Floating and sinking: the imprint of massive scalars around rotating black holes

We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiraling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body sinks. These effects could be a smoking gun of deviations from general relativity.     

On the extendedness of eigenstates in a hierarchical lattice: A critical view

We take a critical view at the basic definition of extended single particle states in a non-translationally invariant system. For this, we present the case of a hierarchical lattice and incorporate long range interactions that are also distributed in a hierarchical fashion. We show that it is possible to explicitly construct eigenstates with constant amplitudes (normalized to unity) at every lattice point for special values of the electron-energy. However, the end-to-end transmission, corresponding to the above energy of the electron in such a hierarchical system depends strongly on a special correlation between the numerical values of the parameters of the Hamiltonian. Keeping the energy and the distribution of the amplitudes invariant, one can transform the lattice from conducting to insulating simply by tuning the numerical values of the long range interaction. The values of these interactions themselves display a fractal character.     

Percolative dielectric behavior of wet chemical synthesized lead lanthanum titanate-cobalt iron oxide composite thin films

We have investigated the electrical and magnetic properties of solution synthesized Pb_0.85La_0.15TiO₃-CoFe₂O₄ composite thin films. These composite films exhibit both polarization as well as magnetic hysteresis characteristics at room temperature. The dielectric constant of the composite films is found to increase remarkably up to 6.0 vol% CFO contents. The increase of the dielectric constant and loss tangent follow a general percolation model originally developed for metal-ceramic composites. It is argued that Maxwell-Wagner polarization, as well as diffusion of transition metal cation(s) from CFO to PLT15 lattice are responsible for the percolative behavior of the dielectric properties in these films.     

Dioxygen‐Mediated Decarbonylative CH Alkylation of Heteroaromatic Bases with Aldehydes

An operationally simple and economical method for the direct alkylation of heteroaromatic bases employing readily available aldehydes as alkyl radical precursors and molecular oxygen as a reagent is presented. This simple transformation demonstrates a broad substrate scope with respect to aldehydes and nitrogen heterocycles, enabling the introduction of several medicinally important yet challenging alkyl moieties, such as ethyl, isopropyl, tert‐butyl, and cyclohexyl to the different classes of heterocyclic bases in good to excellent yields.     

A study of diquark and meson condensation in the Nambu–Jona-Lasinio model and Fermi momentum

Using a three- and four-dimensional Pauli–Villars regularization scheme, we investigate quark–antiquark and diquark condensation in the framework of the Nambu–Jona-Lasinio model. Using the particle Fermi momentum as a cutoff parameter, we study the energy gap width and coherence length for the meson condensate 〈\(q\bar q\)〉. We also study the energy gap width and critical coherence length (the distance over which there would be no diquark condensation) for the diquark 〈qq〉 and the dependence on the Fermi momentum. We obtain an estimate of the Fermi momentum value for meson and diquark condensates with an energy gap width of the order of 100 MeV.     

New design strategy for the two-photon active material based on push-pull substituted bisanthene molecule

In the present work, we have critically examined the origin of strong two-photon transition probability of a donor-acceptor substituted bisanthene molecule that imitates a small piece of edge passivated (4, 4) graphene nanoribbon. In our calculations, we have considered -OMe, and -NH(2) as donors and -NO(2) as an acceptor. The one- and two-photon absorption parameters are evaluated using state-of-the-art linear and quadratic response theory, respectively, and all these calculations are carried out within the framework of time dependent density functional theory. To give a proper judgment on our findings, we have used the long-range corrected CAMB3LYP functional for all of the time dependent calculations. The present investigation reveals that the bisanthene molecule with three pairs of donor/acceptor moiety has a lower two-photon transition probability than that of a suitably designed bisanthene with only a single pair of donor/acceptor moiety. This in silico observation is consistent for all of the donor/acceptor moieties chosen in the present work. A comprehensive analysis at the two state model level of theory clearly offers us a verdict that by placing the donor/acceptor moiety in a suitable position of bisanthene, we can create a significant asymmetry in the electron density in the first excited state, which eventually leads to a significant difference in the ground and excited state dipole moment and is attributed to the higher two-photon transition probability of a particular bisanthene with a single pair of donor/acceptor moiety than bisanthene with three pairs of donor/acceptor.     

MRDCI study of the low-lying electronic states of PbSi

Electronic states of the PbSi molecule up to 4 eV have been studied by carrying out ab initio based MRDCI calculations which include relativistic effective core potentials (RECPs) of both the atoms. The use of semicore RECPs of Pb produces better dissociation limits than the full-core one. However, the (3)P(0)-(3)P(1) splitting due to Pb is underestimated by about 4000 cm(-1). At least 25 bound electronic states of the Λ-S symmetry are predicted for PbSi. The computed zero-field-splitting in the ground state is about 544 cm(-1). A strong spin-orbit mixing changes the nature of the potential energy curves of many Ω states. The overall splitting among the spin components of A(3)Π is computed to be 4067 cm(-1). However, the largest spin-orbit splitting is reported for the (3)Δ state. A number of spin-allowed and spin-forbidden transitions are predicted. The partial radiative lifetime for the A(3)Π-X(3)Σ(-) transition is of the order of milliseconds. The computed bond energy in the ground state is 1.68 eV, considering the spin-orbit coupling. The vertical ionization energy for the ionization to the X(4)Σ(-) ground state of PbSi(+) is about 6.93 eV computed at the same level of calculations.     

A survey of the potential energy surface for the (benzene)13 cluster

We report on a survey of the potential energy surface for the 13-molecule benzene cluster, (C(6)H(6))(13), bound by an atom-atom intermolecular potential developed from first principles. The potential, which has an anisotropic repulsion term, is found to support distinct pairs of structures of C(3), C(i), and S(6) symmetry as low-lying minima, including a C(3) global minimum. The organisation of the low-lying region of the potential energy surface suggests that one of the S(6) structures is likely to act as a kinetic trap, hindering efficient relaxation to the global minimum, in agreement with the hypothesis that two isomers coexist in this system, suggested by spectroscopic experiments.     

Kinetic market models with single commodity having price fluctuations

We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of trading or exchange of money and commodity proceeds, with local (in time) fluctuations in the price of the commodity. These distributions are studied in markets with agents having uniform and random saving factors. The self-organizing features in money distribution are similar to the cases without any commodity (or with consumable commodities), while the commodity distribution shows an exponential decay. The wealth distribution shows interesting behavior: gamma like distribution for uniform saving propensity and has the same power-law tail, as that of the money distribution, for a market with agents having random saving propensity.     

A note on a class of singular integro-differential equations

A simplified analysis is employed to handle a class of singular integro-differential equations for their solutions