Showing papers on "Amplitude published in 2019"
TL;DR: All-dielectric metasurface holograms with independent and complete control of the amplitude and phase at up to two optical frequencies simultaneously to generate two- and three-dimensional holographic objects are demonstrated.
Abstract: Metasurfaces are optically thin metamaterials that promise complete control of the wavefront of light but are primarily used to control only the phase of light. Here, we present an approach, simple in concept and in practice, that uses meta-atoms with a varying degree of form birefringence and rotation angles to create high-efficiency dielectric metasurfaces that control both the optical amplitude and phase at one or two frequencies. This opens up applications in computer-generated holography, allowing faithful reproduction of both the phase and amplitude of a target holographic scene without the iterative algorithms required in phase-only holography. We demonstrate all-dielectric metasurface holograms with independent and complete control of the amplitude and phase at up to two optical frequencies simultaneously to generate two- and three-dimensional holographic objects. We show that phase-amplitude metasurfaces enable a few features not attainable in phase-only holography; these include creating artifact-free two-dimensional holographic images, encoding phase and amplitude profiles separately at the object plane, encoding intensity profiles at the metasurface and object planes separately, and controlling the surface textures of three-dimensional holographic objects.
257 citations
TL;DR: In this paper, the authors combine peak theory and the numerical analysis of gravitational collapse in the radiation dominated era, and show that the abundance of primordial black holes, generated by an enhancement in the inflationary power spectrum, is extremely dependent on the shape of the peak.
Abstract: In this Letter, combining peak theory and the numerical analysis of gravitational collapse in the radiation dominated era, we show that the abundance of primordial blacks holes, generated by an enhancement in the inflationary power spectrum, is extremely dependent on the shape of the peak. Given the amplitude of the power spectrum, we show that the density of primordial black holes generated from a narrow peak is exponentially smaller than in the case of a broad peak. Specifically, for a top-hat profile of the power spectrum in Fourier space, we find that to have primordial black holes comprising all of the dark matter, one would only need a power spectrum amplitude an order of magnitude smaller than suggested previously, whereas in the case of a narrow peak, one would instead need a much larger power spectrum amplitude, which in many cases would invalidate the perturbative analysis of cosmological perturbations. Finally, we show that, although critical collapse gives a broad mass spectrum, the density of primordial black holes formed is dominated by masses roughly equal to the cosmological horizon mass measured at horizon crossing.
219 citations
TL;DR: In this article, the process of primordial black hole formation is studied within spherical symmetry, using the gradient expansion approximation in the long wavelength limit, where the initial perturbations are functions only of a time-independent curvature profile.
Abstract: Primordial black holes may have formed in the radiative era of the early Universe from the collapse of large enough amplitude perturbations of the metric. These correspond to non linear energy density perturbations characterized by an amplitude larger than a certain threshold, measured when the perturbations reenter the cosmological horizon. The process of primordial black hole formation is studied here within spherical symmetry, using the gradient expansion approximation in the long wavelength limit, where the pressure gradients are small, and the initial perturbations are functions only of a time-independent curvature profile. In this regime it is possible to understand how the threshold for primordial black hole formation depends on the shape of the initial energy density profile, clarifying the relation between local and averaged measures of the perturbation amplitude. Although there is no universal threshold for primordial black hole formation, the averaged mass excess of the perturbation depends on the amplitude of the energy density peak, and it is possible to formulate a well-defined criterion to establish when a cosmological perturbation is able to form a black hole in terms of one of these two key quantities. This gives understanding of how the abundance of primordial black holes depends on the shape of the inflationary power spectrum of cosmological perturbations.
204 citations
TL;DR: In this paper, the Schrodinger equation with arbitrary power of nonlinearity is considered and the influence of the non-linearity degree on the structure of periodic and solitary waves is studied.
198 citations
TL;DR: In this article, a single-and double-soliton rational solution for the VcSK model is presented. But the model is not considered in this paper, as the authors assume that the velocity, the amplitude and the shape of the wave cannot be affected by variable coefficients, and there is an inelastic collision (the collision that makes change in amplitude of the soliton waves and shifts in their trajectories).
