Semiclassical theory for spatial density oscillations in fermionic systems

We investigate the particle and kinetic-energy densities for a system of $N$ fermions bound in a local (mean-field) potential $V(bfr)$. We generalize a recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev. Lett. {bf 100}, 200408 (2008)], in which the densities are calculated in terms of the closed orbits of the corresponding classical system, to $D>1$ dimensions. We regularize the semiclassical results $(i)$ for the U(1) symmetry breaking occurring for spherical systems at $r=0$ and $(ii)$ near the classical turning points where the Friedel oscillations are predominant and well reproduced by the shortest orbit going from $r$ to the closest turning point and back. For systems with spherical symmetry, we show that there exist two types of oscillations which can be attributed to radial and non-radial orbits, respectively. The semiclassical theory is tested against exact quantum-mechanical calculations for a variety of model potentials. We find a very good overall numerical agreement between semiclassical and exact numerical densities even for moderate particle numbers $N$. Using a local virial theorem, shown to be valid (except for a small region around the classical turning points) for arbitrary local potentials, we can prove that the Thomas-Fermi functional $tau_{text{TF}}[rho]$ reproduces the oscillations in the quantum-mechanical densities to first order in the oscillating parts.

Analytic approach to bifurcation cascades in a class of generalized Henon-Heiles potentials

We derive stability traces of bifurcating orbits in Henon-Heiles potentials near their saddles

Coupling of Surface and Volume Dipole Oscillations in C-60 Molecules

We first give a short review of the ``local-current approximation (LCA), derived from a general variation principle, which serves as a semiclassical description of strongly collective excitations in finite fermion systems starting from their quantum-mechanical mean-field ground state. We illustrate it for the example of coupled translational and compressional dipole excitations in metal clusters. We then discuss collective electronic dipole excitations in C$_{60}$ molecules (Buckminster fullerenes). We show that the coupling of the pure translational mode (``surface plasmon) with compressional volume modes in the semiclasscial LCA yields semi-quantitative agreement with microscopic time-dependent density functional (TDLDA) calculations, while both theories yield qualitative agreement with the recent experimental observation of a ``volume plasmon.