Magneto-optical conductivity in graphene including electron-phonon coupling

We show how coupling to an Einstein phonon $\omega_E$ affects the absorption peaks seen in the optical conductivity of graphene under a magnetic field $B$. The energies and widths of the various lines are shifted, and additional peaks arise in the spectrum. Some of these peaks are Holstein sidebands, resulting from the transfer of spectral weight in each Landau level (LL) into phonon-assisted peaks in the spectral function. Other additional absorption peaks result from transitions involving split LLs, which occur when a LL falls sufficiently close to a peak in the self-energy. We establish the selection rules for the additional transitions and characterize the additional absorption peaks. For finite chemical potential, spectral weight is asymmetrically distributed about the Dirac point; we discuss how this causes an asymmetry in the transitions due to left- and right-handed circularly polarized light and therefore oscillatory behavior in the imaginary part of the off-diagonal Hall conductivity. We also find that the semiclassical cyclotron resonance region is renormalized by an effective-mass factor but is not directly affected by the additional transitions. Last, we discuss how the additional transitions can manifest in broadened, rather than split, absorption peaks due to large scattering rates seen in experiment.Comment: 24 pages, 21 figure

Phonon structures in the electronic density of states of graphene in magnetic field

Unlike in ordinary metals, in graphene, phonon structure can be seen in the quasiparticle electronic density of states, because the latter varies on the scale of the phonon energy. In a magnetic field, quantization into Landau levels creates even more significant variations. We calculate the density of states incorporating electron-phonon coupling in this case and find that the coupling has pronounced new effects: shifting and broadening of Landau levels, creation of new peaks, and splitting of any Landau levels falling near one of the new peaks. Comparing our calculations with a recent experiment, we find evidence for a phonon with energy similar to but somewhat greater than the optical $E_{2g}$ mode and a coupling corresponding to a mass enhancement parameter $\lambda \simeq 0.07$.Comment: 6 pages, 4 figures, final version to be published in EP

Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals

We present a method to integrate the equations of motion that govern bound, accelerated orbits in Schwarzschild spacetime. At each instant the true worldline is assumed to lie tangent to a reference geodesic, called an osculating orbit, such that the worldline evolves smoothly from one such geodesic to the next. Because a geodesic is uniquely identified by a set of constant orbital elements, the transition between osculating orbits corresponds to an evolution of the elements. In this paper we derive the evolution equations for a convenient set of orbital elements, assuming that the force acts only within the orbital plane; this is the only restriction that we impose on the formalism, and we do not assume that the force must be small. As an application of our method, we analyze the relative motion of two massive bodies, assuming that one body is much smaller than the other. Using the hybrid Schwarzschild/post-Newtonian equations of motion formulated by Kidder, Will, and Wiseman, we treat the unperturbed motion as geodesic in a Schwarzschild spacetime whose mass parameter is equal to the system's total mass. The force then consists of terms that depend on the system's reduced mass. We highlight the importance of conservative terms in this force, which cause significant long-term changes in the time-dependence and phase of the relative orbit. From our results we infer some general limitations of the radiative approximation to the gravitational self-force, which uses only the dissipative terms in the force.Comment: 18 pages, 6 figures, final version to be published in Physical Review

Plasma Diagnostics by Antenna Impedance Measurements

The impedance of an electrically short antenna immersed in a plasma provides an excellent in situ diagnostic tool for electron density and other plasma parameters. By electrically short we mean that the wavelength of the free-space electromagnetic wave that would be excited at the driving frequency is much longer than the physical size of the antenna. Probes using this impedance technique have had a long history with sounding rockets and satellites, stretching back to the early 1960s. This active technique could provide information on composition and temperature of plasmas for comet or planetary missions. Advantages of the impedance probe technique are discussed and two classes of instruments built and flown by SDL-USU for determining electron density (the capacitance and plasma frequency probes) are described