Abstract: The main concern of the present article is to study the fifth-order variable-coefficient Sawada–Kotera (VcSK) equation which describes the motion of long waves in shallow water under the gravity. A single- and double-soliton rational solutions for this model are formally retrieved through the generalized unified method. For a single-soliton wave, the velocity, the amplitude and the shape of the wave cannot be affected by variable coefficients. There is an inelastic collision (the collision that makes change in amplitude of the soliton waves and shifts in their trajectories) between the double-soliton waves due to the time-varying field in a graded-index waveguide. It hoped that the established solutions can be used to enrich the dynamic behaviors of the VcSK equation.
138 citations
TL;DR: The multi-Regge limit of the nonplanar terms, analyze its subleading power corrections, and analytically present the leading logarithmic terms are studied.
Abstract: We compute the symbol of the full-color two-loop five-particle amplitude in N=4 super Yang-Mills theory, including all nonplanar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the nonplanar terms, analyze its subleading power corrections, and analytically present the leading logarithmic terms.
116 citations
TL;DR: This paper proposes a quantum amplitude estimation algorithm without the use of expensive controlled operations to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations.
Abstract: This paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.
108 citations
TL;DR: In this article, the logarithmic terms in the soft theorem in four dimensions were explored by analyzing classical scattering with generic incoming and outgoing states and one-loop quantum scattering amplitudes.
Abstract: We explore the logarithmic terms in the soft theorem in four dimensions by analyzing classical scattering with generic incoming and outgoing states and one loop quantum scattering amplitudes. The classical and quantum results are consistent with each other. Although most of our analysis in quantum theory is carried out for one loop amplitudes in a theory of (charged) scalars interacting via gravitational and electromagnetic interactions, we expect the results to be valid more generally.
107 citations
TL;DR: In this paper, the relation between nonplanar correlators and higher-genus closed string amplitudes in type IIB string theory was explored and exploited by using conformal field theory techniques, and the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions was constructed.
Abstract: We explore and exploit the relation between non-planar correlators in $$ \mathcal{N} $$
= 4 super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory. By conformal field theory techniques we construct the genus-one, four-point string amplitude in AdS5 × S5 in the low-energy expansion, dual to an $$ \mathcal{N} $$
= 4 super-Yang-Mills correlator in the ’t Hooft limit at order 1/c2 in a strong coupling expansion. In the flat space limit, this maps onto the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions. Using this approach we reproduce several results obtained via string perturbation theory. We also demonstrate a novel mechanism to fix subleading terms in the flat space limit of AdS amplitudes by using string/M-theory.
106 citations
TL;DR: The full-color two-loop five-gluon amplitude for the all-plus helicity configuration is computed in a compact form containing logarithms, dilogarithm, and rational functions and is fully analytic and valid in the physical scattering region.
Abstract: We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms, and rational functions.
105 citations
TL;DR: In this article, the symbol of the two-loop five-point scattering amplitude in supersymmetric Yang-Mills theory, including its full color dependence, was computed, and the symbol was used to construct the symbol for all two-layer nonplanar massless master integrals.
Abstract: We compute the symbol of the two-loop five-point scattering amplitude in N=4 supersymmetric Yang-Mills theory, including its full color dependence. This requires constructing the symbol of all two-loop five-point nonplanar massless master integrals, for which we give explicit results.
TL;DR: In this paper, a 2.8 s pulsation in the X-ray emission of the ULX source M51 ULX-7 within the UNSEeN project was discovered, which was designed to hunt for new pulsating ULXs with XMM-Newton.
