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arXiv · 0802.3312

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

Jérôme Roccia·Matthias Brack
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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.

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Jérôme Roccia, Matthias Brack. 2008-05-06. Closed-Orbit Theory of Spatial Density Oscillations in Finite Fermion Systems. https://doi.org/10.1103/physrevlett.100.200408

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