Singularity: Raychaudhuri Equation once again

I first recount Raychaudhuri's deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity.Comment: 11 pages, Contribution to Special issue of Pramana on Raychaudhuri Equation at Cross-roads, edited by Naresh Dadhich, Pankaj Joshi and Probir Ro

Magnetoresistance of metallic perovskite oxide LaNiO3−δ_{3-\delta}

We report a study of the magnetoresistance (MR) of the metallic perovskite oxide LaNiO$_{3-\delta}$ as a function of the oxygen stoichiometry $\delta$ ($\delta \leq$ 0.14), magnetic field (H $\leq 6T$) and temperature (1.5K $\leq$ T $\leq$ 25K). We find a strong dependence of the nature of MR on the oxygen stoichiometry. The MR at low temperatures change from positive to negative as the sample becomes more oxygen deficient (i.e, $\delta$ increases). Some of the samples which are more resistive, show a resistivity minima at $T_{min}$ $\approx$ 20K. We find that in these samples the MR is positive at T > $T_{min}$ and negative for T < $T_{min}$. We conclude that in the absence of strong magnetic interaction, the negative MR in these oxides can arise from weak localisation effects.Comment: 10 pages in REVTeX format, 4 eps fig

Point contact spectroscopy and temperature dependence of resistivity of metallic sodium tungsten bronzes- role of optical phonons

In this paper we report the results of electrical resistivity (1.5≤T≤300K) and point contact spectroscopy (PCS) measurements on single crystals of metallic sodium tungsten bronze with varying sodium content. We have shown that the electron-phonon coupling function as measured through PCS can explain quantitatively the large temperature dependence of resistivity ρ seen in these materials over the entire temperature range. The electron-phonon coupling function shows predominately large peaks for phonon frequency range of 30 meV≤ω≤100 meV which match well with the calculated optical phonons for WO6 octahedron. The integrated electron-phonon coupling constant λ from this data is ≈0.25-0.45, depending on the Na content

Colossal electroresistance in ferromagnetic insulating state of single crystal Nd0.7_0.7Pb0.3_0.3MnO3_3

Colossal electroresistance (CER) has been observed in the ferromagnetic insulating (FMI) state of a manganite. Notably, the CER in the FMI state occurs in the absence of magnetoresistance (MR). Measurements of electroresistance (ER) and current induced resistivity switching have been performed in the ferromagnetic insulating state of a single crystal manganite of composition Nd$_0.7$Pb$_0.3$MnO$_3$ (NPMO30). The sample has a paramagnetic to ferromagnetic (Curie) transition temperature, Tc = 150 K and the ferromagnetic insulating state is realized for temperatures, T <~ 130 K. The colossal electroresistance, arising from a strongly nonlinear dependence of resistivity ($\rho$) on current density (j), attains a large value ($\approx 100$) in the ferromagnetic insulating state. The severity of this nonlinear behavior of resistivity at high current densities is progressively enhanced with decreasing temperature, resulting ultimately, in a regime of negative differential resistivity (NDR, d$\rho$/dj < 0) for temperatures <~ 25 K. Concomitant with the build-up of the ER however, is a collapse of the MR to a small value (< 20%) even in magnetic field, H = 7 T. This demonstrates that the mechanisms that give rise to ER and MR are effectively decoupled in the ferromagnetic insulating phase of manganites. We establish that, the behavior of ferromagnetic insulating phase is distinct from the ferromagnetic metallic (FMM) phase as well as the charge ordered insulating (COI) phase, which are the two commonly realized ground state phases of manganites.Comment: 24 pages (RevTeX4 preprint), 8 figures, submitted to PR

Non-linear electrical conduction and broadband noise in charge-ordered rare earth manganate Nd_0.5Ca_0.5MnO_3

Measurements of the dc transport properties and the low-frequency conductivity noise in films of charge ordered Nd_0.5Ca_0.5MnO_3 grown on Si subtrate reveal the existence of a threshold field in the charge ordered regime beyond which strong non linear conduction sets in along with a large broad band conductivity noise. Threshold-dependent conduction disappears as T -> T_{CO}, the charge ordering temperature. This observation suggests that the charge ordered state gets depinned at the onset of the non-linear conduction.Comment: 3 pages of two-column text and 4 eps figure

Collapse of the charge ordering gap of Nd_{0.5}Sr_{0.5}MnO_{3} in an applied magnetic field

We report results of tunneling studies on the charge ordering compound Nd_{0.5}Sr_{0.5}MnO_{3} in a magnetic field up to 6T and for temperature down to 25K.We show that a gap (2\Delta_{CO} \approx 0.5eV opens up in the density of state (DOS) at the Fermilevel (E_F) on charge ordering (T_{CO}=150K) which collapses in an applied magnetic field when the charge ordered state melts. There is a clear correspondence between the behavior of the resistivity and the gap formation and its collapse in an applied magnetic field. We conclude that a gap in the DOS at E_F is necessary for the stability of the charge ordered state.Comment: 4 pages REVTeX, 5 postscript figures included, submitted to Phys. Rev. Let

A four-neutrino mixing scheme for observed neutrino data

It has been observed that simultaneous explanation of the solar and atmospheric neutrino deficits and the reported evidence for $\nu_{\mu}\to \nu_{e}$ oscillation from the Los Alamos Liquid Scintillator Detector (LSND) requires at least one extra neutrino species in addition to the three known ones. The extra neutrino must be sterile with respect to the known weak interactions. We present a new mass matrix for these four neutrinos in which the LSND effect and the atmospheric neutrino deficit are governed by only one parameter. We investigate the phenomenological implications of such a mass matrix ansatz and suggest possible ways to understand it in gauge theories.Comment: 15 pages Latex, One figure, OSU-HEP-98-2; UMD-PP-98-9

Electromagnetic duality in general relativity

By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts giving rise to the same vacuum solutions but the gravitational constant changes sign. Further by modifying the equation it is possible to construct interesting dual solutions to vacuum as well as to flat spacetimes.Comment: 18 pages, LaTEX versio