Abstract: We discovered 2.8 s pulsations in the X-ray emission of the ultraluminous X-ray source (ULX) M51 ULX-7 within the UNSEeN project, which was designed to hunt for new pulsating ULXs (PULXs) with XMM-Newton. The pulse shape is sinusoidal and large variations of its amplitude were observed even within single exposures (pulsed fraction from less than 5% to 20%). M51 ULX-7 is a variable source, generally observed at an X-ray luminosity between $10^{39}$ and $10^{40}$ erg s$^{-1}$, located in the outskirts of the spiral galaxy M51a at a distance of 8.6 Mpc. According to our analysis, the X-ray pulsar orbits in a 2-d binary with a projected semi-major axis $a_\mathrm{X} \sin i \simeq$ 28 lt-s. For a neutron star (NS) of 1.4 $M_{\odot}$, this implies a lower limit on the companion mass of 8 $M_{\odot}$, placing the system hosting M51 ULX-7 in the high-mass X-ray binary class. The barycentric pulse period decreased by $\simeq$0.4 ms in the 31 d spanned by our May -- June 2018 observations, corresponding to a spin-up rate $\dot{P} \simeq -1.5\times10^{-10}\text{s s}^{-1}$. In an archival 2005 XMM-Newton exposure, we measured a spin period of $\sim$3.3 s, indicating a secular spin-up of $\dot{P}_{\mathrm{sec}}\simeq -10^{-9}\text{ s s}^{-1}$, a value in the range of other known PULXs. Our findings suggest that the system consists of an OB giant and a moderately magnetic (dipole field component in the range $10^{12}$ G $\lesssim B_{\mathrm{dip}}\lesssim 10^{13}$G) accreting NS with weakly beamed emission ($1/12\lesssim b\lesssim1/4$).
TL;DR: In this paper, a model for the ringdown of accurate numerical relativity simulations was proposed to estimate the mass and spin of the remnant black hole from binary black hole mergers by comparing the ring down gravitational wave signal to results from studies of perturbed Kerr spacetimes.
Abstract: It is possible to infer the mass and spin of the remnant black hole from binary black hole mergers by comparing the ringdown gravitational wave signal to results from studies of perturbed Kerr spacetimes. Typically, these studies are based on the fundamental quasinormal mode of the dominant l=m=2 harmonic. By modeling the ringdown of accurate numerical relativity simulations, we find, in agreement with previous findings, that the fundamental mode alone is insufficient to recover the true underlying mass and spin, unless the analysis is started very late in the ringdown. Including higher overtones associated with this l=m=2 harmonic resolves this issue and provides an unbiased estimate of the true remnant parameters. Further, including overtones allows for the modeling of the ringdown signal for all times beyond the peak strain amplitude, indicating that the linear quasinormal regime starts much sooner than previously expected. This result implies that the spacetime is well described as a linearly perturbed black hole with a fixed mass and spin as early as the peak. A model for the ringdown beginning at the peak strain amplitude can exploit the higher signal-to-noise ratio in detectors, reducing uncertainties in the extracted remnant quantities. These results should be taken into consideration when testing the no-hair theorem.
TL;DR: In this paper, the authors used the Sound Shell Model to calculate the power spectrum of the first order early Universe phase transitions using the sound shell model, and showed that the time dependence of the bubble nucleation rate affects the shape of the spectrum, and that an exponentially increasing nucleation speed produces higher amplitude gravitational waves at a longer wavelength than simultaneous nucleation.
Abstract: We calculate gravitational wave power spectra from first order early Universe phase transitions using the Sound Shell Model. The model predicts that the power spectrum depends on the mean bubble separation, the phase transition strength, the phase boundary speed, with the overall frequency scale set by the nucleation temperature. There is also a dependence on the time evolution of the bubble nucleation rate. The gravitational wave peak power and frequency are in good agreement with published numerical simulations, where bubbles are nucleated simultaneously. Agreement is particularly good for detonations, but the total power for deflagrations is predicted higher than numerical simulations show, indicating refinement of the model of the transfer of energy to the fluid is needed for accurate computations. We show how the time-dependence of the bubble nucleation rate affects the shape of the power spectrum: an exponentially rising nucleation rate produces higher amplitude gravitational waves at a longer wavelength than simultaneous nucleation. We present an improved fit for the predicted gravitational wave power spectrum in the form of a double broken power law, where the two breaks in the slope happen at wavenumber corresponding to the mean bubble separation and the thickness of the fluid shell surrounding the expanding bubbles, which in turn is related to the difference of the phase boundary speed from the speed of sound.
