Momentum flux density, kinetic energy density, and their fluctuations for one-dimensional confined gases of noninteracting fermions
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 Ekin[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 Ekin[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:cond-mat/0011331
- Bibcode:
- 2001PhRvA..63f3604M
- Keywords:
-
- 03.75.Fi;
- 05.30.Fk;
- 31.15.Ew;
- Fermion systems and electron gas;
- Density-functional theory;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 10 pages, 5 figures