Abstract
The Fredholm equations for one-dimensional two-component Fermions with repulsive and with attractive delta-function interactions are solved by an asymptotic expansion for A) strong repulsion, B) weak repulsion, C) weak attraction and D) strong attraction. Consequently, we obtain the first few terms of the expansion of ground state energy for the Fermi gas with polarization for these regimes. We also prove that the two sets of the Fredhom equations for weakly repulsive and attractive interactions are identical as long as the integration boundaries match each other between the two sides. Thus the asymptotic expansions of the energies of the repulsive and attractive Fermions are identical to all orders in this region. The identity of the asymptotic expansions may not mean that the energy analytically connects.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.