TL;DR: In this article, the Bathe implicit time integration method is considered and the authors focus on the time step splitting ratio and the spectral radius at large time steps to improve and generalize the scheme.
TL;DR: In this article, a new type of metasurface with both phase and amplitude modulations is proposed, which is composed of C-shaped particles and can generate and control multiple beams using amplitude and phase responses simultaneously.
Abstract: Owing to the capability of providing a certain phase gradient on the interface between two media, metasurfaces have shown great promise for altering the directions of outgoing electromagnetic (EM) waves arbitrarily. With the suitable arrangement of particles on metasurfaces, anomalous reflection and refraction have been observed in wide frequency ranges. To completely control the propagation of EM waves, both phase and amplitude profiles are required in some applications. Herein, we propose a new type of metasurface with both phase and amplitude modulations, which is composed of C-shaped particles and can generate and control multiple beams using amplitude and phase responses simultaneously. An addition theorem of complex reflection coefficients is presented to acquire various states of multiple beams reflected from designed metasurfaces. Meanwhile, the intensities of multiple beams can be separately modulated as desired benefitting from the independent controls of phase and amplitude profiles. All the experimental results have good agreements with the numerical simulations. The presented method opens a new way to form and manipulate multiple beams using metasurfaces, which can find potential applications in beam shaping, radar detection systems, and high-quality holography.
TL;DR: In this paper, the authors presented a search for gravitational-wave emission from 221 pulsars with rotation frequencies of 10$ Hz using advanced LIGO data from its first and second observing runs spanning 2015-2017.
Abstract: We present a search for gravitational waves from 221 pulsars with rotation frequencies $\gtrsim 10$ Hz. We use advanced LIGO data from its first and second observing runs spanning 2015-2017, which provides the highest-sensitivity gravitational-wave data so far obtained. In this search we target emission from both the $l = m = 2$ mass quadrupole mode, with a frequency at twice that of the pulsar's rotation, and from the $l = 2$, $m = 1$ mode, with a frequency at the pulsar rotation frequency. The search finds no evidence for gravitational-wave emission from any pulsar at either frequency. For the $l = m = 2$ mode search, we provide updated upper limits on the gravitational-wave amplitude, mass quadrupole moment, and fiducial ellipticity for 167 pulsars, and the first such limits for a further 55. For 20 young pulsars these results give limits that are below those inferred from the pulsars' spin-down. For the Crab and Vela pulsars our results constrain gravitational-wave emission to account for less than 0.017% and 0.18% of the spin-down luminosity, respectively. For the recycled millisecond pulsar J0711-6830 our limits are only a factor of 1.3 above the spin-down limit, assuming the canonical value of $10^{38}$ kg m$^2$ for the star's moment of inertia, and imply a gravitational-wave-derived upper limit on the star's ellipticity of $1.2\!\times\!10^{-8}$. We also place new limits on the emission amplitude at the rotation frequency of the pulsars.
TL;DR: In this paper, an extension of the NRTidal model for binary neutron star (BNS) waveforms is presented, which includes a new closed-form expression for the tidal contribution to the GW phase.
Abstract: Accurate and fast gravitational waveform (GW) models are essential to extract information about the properties of compact binary systems that generate GWs. Building on previous work, we present an extension of the NRTidal model for binary neutron star (BNS) waveforms. The upgrades are: (i) a new closed-form expression for the tidal contribution to the GW phase which includes further analytical knowledge and is calibrated to more accurate numerical relativity data than previously available; (ii) a tidal correction to the GW amplitude; (iii) an extension of the spin-sector incorporating equation-of-state-dependent finite size effects at quadrupolar and octupolar order; these appear in the spin-spin tail terms and cubic-in-spin terms, both at 3.5PN. We add the new description to the precessing binary black hole waveform model IMRPhenomPv2 to obtain a frequency-domain precessing binary neutron star model. In addition, we extend the SEOBNRv4_ROM and IMRPhenomD aligned-spin binary black hole waveform models with the improved tidal phase corrections. Focusing on the new IMRPhenomPv2_NRTidalv2 approximant, we test the model by comparing with numerical relativity waveforms as well as hybrid waveforms combining tidal effective-one-body and numerical relativity data. We also check consistency against a tidal effective-one-body model across large regions of the BNS parameter space.
