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At least 109 records · Page 6

Radar Measurements of the Vibration Amplitude

We propose a method for measuring the harmonic vibration amplitude of a reflector using a coherent radar station. A mathematical model describing the dependence of the Doppler spectrum of the reflected radio signal on the ratio of the vibration amplitude to the radiation wavelength is constructed. The vibration amplitude is calculated from the amplitude ratio of the third to first or fourth to second harmonics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Generation of Giant Amplitude Pulses in a Klystron Chaos Auto-Oscillator

The presented experimental results demonstrate that microwave pulses of giant amplitude are generated in a klystron generator operating in the self-excited mode of chaotic oscillations. The auto-oscillator is assembled using a noisetron scheme that contains two five-cavity floating-drift klystrons serially connected in a ring, one of which operates in the mode of linear signal amplification (the linear klystron) and the other works in the mode of nonlinear signal amplification (the nonlinear klystron). It is established that, at a certain value of the beam current of a nonlinear klystron, intermittency of chaos–chaos type is realized in the auto-oscillation system in the form of chaotic sequences of microwave pulses of giant amplitude formed over the chaotic amplitude background. This type of intermittency is caused by the amplitude bistability of the nonlinear floating-drift klystron.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

An analytic result for the 0 → ggHHH amplitude

We present a fully analytic calculation of the leading-order one-loop amplitude for triple Higgs production via gluon fusion, gg → HHH, retaining full dependence on the mass of the heavy quark circulating in the loop. This amplitude provides a direct probe of the triple and quartic Higgs self-couplings, the measurement of which is a central goal of current and future colliders. The amplitude can be presented in compact form thanks to the use of analytic reconstruction techniques, based on finite-field and p-adic evaluations, multivariate partial fraction decompositions, and primary decompositions to identify common numerator factors. Although full analytic results are given in the text and in the supplementary material, the main thrust of this paper is to further test and illustrate these analytic reconstruction techniques in a concrete physical example. Our results provide a compact and efficient representation of the matrix element for this process, enabling evaluations that are more than an order of magnitude faster than existing numerical alternatives. Full analytic control of the leading-order, loop-induced amplitude is an important step towards handling more complex 2-loop or real-radiation corrections to this and related processes.

Campbell, John M. [Fermilab] (ORCID:00000002136193↗

Investigating the universality of five-point QCD scattering amplitudes at high energy

We investigate 2 → 3 QCD scattering amplitudes in multi-Regge kinematics, i.e. where the final partons are strongly ordered in rapidity. In this regime amplitudes exhibit intriguing factorisation properties which can be understood in terms of effective degrees of freedom called reggeons. Working within the Balitsky/JIMWLK framework, we predict these amplitudes for the first time to next-to-next-to-leading logarithmic order, and compare against the limit of QCD scattering amplitudes in full colour and kinematics. We find that the latter can be described in terms of universal objects, and that the apparent non-universality arising at NNLL comes from well-defined and under-control contributions that we can predict. Thanks to this observation, we extract for the first time the universal vertex that controls the emission of the central-rapidity gluon, both in QCD and $\mathcal{N}$ = 4 super Yang-Mills.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Decay amplitudes to three hadrons from finite-volume matrix elements

We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g - 2.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Non-Boolean quantum amplitude amplification and quantum mean estimation

This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-Boolean oracles. The action of a non-Boolean oracle $U_\varphi $ on an eigenstate $\mathinner {|{x}\rangle }$ is to apply a state-dependent phase-shift $\varphi (x)$. Unlike Boolean oracles, the eigenvalues $\exp (i\varphi (x))$ of a non-Boolean oracle are not restricted to be $\pm 1$. Two new oracular algorithms based on such non-Boolean oracles are introduced. The first is the non-Boolean amplitude amplification algorithm, which preferentially amplifies the amplitudes of the eigenstates based on the value of $\varphi (x)$. Starting from a given initial superposition state $\mathinner {|{\psi _0}\rangle }$, the basis states with lower values of $\cos (\varphi )$ are amplified at the expense of the basis states with higher values of $\cos (\varphi )$. The second algorithm is the quantum mean estimation algorithm, which uses quantum phase estimation to estimate the expectation $\mathinner {\langle {\psi _0|U_\varphi |\psi _0}\rangle }$, i.e., the expected value of $\exp (i\varphi (x))$ for a random x sampled by making a measurement on $\mathinner {|{\psi _0}\rangle }$. It is shown that the quantum mean estimation algorithm offers a quadratic speedup over the corresponding classical algorithm. Both algorithms are demonstrated using simulations for a toy example. Potential applications of the algorithms are briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analysis of Electric and Magnetic Lightning-Generated Wave Amplitudes Measured by the Van Allen Probes

