A New Perspective on Path Integral Quantum Mechanics in Curved Space-Time

A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a locally curved background, such as described by Fermi or Riemann normal co-ordinates, this approach requires use of a constructed operator to rotate the initial, intermediate, and final position ket vectors onto their respective local tangent spaces, defined at each local time step along some arbitrary classical reference worldline. Local time translation is described using a quantum mechanical representation of Lie transport, that while strictly non-unitary in operator form, nevertheless correctly recovers the free-particle Lagrangian in curved space-time, along with new contributions. This propagator yields the prediction that all probability violating terms due to curvature contribute to a quantum violation of the weak equivalence principle, while the remaining terms that conserve probability also correspondingly satisfy the weak equivalence principle, at least to leading-order in the particle's Compton wavelength. Furthermore, this propagator possesses an overall curvature-dependent and gauge-invariant phase factor that can be interpreted as the gravitational Aharonov-Bohm effect and Berry's phase.Comment: 14 pages, 1 figure; major additions and revisions introduced; main conclusions are unchanged; new affiliation adde

The Lick-Carnegie Exoplanet Survey: A Saturn-Mass Planet in the Habitable Zone of the Nearby M4V Star HIP 57050

Precision radial velocities from Keck/HIRES reveal a Saturn-mass planet orbiting the nearby M4V star HIP 57050. The planet has a minimum mass of 0.3 Jupiter-mass, an orbital period of 41.4 days, and an orbital eccentricity of 0.31. V-band photometry reveals a clear stellar rotation signature of the host star with a period of 98 days, well separated from the period of the radial velocity variations and reinforcing a Keplerian origin for the observed velocity variations. The orbital period of this planet corresponds to an orbit in the habitable zone of HIP 57050, with an expected planetary temperature of approximately 230 K. The star has a metallicity of [Fe/H] = 0.32+/-0.06 dex, of order twice solar and among the highest metallicity stars in the immediate solar neighborhood. This newly discovered planet provides further support that the well-known planet-metallicity correlation for F, G, and K stars also extends down into the M-dwarf regime. The a priori geometric probability for transits of this planet is only about 1%. However, the expected eclipse depth is ~7%, considerably larger than that yet observed for any transiting planet. Though long on the odds, such a transit is worth pursuing as it would allow for high quality studies of the atmosphere via transmission spectroscopy with HST. At the expected planetary effective temperature, the atmosphere may contain water clouds.Comment: 20 pages, 5 figures, 3 tables, to appear in the May 20 issue of ApJ

Electrodynamics in Friedmann-Robertson-Walker Universe: Maxwell and Dirac fields in Newman-Penrose formalism

Maxwell and Dirac fields in Friedmann-Robertson-Walker spacetime is investigated using the Newman-Penrose method. The variables are all separable, with the angular dependence given by the spin-weighted spherical harmonics. All the radial parts reduce to the barrier penetration problem, with mostly repulsive potentials representing the centrifugal energies. Both the helicity states of the photon field see the same potential, but that of the Dirac field see different ones; one component even sees attractive potential in the open universe. The massless fields have the usual exponential time dependencies; that of the massive Dirac field is coupled to the evolution of the cosmic scale factor $a$. The case of the radiation filled flat universe is solved in terms of the Whittaker function. A formal series solution, valid in any FRW universe, is also presented. The energy density of the Maxwell field is explicitly shown to scale as $a^{-4}$. The co-moving particle number density of the massless Dirac field is found to be conserved, but that of the massive one is not. Particles flow out of certain regions, and into others, creating regions that are depleted of certain linear and angular momenta states, and others with excess. Such current of charged particles would constitute an electric current that could generate a cosmic magnetic field. In contrast, the energy density of these massive particles still scales as $a^{-4}$.Comment: 18 pages including 9 figure

THE HYDROGEN-FUELLED INTERNAL COMBUSTION ENGINES FOR MARINE APPLICATIONS WITH A CASE STUDY

Modern marine power plants have been designed to improve the overall ship’s efficiency. This pushed the designers of marine machinery to search for unconventional fuels for these plants. During the previous years, diesel oil has been extensively used on-board ships. Due to the high price of light diesel oil and the environmental problems resulting from the use of heavy fuel oil, it has become necessary to search for an alternative to traditional fuels. As a result, natural gas fuel has been used on-board some types of ships, especially short-voyage cruise ships. Unfortunately, there are still some technical and logistic problems related to the use of natural gas as a fuel, especially as it is considered a non-renewable energy source. The use of hydrogen fuel on-board ships, particularly in modern power plants may contribute to overcoming the above problems. The present paper considers the possibility of the use of hydrogen fuel for marine applications and discusses different stages of hydrogen gas cycle beginning with hydrogen generation process from clean energy until using it as fuel for internal combustion engines on-board one RO/RO ship, named Taba, operating in the Mediterranean Sea. Compared to the diesel engine, the hydrogen fuelled engine is found to be lower in thermal efficiency and fuel consumption, however, some adjustments are needed

Lp-cohomology of negatively curved manifolds

We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds

Dynamical Theory of Artificial Optical Magnetism Produced by Rings of Plasmonic Nanoparticles

We present a detailed analytical theory for the plasmonic nanoring configuration first proposed in [A. Alu, A. Salandrino, N. Engheta, Opt. Expr. 14, 1557 (2006)], which is shown to provide negative magnetic permeability and negative index of refraction at infrared and optical frequencies. We show analytically how the nanoring configuration may provide superior performance when compared to some other solutions for optical negative index materials, offering a more 'pure' magnetic response at these high frequencies, which is necessary for lowering the effects of radiation losses and absorption. Sensitivity to losses and the bandwidth of operation of this magnetic inclusion are also investigated in details and compared with other available setups.Comment: 34 pages, 3 figure