Momentum flux density, kinetic energy density, and their fluctuations for one-dimensional confined gases of noninteracting fermions - art. no. 063604

We present a Green's-function method for the evaluation of the particle den sity profile and of the higher moments of the one-body density matrix in me soscopic systems containing a large number N of Fermi particles moving inde pendently on a line under an external potential. The usefulness of the meth od is illustrated by applications to a Fermi gas confined in a harmonic pot ential well, for which we evaluate the momentum Aux density, entering the e quations of generalized hydrodynamics, and the kinetic energy density, whic h is relevant to the density-functional theory. As a further application of the method we explicitly display the quantum mean square fluctuations of t hese quantities. We also study some properties of the kinetic energy functi onal E-kin[n(chi)] in the same system. Whereas a local approximation to the kinetic energy density is demonstrably wrong, an exact single-valued relat ionship between the density derivative of E-kin[n(chi)] and the particle de nsity n(chi) is demonstrated and evaluated for various values of the number of particles in the system.