The Generalized Gutzwiller Method for n=>2 Correlated Orbitals: Itinerant Ferromagnetism in eg-bands

Using the generalized Gutzwiller method we present results on the ferromagnetic behavior of extended Hubbard models with two degenerate eg orbitals. We find significant differences to results obtained from Hartree-Fock theory.Comment: 7 pages in Latex, 3 figures. Accepted for publication in Physica

Nonintegrability and Chaos in the Anisotropic Manev Problem

The anisotropic Manev problem, which lies at the intersection of classical, quantum, and relativity physics, describes the motion of two point masses in an anisotropic space under the influence of a Newtonian force-law with a relativistic correction term. Using an extension of the Poincare'-Melnikov method, we first prove that for weak anisotropy, chaos shows up on the zero-energy manifold. Then we put into the evidence a class of isolated periodic orbits and show that the system is nonintegrable. Finally, using the geodesic deviation approach, we prove the existence of a large non-chaotic set of uniformly bounded and collisionless solutions

Dynamical Friction and Resonance Trapping in Planetary Systems

A restricted planar circular three-body system, consisting of the Sun and two planets, is studied as a simple model for a planetary system. The mass of the inner planet is considered to be larger and the system is assumed to be moving in a uniform interplanetary medium with constant density. Numerical integrations of this system indicate a resonance capture when the dynamical friction of the interplanetary medium is taken into account. As a result of this resonance trapping, the ratio of orbital periods of the two planets becomes nearly commensurate and the eccentricity and semimajor axis of the orbit of the outer planet and also its angular momentum and total energy become constant. It appears from the numerical work that the resulting commensurability and also the resonant values of the orbital elements of the outer planet are essentially independent of the initial relative positions of the two bodies. The results of numerical integrations of this system are presented and the first-order partially averaged equations are studied in order to elucidate the behavior of the system while captured in resonance.Comment: plainTeX, 30 pages, 18 graphs, accepted by MNRA

Statistics of photodissociation spectra: nonuniversal properties

We consider the two-point correlation function of the photodissociation cross section in molecules where the fragmentation process is indirect, passing through resonances above the dissociation threshold. In the limit of overlapping resonances, a formula is derived, relating this correlation function to the behavior of the corresponding classical system. It is shown that nonuniversal features of the two-point correlation function may have significant experimental manifestations.Comment: 4 pages, 1 figur

Statistical properties of periodic orbits in 4-disk billiard system: pruning-proof property

Periodic orbit theory for classical hyperbolic system is very significant matter of how we can interpret spectral statistics in terms of semiclassical theory. Although pruning is significant and generic property for almost all hyperbolic systems, pruning-proof property for the correlation among the periodic orbits which gains a resurgence of second term of the random matrix form factor remains open problem. In the light of the semiclassical form factor, our attention is paid to statistics for the pairs of periodic orbits. Also in the context of pruning, we investigated statistical properties of the "actual" periodic orbits in 4-disk billiard system. This analysis presents some universality for pair-orbits' statistics. That is, even if the pruning progresses, there remains the periodic peak structure in the statistics for periodic orbit pairs. From that property, we claim that if the periodic peak structure contributes to the correlation, namely the off-diagonal part of the semiclassical form factor, then the correlation must remain while pruning progresse.Comment: 30 pages, 58 figure

Semiclassical Green Function in Mixed Spaces

A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations of Green functions as two special cases of the form.Comment: 8 pages, typeset by Scientific Wor

Singularity in classical and quantum Kepler Problem with Weak Anisotropy

Anisotropic Kepler problem is investigated by perturbation method in both classical and quantum mechanics. In classical mechanics, due to the singularity of the potential, global diffusion in phase space occurs at an arbitrarily small perturbation parameter. In quantum mechanics, the singularity induces a large transition amplitude between quasi degenerate eigen states, which generically decays as $\hbar$ in the semi-classical limit.Comment: 6 pages, 2 figures, 1 tabl