Search

The Wheeler equation has an extension in the Kerr background. It has an exact solution representing a running harmonic wave in the tortoise coordinate. The wave models astrophysical jets in a new light because it collimates along the axis of spacetime rotation, increasingly tightly when rotation quickens. The model endorses a previous numerical work suggesting intrinsic collimation of jet fuelled by a Penrose-like process. It also endorses a previous theoretical work to crop one-way running waves from the exact solutions to Heun's equation., Comment: 7 pages, 4 figures

The Wheeler equation, for electromagnetic disturbances in a gravitational field, was found by Fiziev to have exact solutions both above and below the event horizon, in the form of waves propagating both inwardly and outwardly. This observation can be interpreted and verified from the optical point of view, entirely on the basis of the Schwarzschild metric for length contraction and time dilation, in order to derive a differential version of Snell's law for the Schwarzschild black hole. It reveals interesting physics, including the correct amount of light deflection by the Sun, internal and external Oppenheimer-Snyder cones of the black hole, properties of its phonon sphere and the conclusion that light-rays are kept below the horizon by length contraction and time dilation rather than deflection., Comment: 8 pages, 5 figures

With the help of the McMillan formula and virtual crystal model, we predict $T_c$ may exceed 34 K in a beryllium-based alloy with a specific composition, reminiscent of $T_c$ = 35 K in the first cuprate superconductor. This may similarly inspire research efforts to seek high temperature superconductors in ambient., Comment: Accepted by Solid State Communications on 23/10/19

With a generic model for the electron-phonon spectral density, two simple expressions are derived to estimate the transition temperature and gap-to-temperature ratio in conventional superconductors. They entail that on average the numerical value of the phonon exchange factor, $\lambda$, is limited to 2.67, so that room temperature superconductivity may be attained only with a Debye temperature of about 1800 K or higher, in materials that may or may not involve hydrogen. They also show that a Be-Pb alloy may become a superconductor at $\sim$44 K., Comment: An application of the model to alloys is added to the manuscript, previously accepted into Solid State Communications on 03/05/19

The understanding of the kinetic properties of hydrogen (isotopes) adatoms on graphene is important in many fields. The kinetic properties of hydrogen-isotope (H, D and T) monomers were simulated using a composite method consisting of density functional theory, density functional perturbation theory and harmonic transition state theory. The kinetic changes of the magnetic property and the aromatic $\pi$ bond of the hydrogenated graphene during the desorption and diffusion of the hydrogen monomer was discussed. The vibrational zero-point energy corrections in the activation energies were found to be significant, ranging from 0.072 to 0.205 eV. The results obtained from quantum-mechanically modified harmonic transition state theory were compared with the ones obtained from classical-limit harmonic transition state theory over a wide temperature range. The phonon spectra of hydrogenated graphene were used to closely explain the (reversed) isotope effects in the prefactor, activation energy and jump frequency of the hydrogen monomer. The kinetic properties of the hydrogen-isotope monomers were simulated under conditions of annealing for 10 minutes and of heating at a constant rate (1.0 K/s). The isotope effect was observed; that is, a hydrogen monomer of lower mass is desorbed and diffuses more easily (with lower activation energies). The results presented herein are very similar to other reported experimental observations. This study of the kinetic properties of the hydrogen monomer and many other involved implicit mechanisms provides a better understanding of the interaction between hydrogen and graphene., Comment: Accepted by J. Phys. Chem. C

The BCS theory of superconductivity is extended to recognize pairing of electrons by both normal and umklapp scattering. Application of the variational approach shows that coexistence of normal and umklapp scattering frustrates superconductivity., Comment: 9 pages, 5 figures. to be published in Journal of Physics: Condensed Matter

In a superconductor electrons form pairs for which the end states of normal and umklapp scattering may overlap. This cuts electron pairing off at a phonon frequency, $\omega_c$, low compared with the Debye frequency, $\omega_D$. Using this insight, correct values of $2\Delta/k_BT_c$ (average error 8.9%) for 12 superconductive metals, including Hg and Pb, are achieved from simple BCS formalism with an average $\omega_c/\omega_D$ of 0.148: Landau's idea of a Fermi liquid may cover strong-coupling superconductors. The cancellation between normal and umklapp scattering may be more important than a strong electron-phonon interaction in reaching a high critical temperature $T_c$.

The paper has been withdrawn, Comment: 14 pages, 5 figures

MgB_2 is considered as a binary system with 2D electrons. The classic BCS theory is applied to this system. The transition temperature is found to be relatively high, because 2D electrons are more capable of moving with the atoms, on top of other features of this system to enhance the electron-phonon interaction. This system may also shed light on the nature of superconductivity in cuprates., Comment: 4 pages, 1 figure

The Hamiltonian and trial function in the BCS theory are improved to test the limit of this theory. The Cooper pairs arise from standing electron waves, ready to move with atoms, giving high Tc. The Hamiltonian is derived from alternating layers of light and heavy atoms, giving a forbidden zone hosting no standing wave pairs. The exchange term may force singlet pairs into this zone, leaving triplet pairs outside, giving magnetic excitations. If the Fermi energy is crossed only by the CuO2 band, then the forbidden zone and triplet pairs will vanish, consistent with experimental evidence., Comment: 12 pages, 1 figure included