Nonadiabatic extension of the Heisenberg model

The localized states within the Heisenberg model of magnetism should be represented by best localized Wannier functions forming a unitary transformation of the Bloch functions of the narrowest partly filled energy bands in the metals. However, as a consequence of degeneracies between the energy bands near the Fermi level, in any metal these Wannier functions cannot be chosen symmetry-adapted to the complete paramagnetic group M^P. Therefore, it is proposed to use Wannier functions with the reduced symmetry of a magnetic subgroup M of M^P [case (a)] or spin dependent Wannier functions [case (b)]. The original Heisenberg model is reinterpreted in order to understand the pronounced symmetry of these Wannier functions. While the original model assumes that there is exactly one electron at each atom, the extended model postulates that in narrow bands there are as many as possible atoms occupied by exactly one electron. However, this state with the highest possible atomiclike character cannot be described within the adiabatic (or Born-Oppenheimer) approximation because in the (true) nonadiabatic system the electrons move on localized orbitals that are still symmetric on the average of time, but not at any moment. The nonadiabatic states have the same symmetry as the adiabatic states and determine the commutation properties of the nonadiabatic Hamiltonian H^n. The nonadiabatic Heisenberg model is a purely group- theoretical model which interprets the commutation properties of H^n that are explicitly given in this paper for the two important cases (a) and (b). There is evidence that the occurrence of these two types of Wannier functions in the band structure of a metal is connected with the occurrence of magnetism and superconductivity, respectively

Finite difference time domain modeling of spiral antennas

The objectives outlined in the original proposal for this project were to create a well-documented computer analysis model based on the finite-difference, time-domain (FDTD) method that would be capable of computing antenna impedance, far-zone radiation patterns, and radar cross-section (RCS). The ability to model a variety of penetrable materials in addition to conductors is also desired. The spiral antennas under study by this project meet these requirements since they are constructed of slots cut into conducting surfaces which are backed by dielectric materials

Atomic X-Ray Spectra of Accretion Disk Atmospheres in the Kerr Metric

We calculate the atmospheric structure of an accretion disk around a Kerr black hole and obtain its X-ray spectrum, which exhibits prominent atomic transitions under certain circumstances. The gravitational and Doppler (red)shifts of the C V, C VI, O VII, O VIII, and Fe I-XXVI emission lines are observable in active galaxies. We quantify the line emissivities as a function of radius, to identify the effects of atmospheric structure, and to determine the usefulness of these lines for probing the disk energetics. The line emissivities do not always scale linearly with the incident radiative energy, as in the case of Fe XXV and Fe XXVI. Our model incorporates photoionization and thermal balance for the plasma, the hydrostatic approximation perpendicular to the plane of the disk, and general relativistic tidal forces. We include radiative recombination rates, fluorescence yields, Compton scattering, and photoelectric opacities for the most abundant elements.Comment: 4 pages, 1 figure, to appear in the Proc. of the 10th Marcel Grossmann Meeting on General Relativity, World Scientific, Rio de Janeiro, July 20-26, 200