Effects of electron-phonon coupling on Landau levels in graphene

We calculate the density of states (DOS) in graphene for electrons coupled to a phonon in an external magnetic field. We find that coupling to an Einstein mode of frequency $\omega_E$ not only shifts and broadens the Landau levels (LLs), but radically alters the DOS by introducing a new set of peaks at energies $E_n\pm\omega_E$, where $E_n$ is the energy of the $n$th LL. If one of these new peaks lies sufficiently close to a LL, it causes the LL to split in two; if the system contains an energy gap, a LL may be split in three. The new peaks occur outside the interval $(-\omega_E,\omega_E)$, leaving the LLs in that interval largely unaffected. If the chemical potential is greater than the phonon frequency, the zeroth LL lies outside the interval and can be split, eliminating its association with a single Dirac point. We find that coupling to an extended phonon distribution such as a Lorentzian or Debye spectrum does not qualitatively alter these results.Comment: 16 pages, 17 figures, 1 table. Accepted for publication in PR

Second-order gravitational self-force

Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The motion is found to be geodesic in a certain locally defined regular geometry satisfying Einstein's equation at second order. I outline a method of numerically obtaining both the metric of that regular geometry and the complete second-order metric perturbation produced by the body.Comment: 5 pages, added clarifications in response to referee comments, accepted for publication in PR

Gravitational redshift of galaxies in clusters as predicted by general relativity

The theoretical framework of cosmology is mainly defined by gravity, of which general relativity is the current model. Recent tests of general relativity within the \Lambda Cold Dark Matter (CDM) model have found a concordance between predictions and the observations of the growth rate and clustering of the cosmic web. General relativity has not hitherto been tested on cosmological scales independent of the assumptions of the \Lambda CDM model. Here we report observation of the gravitational redshift of light coming from galaxies in clusters at the 99 per cent confidence level, based upon archival data. The measurement agrees with the predictions of general relativity and its modification created to explain cosmic acceleration without the need for dark energy (f(R) theory), but is inconsistent with alternative models designed to avoid the presence of dark matter.Comment: Published in Nature issued on 29 September 2011. This version includes the Letter published there as well as the Supplementary Information. 23 pages, 7 figure

Multicenter, randomized study to optimize bowel for colon capsule endoscopy

AIM To assess the cleansing efficacy and safety of a new Colon capsule endoscopy (CCE) bowel preparation regimen. METHODS This was a multicenter, prospective, randomized, controlled study comparing two CCE regimens. Subjects were asymptomatic and average risk for colorectal cancer. The second generation CCE system (PillCam® COLON 2; Medtronic, Yoqneam, Israel) was utilized. Preparation regimens differed in the 1st and 2nd boosts with the Study regimen using oral sulfate solution (89 mL) with diatrizoate meglumine and diatrizoate sodium solution (“diatrizoate solution”) (boost 1 = 60 mL, boost 2 = 30 mL) and the Control regimen oral sulfate solution (89 mL) alone. The primary outcome was overall and segmental colon cleansing. Secondary outcomes included safety, polyp detection, colonic transit, CCE completion and capsule excretion = 12 h. RESULTS Both regimens had similar cleansing efficacy for the whole colon (Adequate: Study = 75.9%, Control = 77.3%; P = 0.88) and individual segments. In the Study group, CCE completion was superior (Study = 90.9%, Control = 76.9%; P = 0.048) and colonic transit was more often \u3c 40 min (Study = 21.8%, Control = 4%; P = 0.0073). More Study regimen subjects experienced adverse events (Study = 19.4%, Control = 3.4%; P = 0.0061), and this difference did not appear related to diatrizoate solution. Adverse events were primarily gastrointestinal in nature and no serious adverse events related either to the bowel preparation regimen or the capsule were observed. There was a trend toward higher polyp detection with the Study regimen, but this did not achieve statistical significance for any size category. Mean transit time through the entire gastrointestinal tract, from ingestion to excretion, was shorter with the Study regimen while mean colonic transit times were similar for both study groups. CONCLUSION A CCE bowel preparation regimen using oral sulfate solution and diatrizoate solution as a boost agent is effective, safe, and achieved superior CCE completion. © The Author(s) 2017. Published by Baishideng Publishing Group Inc. All rights reserved

The self-consistent gravitational self-force

I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed; I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long timescales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.Comment: 44 pages, 4 figure