$2{k}_{F}$-Friedel to $4{k}_{F}$-Wigner oscillations in one-dimensional Fermi gases under confinement

$2 k_{F}$ -Friedel to $4 k_{F}$ -Wigner oscillations in one-dimensional Fermi gases under confinement

Gao Xianlong

Phys. Rev. A 86, 023616 – Published 14 August 2012

Abstract

Density oscillations of confined one-dimensional Fermi gases of contact repulsive interactions in a continuous space are discussed within Bethe-ansatz-based spin-density-functional theory. The results are compared against the exact analytical and the exact diagonalization method. For an unpolarized system, the number of peaks in the density profiles is doubled, signaling the crossover of the $2 k_{F}$ -Friedel to $4 k_{F}$ -Wigner oscillations (with $k_{F}$ being the Fermi wave vector). For both unpolarized and polarized systems, a threshold of the short-range interaction strength can be found where $N_{f}$ -peak Wigner oscillations of a $4 k_{F}$ wave vector appear in the density profile ( $N_{f}$ is the total particle number).