-el #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.cond-mat/0410597
9 pages, 1 figure
openalex publication_date 2004/10/24 · arxiv created 2005/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cold atom traps and certain neutron star layers may contain fermions with separation much larger than the range of pair-wise potentials yet much shorter than the scattering length. Such systems can display \em universal characteristics independent of the details of the short range interactions. In particular, the energy per particle is a fraction ξ of the Fermi energy of the free Fermion system. Our main result is that for space dimensions D smaller than two and larger than four a specific extension of this problem readily yields ξ=1 for all D ≤ 2 whereas ξ is rigorously non-positive (and potentially vanishing) for all D ≥ 4. We discuss the D=3 case. A particular unjustified recipe suggests ξ=1/2 in D=3.