126 research outputs found
Number-parity effect for confined fermions in one dimension
For spin-polarized fermions with harmonic pair interactions in a
-dimensional trap an odd-even effect is found. The spectrum of the
-particle reduced density matrix of the system's ground state differs
qualitatively for odd and even. This effect does only occur for strong
attractive and repulsive interactions. Since it does not exists for bosons, it
must originate from the repulsive nature implied by the fermionic exchange
statistics. In contrast to the spectrum, the -particle density and
correlation function for strong attractive interactions do not show any
sensitivity on the number parity. This also suggests that
reduced-density-matrix-functional theory has a more subtle -dependency than
density functional theory.Comment: published versio
Duality of reduced density matrices and their eigenvalues
For states of quantum systems of particles with harmonic interactions we
prove that each reduced density matrix obeys a duality condition. This
condition implies duality relations for the eigenvalues of
and relates a harmonic model with length scales with
another one with inverse lengths . Entanglement
entropies and correlation functions inherit duality from . Self-duality
can only occur for noninteracting particles in an isotropic harmonic trap
Structural quantities of quasi-two-dimensional fluids
Quasi-two-dimensional fluids can be generated by confining a fluid between
two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous
structure perpendicular to the walls due to the loss of translational symmetry.
Taking the transversal degrees of freedom as a perturbation to an appropriate
2D reference fluid we provide a systematic expansion of the -particle
density for arbitrary . To leading order in the slit width this density
factorizes into the densities of the transversal and lateral degrees of
freedom. Explicit expressions for the next-to-leading order terms are
elaborated analytically quantifying the onset of inhomogeneity. The case
yields the density profile with a curvature given by an integral over the
pair-distribution function of the corresponding 2D reference fluid, which
reduces to its 2D contact value in the case of pure excluded-volume
interactions. Interestingly, we find that the 2D limit is subtle and requires
stringent conditions on the fluid-wall interactions. We quantify the rapidity
of convergence for various structural quantities to their 2D counterparts.Comment: 12 page
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