Momentum flux density, kinetic energy density, and their fluctuations for onedimensional confined gases of noninteracting fermions
Abstract
We present a Green'sfunction method for the evaluation of the particle density profile and of the higher moments of the onebody 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 densityfunctional 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_{kin}[n(x)] in the same system. Whereas a local approximation to the kinetic energy density is demonstrably wrong, an exact singlevalued relationship between the density derivative of E_{kin}[n(x)] and the particle density n(x) is demonstrated and evaluated for various values of the number of particles in the system.
 Publication:

Physical Review A
 Pub Date:
 June 2001
 DOI:
 10.1103/PhysRevA.63.063604
 arXiv:
 arXiv:condmat/0011331
 Bibcode:
 2001PhRvA..63f3604M
 Keywords:

 03.75.Fi;
 05.30.Fk;
 31.15.Ew;
 Fermion systems and electron gas;
 Densityfunctional theory;
 Condensed Matter  Statistical Mechanics
 EPrint:
 10 pages, 5 figures