TL;DR: In this paper, a spin-torque nano-oscillator was used to phase-lock the oscillator to the input waveform, which carries information in its modulated frequency.
Abstract: Spin-torque nano-oscillators can emulate neurons at the nanoscale. Recent works show that the non-linearity of their oscillation amplitude can be leveraged to achieve waveform classification for an input signal encoded in the amplitude of the input voltage. Here, we show that the frequency and phase of the oscillator can also be used to recognize waveforms. For this purpose, we phase-lock the oscillator to the input waveform, which carries information in its modulated frequency. In this way, we considerably decrease the amplitude, phase, and frequency noise. We show that this method allows classifying sine and square waveforms with an accuracy above 99% when decoding the output from the oscillator amplitude, phase, or frequency. We find that recognition rates are directly related to the noise and non-linearity of each variable. These results prove that spin-torque nano-oscillators offer an interesting platform to implement different computing schemes leveraging their rich dynamical features.
TL;DR: A method of designing the compound metaoptic is presented, which enables transformation between arbitrary complex-valued field distributions without reflection, absorption, polarization loss, or active components.
Abstract: Metasurfaces allow tailored control of electromagnetic wave fronts. However, due to local conservation of power flow, passive, lossless, and reflectionless metasurfaces have been limited to imparting phase discontinuities---and not power density discontinuities---onto a wave front. Here, we show how the phase and amplitude profiles of a wave front can be independently controlled using two closely spaced phase-discontinuous metasurfaces. The two metasurfaces, each designed to exhibit spatially varying refractive properties, are separated by a wavelength-scale distance and together form a compound metaoptic. A method of designing the compound metaoptic is presented, which enables transformation between arbitrary complex-valued field distributions without reflection, absorption, polarization loss, or active components. Such compound metaoptics may find applications in the optical trapping of particles, displaying three-dimensional holographic images, shrinking the size of optical systems, or producing custom (shaped and steered) far-field radiation patterns.
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TL;DR: In this article, the phase-amplitude metamaterials are used to control both the amplitude and phase at one or two frequencies, which can be used for computer-generated holographic objects.
Abstract: Metasurfaces are optically thin metamaterials that promise complete control of the wavefront of light but are primarily used to control only the phase of light. Here, we present an approach, simple in concept and in practice, that uses meta-atoms with a varying degree of form birefringence and rotation angles to create high-efficiency dielectric metasurfaces that control both the optical amplitude and phase at one or two frequencies. This opens up applications in computer-generated holography, allowing faithful reproduction of both the phase and amplitude of a target holographic scene without the iterative algorithms required in phase-only holography. We demonstrate all-dielectric metasurface holograms with independent and complete control of the amplitude and phase at up to two optical frequencies simultaneously to generate two- and three-dimensional holographic objects. We show that phase-amplitude metasurfaces enable a few features not attainable in phase-only holography; these include creating artifact-free two-dimensional holographic images, encoding phase and amplitude profiles separately at the object plane, encoding intensity profiles at the metasurface and object planes separately, and controlling the surface textures of three-dimensional holographic objects.
TL;DR: In this article, the symbol of the two-loop five-point amplitude in $ \mathcal{N} $ = 8 supergravity is computed and an ansatz for the amplitude whose rational prefactors are based on not only 4-dimensional leading singularities, but also d-dimensional ones is presented.
