Faster than Light Photons in Gravitational Fields II - Dispersion and Vacuum Polarisation

Vacuum polarisation in QED in a background gravitational field induces interactions which effectively violate the strong equivalence principle and affect the propagation of light. In the low frequency limit, Drummond and Hathrell have shown that this mechanism leads to superluminal photon velocities. To confront this phenomenon with causality, however, it is necessary to extend the calculation of the phase velocity \vp(\w) to high frequencies, since it is \vp(\infty) which determines the characteristics of the effective wave equation and thus the causal structure. In this paper, we use a recently constructed expression, valid to all orders in a derivative expansion, for the effective action of QED in curved spacetime to determine the frequency dependence of the phase velocity and investigate whether superluminal velocities indeed persist in the high frequency limit.Comment: 27 pages, 7 figures, TeX with harvma

The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes

This work considers the way that quantum loop effects modify the propagation of light in curved space. The calculation of the refractive index for scalar QED is reviewed and then extended for the first time to QED with spinor particles in the loop. It is shown how, in both cases, the low frequency phase velocity can be greater than c, as found originally by Drummond and Hathrell, but causality is respected in the sense that retarded Green functions vanish outside the lightcone. A "phenomenology" of the refractive index is then presented for black holes, FRW universes and gravitational waves. In some cases, some of the polarization states propagate with a refractive index having a negative imaginary part indicating a potential breakdown of the optical theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph

Unconventional Gravitational Excitation of a Schwarzschild Black Hole

Besides the well-known quasinormal modes, the gravitational spectrum of a Schwarzschild black hole also has a continuum part on the negative imaginary frequency axis. The latter is studied numerically for quadrupole waves. The results show unexpected striking behavior near the algebraically special frequency $\Omega=-4i$. This reveals a pair of unconventional damped modes very near $\Omega$, confirmed analytically.Comment: REVTeX4, 4pp, 6 EPS figure files. N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. v2: better pole placement in Fig. 1. v3: fixed Refs. [9,20]. v4: added context on "area quantum" research; trimmed one Fig.; textual clarification

Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible complex transformations can be used to obtain invertible real transformations that map a system of nonlinear partial differential equations into a system of linear partial differential equation. Explicit invariant criteria are given that provide procedures for writing down the solutions of the linearized equations. A few non-trivial examples are mentioned.Comment: This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published articl

Natural history and evolution of an elevational generalist, the Cinereous Conebill (Conirostrum cinereum)

Elevational generalism is relatively rare in the tropical Andes Mountains, likely owing to the inherent requirements of enduring a high degree of climatic zonation and coping with hypoxic stress. The Cinereous Conebill (Conirostrum cinereum) appears to be an exception, and inhabits a continuous elevational distribution that spans over 4,500 m. Two subspecies, cinereum and fraseri, are restricted to high elevations and may be isolated, whereas the third and most widespread, littorale, occurs continuously along the western slope of the Andes from 0 to over 4,500 m. First, we aim to characterize the morphology, genetics, and climatic niche of the three subspecies using a comparative biogeographic approach to explore patterns and timing of differentiation and to consider possible mechanisms of diversification. Second, we study whether hemoglobin adaptation plays a role in this elevational generalist’s ability to thrive in high-elevation environments, and whether localized adaptation is possible despite altitudinal migration and gene flow. We used a comparative phylogeographic framework to examine whether lineage divergence within C. cinereum is associated with climatic, geographic, and/or physiological barriers leading to incipient speciation

Electron dose calculations using the Method of Moments

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134898/1/mp7920.pd

The Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index

The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit and it is shown how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The general formalism is illustrated in a number of examples, in some of which it is found that the refractive index develops a negative imaginary part, implying an amplification of photons as an electromagnetic wave propagates through curved spacetime.Comment: 54 pages, 19 figures, corrected some signs in formulae and graph

On stellar statistics

In this paper a method is proposed for treating the fundamental equation of stellar statistics which will take into account the known cloud structure of the interstellar absorbing matter. The method is based on the determination and the interpretation of the fluctuations in the numbers of stars, N(m), per unit solid angle, and brighter than a given apparent magnitude, m, in the various parts of the sky. The marked dependence of these fluctuations on the galactic latitude confirms their relation to the interstellar clouds. Theoretical formulae are derived for the dispersions to be expected in N(m) as a function of the galactic latitude on certain idealized distributions of stars and clouds. The results of star counts tabulated by van Rhijn and by Baker and Kiefer are analyzed in terms of these formulae, and a theoretical prediction based on them is verified. The analysis discloses the importance of taking into account the dispersion in the transparencies of the interstellar clouds as a factor in these considerations