Closed-Orbit Theory of Spatial Density Oscillations in Finite Fermion Systems

Abstract

We investigate the particle and kinetic-energy densities for $N$ non-interacting fermions confined in a local potential. Using Gutzwiller's semi-classical Green function, we describe the oscillating parts of the densities in terms of closed non-periodic classical orbits. We derive universal relations between the oscillating parts of the densities for potentials with spherical symmetry in arbitrary dimensions, and a ``local virial theorem'' valid also for arbitrary non-integrable potentials. We give simple analytical formulae for the density oscillations in a one-dimensional potential.

LaTeX, 4 pages, 1 figure; to be published (in slightly shortened form) in Physical Review Letters; (v4) corrected misprint in eq. (21)