Abstract: We compute the symbol of the two-loop five-point amplitude in $ \mathcal{N} $ = 8 supergravity. We write an ansatz for the amplitude whose rational prefactors are based on not only 4-dimensional leading singularities, but also d-dimensional ones, as the former are insufficient. Our novel d-dimensional unitarity-based approach to the systematic construction of an amplitude’s rational structures is likely to have broader applications, for example to analogous QCD calculations. We fix parameters in the ansatz by performing numerical integration-by-parts reduction of the known integrand. We find that the two-loop five-point $ \mathcal{N} $ = 8 supergravity amplitude is uniformly transcendental. We then verify the soft and collinear limits of the amplitude. There is considerable similarity with the corresponding amplitude for $ \mathcal{N} $ = 4 super-Yang-Mills theory: all the rational prefactors are double copies of the Yang-Mills ones and the transcendental functions overlap to a large degree. As a byproduct, we find new relations between color-ordered loop amplitudes in $ \mathcal{N} $ = 4 super-Yang-Mills theory.
TL;DR: In this paper, the authors employed ensembles of NV center spins to measure macroscopic AC electric fields with high precision, achieving a precision of 10-7 V/μm for an AC electric field with a frequency of 2 kHz and an amplitude of 0.012 V/ μm.
Abstract: Electron spins in solids constitute remarkable quantum sensors. Individual defect centers in diamond were used to detect individual nuclear spins with a nanometer scale resolution, and ensemble magnetometers rival SQUID and vapor cell magnetometers when taking into account room-temperature operation and size. NV center spins can also detect electric field vectors, despite their weak coupling to electric fields. Here, we employ ensembles of NV center spins to measure macroscopic AC electric fields with high precision. We utilize low strain, 12C enriched diamond to achieve the maximum sensitivity and tailor the spin Hamiltonian via the proper magnetic field adjustment to map out the AC electric field strength and polarization and arrive at refined electric field coupling constants. For high-precision measurements, we combine classical lock-in detection with aspects from quantum phase estimation for the effective suppression of technical noise. Eventually, this enables t-1/2 uncertainty scaling of the electric field strength over extended averaging periods, enabling us to reach a precision down to 10-7 V/μm for an AC electric field with a frequency of 2 kHz and an amplitude of 0.012 V/ μm.
TL;DR: In this paper, a compound meta-atom can control the transmitted phase by modulating the gap size of a modified I-shaped structure, and can set the transmitted amplitude by rotating the structure between outer gratings.
Abstract: Metasurfaces continue to drawn significant attention for manipulating light waves, but most to date have controlled either the phase profile or the amplitude profile of the output light---not both. This study proposes a strategy to control the transmitted phase and amplitude, over a wide band. A compound meta-atom can control the transmitted phase by modulating the gap size of a modified I-shaped structure, and can set the transmitted amplitude by rotating the structure between outer gratings. A proof-of-concept experiment points to the possibility of realizing arbitrary beam shapes.
Abstract: The recent detection of ULASJ1342+0928, a bright QSO at $z=7.54$, provides a powerful probe of the ionisation state of the intervening intergalactic medium, potentially allowing us to set strong constraints on the epoch of reionisation (EoR). Here we quantify the presence of Ly$\alpha$ damping wing absorption from the EoR in the spectrum of ULASJ1342+0928. Our Bayesian framework simultaneously accounts for uncertainties on: (i) the intrinsic QSO emission (obtained from reconstructing the Ly$\alpha$ profile from a covariance matrix of emission lines) and (ii) the distribution of HII regions during reionisation (obtained from three different 1.6$^3$ Gpc$^3$ simulations spanning the range of plausible EoR morphologies). Our analysis is complementary to that in the discovery paper (Ba\~nados et al.) and the accompanying method paper (Davies et al.) as it focuses solely on the damping wing imprint redward of Ly$\alpha$ ($1218 < \lambda < 1230$\AA), and uses a different methodology for (i) and (ii). We recover weak evidence for damping wing absorption. Our intermediate EoR model yields a volume-weighted neutral hydrogen fraction at $z=7.5$ of $\bar{x}_{\rm HI} = 0.21\substack{+0.17 \\ -0.19}$ (68 per cent). The constraints depend weakly on the EoR morphology. Our limits are lower than those presented previously, though they are consistent at ~1-1.5$\sigma$. We attribute this difference to: (i) a lower amplitude intrinsic Ly$\alpha$ profile obtained from our reconstruction pipeline, driven by correlations with other high-ionisation lines in the spectrum which are relatively weak; and (ii) only considering transmission redward of Ly$\alpha$ when computing the likelihood, which reduces the available constraining power but makes the results less model-dependent. Our results are consistent with previous estimates of the EoR history, and support the picture of a moderately extended EoR.
