Slater sum for a three-dimensional inhomogeneous fermi fluid with one-dimensional harmonic confinement

摘要

In early work, Bardeen [1] proposed a model whereby a three-dimensional Fermi fluid is confined to a half-space by a planar infinite barrier in the xy plane. Brown, Brown and March [2] subsequently worked out the Slater sum S(z, β), β = 1/k_BT, for this same model of partial confinement. The present work considers S(z,β) for additional harmonic confinement in the z direction. When the harmonic force constant is switched off the Slater sum calculated by Brown, Brown and March is recovered. The off-diagonal Slater sum, namely the canonical density matrix, is treated which in turn yields the Feynman propagator for this model when the reciprocal temperature β is replaced by the pure imaginary time.