Normal forms and complex periodic orbits in semiclassical expansions of Hamiltonian systems

Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space dynamics in their neighborhood. We provide a pedestrian presentation of this classical theory and extend it by including systematically the periodic orbits lying in the complex plane on each side of the bifurcation. This allows for a more coherent and unified treatment of contributions of periodic orbits in semiclassical expansions. The contribution of complex fixed points is find to be exponentially small only for a particular type of bifurcation (the extremal one). In all other cases complex orbits give rise to corrections in powers of $\hbar$ and, unlike the former one, their contribution is hidden in the ``shadow'' of a real periodic orbit.Comment: better ps figures available at http://www.phys.univ-tours.fr/~mouchet or on request to [email protected]

The Riemannium

The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up to a Fermi energy $E_F$. The distribution of the total energy is shown to be non-Gaussian, asymmetric, and independent of $E_F$ in the limit $E_F\to\infty$. The moments of the limit distribution are computed analytically. The autocorrelation function, the finite energy corrections, and a comparison with random matrix theory are also discussed.Comment: 10 pages, 2 figures, 1 tabl

On the ground--state energy of finite Fermi systems

We study the ground--state shell correction energy of a fermionic gas in a mean--field approximation. Considering the particular case of 3D harmonic trapping potentials, we show the rich variety of different behaviors (erratic, regular, supershells) that appear when the number--theoretic properties of the frequency ratios are varied. For self--bound systems, where the shape of the trapping potential is determined by energy minimization, we obtain accurate analytic formulas for the deformation and the shell correction energy as a function of the particle number $N$. Special attention is devoted to the average of the shell correction energy. We explain why in self--bound systems it is a decreasing (and negative) function of $N$.Comment: 10 pages, 5 figures, 2 table

Lithic Utilization Strategies at the Hoover Site, 16TA5, Tangipahoa Parish, Louisiana

Lithic artifacts are frequently abundant at many prehistoric sites in the Lower Mississippi Valley and adjacent areas of the Northern Gulf Coast despite limited resources. These assemblages are beginning to receive the attention required to make meaningful interpretation which in turn can be used as comparable data sets. An understanding of the behavior associated with the full range of the reduction process was sought during the study of the lithic materials from the Hoover site (16TA5) near Ponchatoula. Louisiana. This was achieved through observations on raw material procurement. reduction sequences. tool use. maintenance and discard. and how these tools relate to environmental exploitation. Statistical tests \\ere also applied. Results of this research suggest that the site was inhabited as early as the Archaic Stage and as late as the Coles Creek or Plauqemine Period. It was concluded that prehistoric inhabitants were participating in a full range of tool production beginning with the collection of materials in cobble form from exposures or secondary deposits of the Citronelle Formation located relatively close to the site. These materials were then reduced further to preforms and then to finished tools with heat treating occurring during several stages of this process. These tools were often worked to the point of exhaustion, and the use of expedient tools was not a common practice

Overview of SERI's high efficiency solar cell research

The bulk of the research efforts supported by the Solar Energy Research Institute (SERI) High Efficiency Concepts area has been directed towards establishing the feasibility of achieving very high efficiencies, 30% for concentrator and more than 20% for thin film flat plate, in solar cell designs which could possibly be produced competitively. The research has accomplished a great deal during the past two years. Even though the desired performance levels have not yet been demonstrated, based on the recent progress, a greater portion of the terrestrial photovoltaics community believes that these efficiencies are attainable. The program will now allocate a larger portion of resources to low cost, large area deposition technology. The program is currently shifting greater emphasis on to the study of crystal growth in order to provide the understanding and tools needed to design a large area process

Superfluid Motion of Light

Superfluidity, the ability of a fluid to move without dissipation, is one of the most spectacular manifestations of the quantum nature of matter. We explore here the possibility of superfluid motion of light. Controlling the speed of a light packet with respect to a defect, we demonstrate the presence of superfluidity and, above a critical velocity, its breakdown through the onset of a dissipative phase. We describe a possible experimental realization based on the transverse motion through an array of waveguides. These results open new perspectives in transport optimization.Comment: 4 pages, 3 figure

Level density of a Fermi gas: average growth and fluctuations

We compute the level density of a two--component Fermi gas as a function of the number of particles, angular momentum and excitation energy. The result includes smooth low--energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy--Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low--lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur

Quantitative analysis of microstructures produced by creep of Ti-48Al-2Cr-2Nb-1B: Thermal and athermal mechanisms

A γ-based TiAl alloy with equiaxed microstructure and fine grain size has been studied to analyze the deformation mechanisms responsible for the creep behavior. The microstructures produced by creep and high temperature deformation have been examined by TEM to obtain information about the different aspects characterizing the primary and secondary stages of creep. Mechanical twinning has been confirmed to occur in a fraction of the grains that never exceeds 50% while 1/2 ‹110› dislocations are active within all the γ grains. The twins are only responsible for a small amount of strain, but they lead to a subdivision of the microstructure and determine (directly or indirectly) the hardening process observed during the primary stage of creep. We have proposed that during the secondary stage the creep rate is determined by the unblocking of pinned dislocations by processes such as a pipe diffusion or cross slip that allow thermally activated glide of 1/2‹110› dislocations on (001) plane

Level density of a Fermi gas and integer partitions: a Gumbel-like finite-size correction

We investigate the many-body level density of gas of non-interacting fermions. We determine its behavior as a function of the temperature and the number of particles. As the temperature increases, and beyond the usual Sommerfeld expansion that describes the degenerate gas behavior, corrections due to a finite number of particles lead to Gumbel-like contributions. We discuss connections with the partition problem in number theory, extreme value statistics as well as differences with respect to the Bose gas.Comment: 5 pages, 1 figure, one figure added, accepted for publication in Phys. Rev.