TL;DR: In this paper, the amplitude of the two-loop five-particle amplitude in supergravity was computed in terms of uniform weight four symbols, multiplied by a small set of rational factors.
Abstract: We compute for the first time the two-loop five-particle amplitude in $$ \mathcal{N} $$
= 8 supergravity. Starting from the known integrand, we perform an integration-by-parts reduction and express the answer in terms of uniform weight master integrals. The latter are known to evaluate to non-planar pentagon functions, described by a 31-letter symbol alphabet. We express the final result for the amplitude in terms of uniform weight four symbols, multiplied by a small set of rational factors. We observe that one of the symbol letters is absent from the amplitude. The latter satisfies the expected factorization properties when one external graviton becomes soft, and when two external gravitons become collinear. We verify that the soft divergences of the amplitude exponentiate. We extract the finite remainder function, which depends on fewer rational factors. By analyzing identities involving rational factors and symbols we find a remarkably compact representation in terms of a single seed function, summed over all permutations of external particles. Finally, we work out the multi-Regge limit, and present explicitly the leading logarithmic terms in the limit. The full symbol of the IR-subtracted hard function is provided as a supplementary file.
TL;DR: In this paper, the authors describe a narrow-band search using LIGO O2 data for the continuous wave emission of 33 pulsars and show that no evidence of a continuous wave signal is found, and upper limits on the amplitude over the analyzed frequency and spin-down ranges are computed for each of the targets.
Abstract: Isolated spinning neutron stars, asymmetric with respect to their rotation axis, are expected to be sources of continuous gravitational waves. The most sensitive searches for these sources are based on accurate matched filtering techniques that assume the continuous wave to be phase locked with the pulsar beamed emission. While matched filtering maximizes the search sensitivity, a significant signal-to-noise ratio loss will happen in the case of a mismatch between the assumed and the true signal phase evolution. Narrow-band algorithms allow for a small mismatch in the frequency and spin-down values of the pulsar while coherently integrating the entire dataset. In this paper, we describe a narrow-band search using LIGO O2 data for the continuous wave emission of 33 pulsars. No evidence of a continuous wave signal is found, and upper limits on the gravitational wave amplitude over the analyzed frequency and spin-down ranges are computed for each of the targets. In this search, we surpass the spin-down limit, namely, the maximum rotational energy loss due to gravitational waves emission for some of the pulsars already present in the LIGO O1 narrow-band search, such as J1400-6325, J1813-1246, J1833-1034, J1952+3252, and for new targets such as J0940-5428 and J1747-2809. For J1400-6325, J1833-1034, and J1747-2809, this is the first time the spin-down limit is surpassed.
University of Chicago1, University of Oslo2, Cardiff University3, Fermilab4, National Institute of Standards and Technology5, University of California, Berkeley6, Argonne National Laboratory7, University of Melbourne8, McGill University9, University of KwaZulu-Natal10, California Institute of Technology11, Lawrence Berkeley National Laboratory12, Canadian Institute for Advanced Research13, University of Colorado Boulder14, Harvey Mudd College15, European Southern Observatory16, University of Illinois at Urbana–Champaign17, Stanford University18, University of California, Davis19, University of Paris20, University of Michigan21, University of Minnesota22, Case Western Reserve University23, Yale University24, School of the Art Institute of Chicago25, Harvard University26, University of Toronto27, University of Maryland, College Park28, National Center for Supercomputing Applications29, University of California, Los Angeles30
TL;DR: Wu et al. as discussed by the authors measured the lensing amplitude by taking the ratio of the measured spectrum to the expected spectrum from the best-fit Λ cold dark matter model to the Planck 2015 TT + low P + lensing data set.
