Closed-orbit theory for spatial density oscillations

We briefly review a recently developed semiclassical theory for quantum oscillations in the spatial (particle and kinetic energy) densities of finite fermion systems and present some examples of its results. We then discuss the inclusion of correlations (finite temperatures, pairing correlations) in the semiclassical theory.Comment: LaTeX, 10pp., 2 figure

Periodic orbit theory for the H\'enon-Heiles system in the continuum region

We investigate the resonance spectrum of the H\'enon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the oscillating part of the resonance spectrum semiclassically and Strutinsky smoothing to obtain its smooth part. Although the system in this energy range is almost chaotic, it still contains stable periodic orbits. Using Gutzwiller's trace formula, complemented by a uniform approximation for a codimension-two bifurcation scenario, we are able to reproduce the coarse-grained quantum-mechanical density of states very accurately, including only a few stable and unstable orbits.Comment: LaTeX (v3): 10 pages, 9 figures (new figure 6 added), 1 table; final version for Phys. Rev. E (in print

Semiclassical analysis of the lowest-order multipole deformations of simple metal clusters

We use a perturbative semiclassical trace formula to calculate the three lowest-order multipole (quadrupole \eps_2, octupole \eps_3, and hexadecapole \eps_4) deformations of simple metal clusters with $90 \le N \le 550$ atoms in their ground states. The self-consistent mean field of the valence electrons is modeled by an axially deformed cavity and the oscillating part of the total energy is calculated semiclassically using the shortest periodic orbits. The average energy is obtained from a liquid-drop model adjusted to the empirical bulk and surface properties of the sodium metal. We obtain good qualitative agreement with the results of quantum-mechanical calculations using Strutinsky's shell-correction method.Comment: LaTeX file (v2) 6 figures, to be published in Phys. Lett.

Static Electric Dipole Polarizabilities of Na Clusters

The static electric dipole polarizability of $\mathrm{Na_N}$ clusters with even N has been calculated in a collective, axially averaged and a three-dimensional, finite-field approach for $2\le N \le 20$, including the ionic structure of the clusters. The validity of a collective model for the static response of small systems is demonstrated. Our density functional calculations verify the trends and fine structure seen in a recent experiment. A pseudopotential that reproduces the experimental bulk bond length and atomic energy levels leads to a substantial increase in the calculated polarizabilities, in better agreement with experiment. We relate remaining differences in the magnitude of the theoretical and experimental polarizabilities to the finite temperature present in the experiments.Comment: 7 pages, 3 figures, accepted for publication in the European Physical Journal

Level density of the H\'enon-Heiles system above the critical barrier Energy

We discuss the coarse-grained level density of the H\'enon-Heiles system above the barrier energy, where the system is nearly chaotic. We use periodic orbit theory to approximate its oscillating part semiclassically via Gutzwiller's semiclassical trace formula (extended by uniform approximations for the contributions of bifurcating orbits). Including only a few stable and unstable orbits, we reproduce the quantum-mechanical density of states very accurately. We also present a perturbative calculation of the stabilities of two infinite series of orbits (R$_n$ and L$_m$), emanating from the shortest librating straight-line orbit (A) in a bifurcation cascade just below the barrier, which at the barrier have two common asymptotic Lyapunov exponents $\chi_{\rm R}$ and $\chi_{\rm L}$.Comment: LaTeX, style FBS (Few-Body Systems), 6pp. 2 Figures; invited talk at "Critical stability of few-body quantum systems", MPI-PKS Dresden, Oct. 17-21, 2005; corrected version: passages around eq. (6) and eqs. (12),(13) improve

Finite size corrections to the blackbody radiation laws

We investigate the radiation of a blackbody in a cavity of finite size. For a given geometry, we use semiclassical techniques to obtain explicit expressions of the modified Planck's and Stefan-Boltzmann's blackbody radiation laws as a function of the size and shape of the cavity. We determine the range of parameters (temperature, size and shape of the cavity) for which these effects are accessible to experimental verification. Finally we discuss potential applications of our findings in the physics of the cosmic microwave background and sonoluminescence.Comment: 5 pages, 1 figure, journal versio

On the canonically invariant calculation of Maslov indices

After a short review of various ways to calculate the Maslov index appearing in semiclassical Gutzwiller type trace formulae, we discuss a coordinate-independent and canonically invariant formulation recently proposed by A Sugita (2000, 2001). We give explicit formulae for its ingredients and test them numerically for periodic orbits in several Hamiltonian systems with mixed dynamics. We demonstrate how the Maslov indices and their ingredients can be useful in the classification of periodic orbits in complicated bifurcation scenarios, for instance in a novel sequence of seven orbits born out of a tangent bifurcation in the H\'enon-Heiles system.Comment: LaTeX, 13 figures, 3 tables, submitted to J. Phys.