On the motion of particles in covariant Horava-Lifshitz gravity and the meaning of the A-field

We studied the low energy motion of particles in the general covariant. version of Horava-Lifshitz gravity proposed by Horava and Melby-Thompson. Using a scalar field coupled to gravity according to the minimal substitution recipe proposed by da Silva and taking the geometrical optics limit, we could write an effective relativistic metric for a general solution. As a result, we discovered that the equivalence principle is not in general recovered at low energies, unless the spatial Laplacian of A vanishes. Finally, we analyzed the motion on the spherical symmetric solution proposed by Horava and Melby-Thompson, where we could find its effective line element and compute spin-0 geodesics. Using standard methods we have shown that such an effective metric cannot reproduce Newton's gravity law even in the weak gravitational field approximation. (C) 2011 Elsevier B.V All rights reserved.

Supersymmetric Isospectral Formalism for the Calculation of Near-Zero Energy States: Application to the Very Weakly Bound He-4 Trimer Excited State

We propose a novel mathematical approach for the calculation of near-zero energy states by solving potentials which are isospectral with the original one. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features are generated by supersymmetric isospectral formalism. The near-zero energy Efimov state in the original potential is effectively trapped in the deep well of the isospectral family and facilitates more accurate calculation of the Efimov state. Application to the first excited state in He-4 trimer is presented.

The generator coordinate method in the unrestricted Hartree-Fock formalism

The generator coordinate method was implemented in the unrestricted Hartree-Fock formalism. Weight functions were built from Gaussian generator functions for 1s, 2s, and 2p orbitals of carbon and oxygen atoms. These weight functions show a similar behavior to those found in the generator coordinate restricted Hartree-Fock method, i.e., they are smooth, continuous, and tend to zero in the limits of integration. Moreover, the weight functions obtained are different for spin-up and spin-down electrons what is a result from spin polarization. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012