Energetics of a strongly correlated Fermi gas

Journal Article · Mon Dec 15 04:00:00 EST 2008 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2008.03.004· OSTI ID:21167680

Tan, Shina ^[1]

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1. Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550 (United States)

The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution: E{sub internal}=h{sup 2}{omega}C/4{pi}am+{sigma}{sub k{sigma}}(h{sup 2}k{sup 2}/2m)(n{sub k{sigma}}= -C/k{sup 4}) where the external potential energy is not included, a is the scattering length, {omega} is the volume, n{sub k{sigma}} is the average number of fermions with wave vector k and spin {sigma}, and C{identical_to}lim{sub k{yields}}{sub {infinity}}k{sup 4}n{sub k{up_arrow}}=lim{sub k{yields}}{sub {infinity}}k{sup 4}n{sub k{down_arrow}}. This result is a universal identity. Its proof is facilitated by a novel mathematical idea, which might be of utility in dealing with ultraviolet divergences in quantum field theories. Other properties of this Fermi system, including pair correlations and the dimer-fermion scattering length, are also studied.

• OSTI ID: 21167680
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 12 Vol. 323; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CORRELATIONS
FERMI GAS
INTERACTIONS
POTENTIAL ENERGY
QUANTUM FIELD THEORY
S WAVES
SCATTERING LENGTHS
SPIN
ULTRAVIOLET DIVERGENCES
VECTORS