© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:cond-mat/0011331 · Physical Review A

Momentum flux density, kinetic energy density, and their fluctuations for one-dimensional confined gases of noninteracting fermions

Anna Minguzzi, Patrizia Vignolo, Monica Tosi

Published May 9, 2001• 10 citations

Abstract

We present a Green's-function method for the evaluation of the particle density profile and of the higher moments of the one-body density matrix in mesoscopic systems containing a large number N of Fermi particles moving independently on a line under an external potential. The usefulness of the method is illustrated by applications to a Fermi gas confined in a harmonic potential well, for which we evaluate the momentum flux density, entering the equations of generalized hydrodynamics, and the kinetic energy density, which is relevant to the density-functional theory. As a further application of the method we explicitly display the quantum mean square fluctuations of these quantities. We also study some properties of the kinetic energy functional ${E}_{\mathrm{kin}}[n(x)]$ in the same system. Whereas a local approximation to the kinetic energy density is demonstrably wrong, an exact single-valued relationship between the density derivative of ${E}_{\mathrm{kin}}[n(x)]$ and the particle density $n(x)$ is demonstrated and evaluated for various values of the number of particles in the system.

DOI: 10.1103/physreva.63.063604

Related papers

Exact Particle and Kinetic-Energy Densities for One-Dimensional Confined Gases of Noninteracting Fermions

Patrizia Vignolo, Anna Minguzzi, M. P. Tosi

We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of noninteracting fermions, and apply it to harmonically confined systems of up to N = 1000 fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi approximation, the exact profiles show negative local pressure in the tails and a prominent shell structure which may become accessible to observation in magnetically trapped gases of fermionic alkali atoms.

arXiv:cond-mat/0009076•Physical Review Letters•Oct 2, 2000•73 citations

Temperature dependence of density profiles for a cloud of noninteracting fermions moving inside a harmonic trap in one dimension

Z. Akdeniz, Patrizia Vignolo, Anna Minguzzi +1 more

We extend to finite temperature a Green's-function method that was previously proposed to evaluate ground-state properties of mesoscopic clouds of noninteracting fermions moving under harmonic confinement in one dimension. By calculations of the particle and kinetic-energy density profiles, we illustrate the role of thermal excitations in smoothing out the quantum shell structure of the cloud and in spreading the particle spill out from quantum tunnel at the edges. We also discuss the approach of the exact density profiles to the predictions of a semiclassical model often used in the theory of confined atomic gases at finite temperature.

arXiv:cond-mat/0205480•Physical Review A•Nov 22, 2002•14 citations

Shell structure in the density profiles for noninteracting fermions in anisotropic harmonic confinement

Patrizia Vignolo, Anna Minguzzi

We develop a Green's function method to evaluate the exact equilibrium particle-density profiles of noninteracting Fermi gases in external harmonic confinement in any spatial dimension and for arbitrary trap anisotropy. While in a spherically symmetric configuration the shell effects are negligible in the case of a large number of particles, we find that for very anisotropic traps the quantum effects due to single-level occupancy and the deviations from the Thomas-Fermi approximation are also visible for mesoscopic clouds.

arXiv:cond-mat/0211102•Physical Review A•May 1, 2003•21 citations

Functional differentiation, line integration, and departures from homogeneity of the single-particle kinetic energy functional for one-dimensional systems of N fermions

N. H. March, Luis Miguel Nieto

The differential virial theorem of March and Young for N fermions moving in a common one-dimensional potential energy V(x) is here combined with the Euler equation of density functional theory expressing the constancy of the chemical potential throughout the entire inhomogeneous particle density. The functional derivative of the single-particle kinetic energy is thereby expressed directly in terms of the kinetic energy density; a line integral being involved in establishing the connection. This result is then used to establish a formula measuring departures from simple homogeneity of the kinetic energy functional: a matter of current interest in density functional theory. Finally, the general theory of the functional derivative of the single-particle kinetic energy with respect to the particle density is exemplified for the case of harmonic confinement of fermions in one dimension.

Journal of Mathematical Physics•Aug 1, 2001•1 citation

Simple Method Obtaining Analytical Expressions of Particle and Kinetic-Energy Densities for One-Dimensional Confined Fermi Gases

Xiaoxue Yang, Ying Wu

We develop a simple approach to obtain explicitly exact analytical expressions of particle and kinetic-energy densities for noninteracting Fermi gases in one-dimensional harmonic confinement, and in one-dimensional box confinement as well.

Communications in Theoretical Physics•Mar 15, 2002•0 citations

Simple Method Obtaining Analytical Expressions of Particle and Kinetic—Energy Densities for One—Dimensional Confined Fermi Gases

YANGXiao-Xue, WUYing

We develop a simple approach to obtain explicitly exact analytical expressions of particle and kinetic-energy densities for noninteracting Fermi gases in one-dimensional harmonic confinement, and in one-dimensional boxconfinement as well.

理论物理通讯：英文版•Jan 1, 2002•0 citations

We present a Green's-function method for the evaluation of the particle density profile and of the higher moments of the one-body density matrix in mesoscopic systems containing a large number N of Fermi particles moving independently on a line under an external potential. The usefulness of the method is illustrated by applications to a Fermi gas confined in a harmonic potential well, for which we evaluate the momentum flux density, entering the equations of generalized hydrodynamics, and the kinetic energy density, which is relevant to the density-functional theory. As a further application of the method we explicitly display the quantum mean square fluctuations of these quantities. We also study some properties of the kinetic energy functional

{E}_{\mathrm{kin}}[n(x)]

in the same system. Whereas a local approximation to the kinetic energy density is demonstrably wrong, an exact single-valued relationship between the density derivative of

{E}_{\mathrm{kin}}[n(x)]

and the particle density

n(x)

is demonstrated and evaluated for various values of the number of particles in the system.

We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of noninteracting fermions, and apply it to harmonically confined systems of up to N = 1000 fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi approximation, the exact profiles show negative local pressure in the tails and a prominent shell structure which may become accessible to observation in magnetically trapped gases of fermionic alkali atoms.

We extend to finite temperature a Green's-function method that was previously proposed to evaluate ground-state properties of mesoscopic clouds of noninteracting fermions moving under harmonic confinement in one dimension. By calculations of the particle and kinetic-energy density profiles, we illustrate the role of thermal excitations in smoothing out the quantum shell structure of the cloud and in spreading the particle spill out from quantum tunnel at the edges. We also discuss the approach of the exact density profiles to the predictions of a semiclassical model often used in the theory of confined atomic gases at finite temperature.

We develop a Green's function method to evaluate the exact equilibrium particle-density profiles of noninteracting Fermi gases in external harmonic confinement in any spatial dimension and for arbitrary trap anisotropy. While in a spherically symmetric configuration the shell effects are negligible in the case of a large number of particles, we find that for very anisotropic traps the quantum effects due to single-level occupancy and the deviations from the Thomas-Fermi approximation are also visible for mesoscopic clouds.

The differential virial theorem of March and Young for N fermions moving in a common one-dimensional potential energy V(x) is here combined with the Euler equation of density functional theory expressing the constancy of the chemical potential throughout the entire inhomogeneous particle density. The functional derivative of the single-particle kinetic energy is thereby expressed directly in terms of the kinetic energy density; a line integral being involved in establishing the connection. This result is then used to establish a formula measuring departures from simple homogeneity of the kinetic energy functional: a matter of current interest in density functional theory. Finally, the general theory of the functional derivative of the single-particle kinetic energy with respect to the particle density is exemplified for the case of harmonic confinement of fermions in one dimension.