TY - JOUR

T1 - One-dimensional multicomponent fermions with δ-function interaction in strong- and weak-coupling limits

T2 - Two-component Fermi gas

AU - Guan, Xi Wen

AU - Ma, Zhong Qi

PY - 2012/3/26

Y1 - 2012/3/26

N2 - The Fredholm equations for one-dimensional two-component fermions with repulsive and with attractive δ-function interactions are solved by an asymptotic expansion for strong repulsion, weak repulsion, weak attraction, and strong attraction. Consequently, we obtain the first few terms of the expansion of the ground-state energy for the Fermi gas with polarization for these regimes. We also prove that the two sets of Fredhom equations for weakly repulsive and attractive interactions are identical as long as the integration boundaries match each other between the two types. Thus the asymptotic expansions of the energies of repulsive and attractive fermions are identical to all orders in this region. The identity of the asymptotic expansions may not mean that the energy connects analytically.

AB - The Fredholm equations for one-dimensional two-component fermions with repulsive and with attractive δ-function interactions are solved by an asymptotic expansion for strong repulsion, weak repulsion, weak attraction, and strong attraction. Consequently, we obtain the first few terms of the expansion of the ground-state energy for the Fermi gas with polarization for these regimes. We also prove that the two sets of Fredhom equations for weakly repulsive and attractive interactions are identical as long as the integration boundaries match each other between the two types. Thus the asymptotic expansions of the energies of repulsive and attractive fermions are identical to all orders in this region. The identity of the asymptotic expansions may not mean that the energy connects analytically.

UR - http://www.scopus.com/inward/record.url?scp=84859044274&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.85.033632

DO - 10.1103/PhysRevA.85.033632

M3 - Article

SN - 1050-2947

VL - 85

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 3

M1 - 033632

ER -