Herein we provide a statistical analysis of both electric and magnetic field wave amplitudes of very low frequency lightning-generated waves (LGWs) based on the equivalent of 11.5 years of observations made by the Van Allen Probes encompassing ~24.6 × 10 6 survey mode measurements. We complement this analysis with data from the ground-based World Wide Lightning Location Network to explore differences between satellite and ground-based measurements. LGW mean amplitudes are found to be low compared with other whistler mode waves (1 ± 1.6 pT and 19 ± 59 μV/m). Extreme events (1/5,000) can reach 100 pT and contributes strongly to the mean power below $L$ = 2. We find excellent correlations between World Wide Lightning Location Network-based power and wave amplitudes in space at various longitudes. We reveal strong dayside ionospheric damping of the LGW electric field. LGW amplitudes drop for $L$ < 2, contrary to the Earth's intense equatorial lightning activity. We conclude that it is difficult for equatorial LGW to propagate and remain at $L$ < 2.

Electric wave power↗

Amplitude mode in the planar triangular antiferromagnet Na 0.9 MnO 2

Amplitude modes arising from symmetry breaking in materials are of broad interest in condensed matter physics. These modes reflect an oscillation in the amplitude of a complex order parameter, yet are typically unstable and decay into oscillations of the order parameter’s phase. This renders stable amplitude modes rare, and exotic effects in quantum antiferromagnets have historically provided a realm for their detection. We report an alternate route to realizing amplitude modes in magnetic materials by demonstrating that an antiferromagnet on a two-dimensional anisotropic triangular lattice (α-Na 0.9 MnO 2 ) exhibits a long-lived, coherent oscillation of its staggered magnetization field. Our results show that geometric frustration of Heisenberg spins with uniaxial single-ion anisotropy can renormalize the interactions of a dense two-dimensional network of moments into largely decoupled, one-dimensional chains that manifest a longitudinally polarized-bound state. This bound state is driven by the Ising-like anisotropy inherent to the Mn 3+ ions of this compound.

36 MATERIALS SCIENCE↗

Piezoresponse amplitude and phase quantified for electromechanical characterization

Piezoresponse force microscopy (PFM) is a powerful characterization technique to readily image and manipulate the ferroelectric domains. PFM gives an insight into the strength of local piezoelectric coupling and polarization direction through PFM amplitude and phase, respectively. Converting measured arbitrary units into units of effective piezoelectric constant remains a challenge, and insufficient methods are often used. While most quantification efforts have been spent on quantifying the PFM amplitude signal, little attention has been given to the PFM phase, which is often arbitrarily adjusted to fit expectations. This is problematic when investigating materials with unknown or negative sign of the probed effective electrostrictive coefficient or strong frequency dispersion of electromechanical responses, because assumptions about the PFM phase cannot be reliably made. The PFM phase can, however, provide important information on the polarization orientation and the sign of the effective electrostrictive coefficient probed by PFM. Most notably, the orientation of the PFM hysteresis loop is determined by the PFM phase. Moreover, when presenting PFM data as a combined signal, the resulting response can be artificially lowered or asymmetric if the phase data have not been correctly processed. Here, we explain the PFM amplitude quantification process and demonstrate a path to identify the phase offset required to extract correct meaning from the PFM phase data. We explore different sources of phase offsets including the experimental setup, instrumental contributions, and data analysis. We discuss the physical working principles of PFM and develop a strategy to extract physical meaning from the PFM amplitude and phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lensing without borders – I. A blind comparison of the amplitude of galaxy–galaxy lensing between independent imaging surveys

