A Novel Method for the Solution of the Schroedinger Eq. in the Presence of Exchange Terms

In the Hartree-Fock approximation the Pauli exclusion principle leads to a Schroedinger Eq. of an integro-differential form. We describe a new spectral noniterative method (S-IEM), previously developed for solving the Lippman-Schwinger integral equation with local potentials, which has now been extended so as to include the exchange nonlocality. We apply it to the restricted case of electron-Hydrogen scattering in which the bound electron remains in the ground state and the incident electron has zero angular momentum, and we compare the acuracy and economy of the new method to three other methods. One is a non-iterative solution (NIEM) of the integral equation as described by Sams and Kouri in 1969. Another is an iterative method introduced by Kim and Udagawa in 1990 for nuclear physics applications, which makes an expansion of the solution into an especially favorable basis obtained by a method of moments. The third one is based on the Singular Value Decomposition of the exchange term followed by iterations over the remainder. The S-IEM method turns out to be more accurate by many orders of magnitude than any of the other three methods described above for the same number of mesh points.Comment: 29 pages, 4 figures, submitted to Phys. Rev.

Interference through quantum dots

We discuss the effect of quantum interference on transport through a quantum dot system. We introduce an indirect coherent coupling parameter alpha, which provides constructive/destructive interference in the transport current depending on its phase and the magnetic flux. We estimate the current through the quantum dot system using the non-equilibrium Green's function method as well as the master equation method in the sequential tunneling regime. The visibility of the Aharonov-Bohm oscillation is evaluated. For a large inter-dot Coulomb interaction, the current is strongly suppressed by the quantum interference effect, while the current is restored by applying an oscillating resonance field with the frequency of twice the inter-dot tunneling energy.Comment: 10 pages, 3 figure

Triple sign reversal of Hall effect in HgBa_{2}CaCu_{2}O_{6} thin films after heavy-ion irradiations

Triple sign reversal in the mixed-state Hall effect has been observed for the first time in ion-irradiated HgBa_{2}CaCu_{2}O_{6} thin films. The negative dip at the third sign reversal is more pronounced for higher fields, which is opposite to the case of the first sign reversal near T_c in most high-T_c superconductors. These observations can be explained by a recent prediction in which the third sign reversal is attributed to the energy derivative of the density of states and to a temperature-dependent function related to the superconducting energy gap. These contributions prominently appear in cases where the mean free path is significantly decreased, such as our case of ion-irradiated thin films.Comment: 4 pages, 3 eps figures, submitted Phys. Rev. Let

Neutrino masses along with fermion mass hierarchy

Recently a new mechanism has been proposed to cure the problem of fermion mass hierarchy in the Standard Model (SM) model. In this scenario, all SM charged fermions other than top quark arise from higher dimensional operators involving the SM Higgs field. This model also predicted some interesting phenomenology of the Higgs boson. We generalize this model to accommodate neutrino masses (Dirac & Majorana) and also obtain the mixing pattern in the leptonic sector. To generate neutrino masses, we add extra three right handed neutrinos $(N_{iR})$ in this model.Comment: 20 pages, the content on results and phenomenology have been expanded, a new section on UV completion of the model has been added and also some new references, this version has been accepted by Physical Review

Inelastic neutron scattering studies of Crystal Field Levels in PrOs4_4As12_{12}

We use neutron scattering to study the Pr$^{3+}$ crystalline electric field (CEF) excitations in the filled skutterudite PrOs$_4$As$_{12}$. By comparing the observed levels and their strengths under neutron excitation with the theoretical spectrum and neutron excitation intensities, we identify the Pr$^{3+}$ CEF levels, and show that the ground state is a magnetic $\Gamma_4^{(2)}$ triplet, and the excited states $\Gamma_1$, $\Gamma_4^{(1)}$ and $\Gamma_{23}$ are at 0.4, 13 and 23 meV, respectively. A comparison of the observed CEF levels in PrOs$_4$As$_{12}$ with the heavy fermion superconductor PrOs$_4$Sb$_{12}$ reveals the microscopic origin of the differences in the ground states of these two filled skutterudites.Comment: 7 pages, 7 figure

Efficiency of Nonlinear Particle Acceleration at Cosmic Structure Shocks

We have calculated the evolution of cosmic ray (CR) modified astrophysical shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of diffusive shock acceleration (DSA) in 1D quasi- parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We model shocks similar to those expected around cosmic structure pancakes as well as other accretion shocks driven by flows with upstream gas temperatures in the range $T_0=10^4-10^{7.6}$K and shock Mach numbers spanning $M_s=2.4-133$. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc \gsim 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. For these models the time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number. The modeled high Mach number shocks all evolve towards efficiencies $\sim 50$%, regardless of the upstream CR pressure. On the other hand, the upstream CR pressure increases the overall CR energy in moderate strength shocks ($M_s \sim {\rm a few}$). (abridged)Comment: 23 pages, 12 ps figures, accepted for Astrophysical Journal (Feb. 10, 2005