Abstract: Author(s): Wu, WLK; Mocanu, LM; Ade, PAR; Anderson, AJ; Austermann, JE; Avva, JS; Beall, JA; Bender, AN; Benson, BA; Bianchini, F; Bleem, LE; Carlstrom, JE; Chang, CL; Chiang, HC; Citron, R; Moran, CC; Crawford, TM; Crites, AT; De Haan, TD; Dobbs, MA; Everett, W; Gallicchio, J; George, EM; Gilbert, A; Gupta, N; Halverson, NW; Harrington, N; Henning, JW; Hilton, GC; Holder, GP; Holzapfel, WL; Hou, Z; Hrubes, JD; Huang, N; Hubmayr, J; Irwin, KD; Knox, L; Lee, AT; Li, D; Lowitz, A; Manzotti, A; McMahon, JJ; Meyer, SS; Millea, M; Montgomery, J; Nadolski, A; Natoli, T; Nibarger, JP; Noble, GI; Novosad, V; Omori, Y; Padin, S; Patil, S; Pryke, C; Reichardt, CL; Ruhl, JE; Saliwanchik, BR; Sayre, JT; Schaffer, KK; Sievers, C; Simard, G; Smecher, G; Stark, AA; Story, KT; Tucker, C; Vanderlinde, K; Veach, T; Vieira, JD; Wang, G; Whitehorn, N; Yefremenko, V | Abstract: We present a measurement of the cosmic microwave background lensing potential using 500 deg2 of 150 GHz data from the SPTpol receiver on the South Pole Telescope. The lensing potential is reconstructed with signal-to-noise per mode greater than unity at lensing multipoles L ≲ 250, using a quadratic estimator on a combination of cosmic microwave background temperature and polarization maps. We report measurements of the lensing potential power spectrum in the multipole range of 100 l L l 2000 from sets of temperature-only (T), polarization-only (POL), and minimum-variance (MV) estimators. We measure the lensing amplitude by taking the ratio of the measured spectrum to the expected spectrum from the best-fit Λ cold dark matter model to the Planck 2015 TT + low P + lensing data set. For the minimum-variance estimator, we find =0.944 0.025 (Sys.) SRC=restricting to only polarization data, we find POL=0.906\pm 0.090 0.040. Considering statistical uncertainties alone, this is the most precise polarization-only lensing amplitude constraint to date (10.1σ) and is more precise than our temperature-only constraint. We perform null tests and consistency checks and find no evidence for significant contamination.
TL;DR: In this paper, it was shown that the classical Lippmann-Schwinger equation is in one-to-one correspondence with the energy equation of a relativistic two-body system.
Abstract: Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A corollary is that the scattering angle can be computed from the amplitude itself, without having to introduce a potential. All results are universal and provide for the case of general relativity a very simple formula for the scattering angle in terms of the classical part of the amplitude, to any order in the post-Minkowskian expansion.
TL;DR: Estimation of amplitude, instantaneous phase, and frequency of a single-phase grid voltage signal are studied and the proposed frequency adaptive CLO technique is robust against various perturbations faced in the practical settings.
Abstract: Estimation of amplitude, instantaneous phase, and frequency of a single-phase grid voltage signal are studied in this letter. The proposed approach uses a novel circular limit cycle oscillator (CLO) coupled with a frequency-locked loop. Due to the nonlinear structure of the CLO, the proposed frequency adaptive CLO technique is robust against various perturbations faced in the practical settings, e.g., the discontinuous jump of phase, frequency, and amplitude. The global stability analysis of the CLO and local stability analysis of the frequency adaptive CLO are performed. Experimental results demonstrate the effectiveness of the proposed technique over a very recent technique proposed in the literature.