ABSTRACT Lensing without borders is a cross-survey collaboration created to assess the consistency of galaxy–galaxy lensing signals (ΔΣ) across different data sets and to carry out end-to-end tests of systematic errors. We perform a blind comparison of the amplitude of ΔΣ using lens samples from BOSS and six independent lensing surveys. We find good agreement between empirically estimated and reported systematic errors which agree to better than 2.3σ in four lens bins and three radial ranges. For lenses with zL > 0.43 and considering statistical errors, we detect a 3–4σ correlation between lensing amplitude and survey depth. This correlation could arise from the increasing impact at higher redshift of unrecognized galaxy blends on shear calibration and imperfections in photometric redshift calibration. At zL > 0.54, amplitudes may additionally correlate with foreground stellar density. The amplitude of these trends is within survey-defined systematic error budgets that are designed to include known shear and redshift calibration uncertainty. Using a fully empirical and conservative method, we do not find evidence for large unknown systematics. Systematic errors greater than 15 per cent (25 per cent) ruled out in three lens bins at 68 per cent (95 per cent) confidence at z < 0.54. Differences with respect to predictions based on clustering are observed to be at the 20–30 per cent level. Our results therefore suggest that lensing systematics alone are unlikely to fully explain the ‘lensing is low’ effect at z < 0.54. This analysis demonstrates the power of cross-survey comparisons and provides a promising path for identifying and reducing systematics in future lensing analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

Two-loop n -point anomalous amplitudes in N=4 supergravity

We compute the anomalous two-loop four-point amplitudes in N=4 pure supergravity, using unitarity and the double-copy construction. Here, we also present all terms determined by four-dimensional cuts in two all-multiplicity two-loop anomalous superamplitudes. This result provides the first two-loop n-point gravity amplitude, up to a class of undetermined terms, which we determine completely at four points. We show that a recently proposed finite counterterm cancels these amplitudes to this order. We argue that the counterterm does not spoil the three-loop finiteness of anomalous amplitudes in the N=4 theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Celestial Dual for Maximal Helicity Violating Amplitudes

It is shown that a 2D conformal field theory consisting of a central charge c Liouville theory, a chiral level one, rank N Kac-Moody algebra, and a weight − 3 / 2 free fermion holographically generate 4D maximal helicity violating tree-level scattering amplitudes. The correlators of this 2D conformal field theory give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large- N and semiclassical large- c limit, according to the holographic dictionary, as a translationally invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact 3D anti–de Sitter Witten diagrams. Published by the American Physical Society 2024

Physics↗

Full complex amplitude control of second-harmonic generation via electrically tunable intersubband polaritonic metasurfaces

Nonlinear intersubband polaritonic metasurfaces based on coupling of the intersubband nonlinear optical response of quantum-engineered semiconductor heterostructures and electromagnetic modes of nanoresonators provide efficient frequency mixing with moderate pump intensities. The resonant nonlinear optical response, represented as a complex function, can be modulated via Stark tuning of intersubband transition energies under applied voltages. However, achieving full complex amplitude control (both phase and magnitude) remains challenging. In this work, we present and experimentally validate electrically tunable nonlinear intersubband polaritonic metasurfaces that achieve complete complex amplitude control for second-harmonic generation (SHG). Through a design featuring two in-plane flipped meta-atoms per unit cell, we achieve complete electrical control of both the amplitude and phase of the metasurface second-order nonlinear susceptibility, with a tuning range of 0 to 30 nm V −1 for the magnitude and 0-2π for the phase of the nonlinear optical response. Using these properties, we achieve complete on-off SHG modulation and beam diffraction tuning through electrically controlled amplitude and phase gratings.

Science & Technology - Other Topics↗

Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements

Nonlinear effects of the various electric field and magnetic field components of storage rings to confine the particles and bend their trajectory can cause substantial amplitude-dependent tune shifts within the beam. Furthermore, tune shifts are often sensitive to variations of system parameters, e.g. total particle momentum offsets $δp$. Such amplitude- and parameter-dependent tune shifts influence the dynamics and stability of a beam in particle storage rings. Thus, it is critical for high precision measurements to analyze and understand these influences. On this basis, we present in this paper normal form methods for the calculation of high order amplitude and system parameter dependencies of the horizontal and vertical tunes in storage rings using the differential algebra (DA) framework within COSY INFINITY. A storage ring is simulated using COSY INFINITY to generate a DA Poincaré return map describing the transverse phase space behavior after each revolution in the storage ring. The map is expanded around the parameter-dependent closed orbit of the system before transforming the resulting map into normal form coordinates to extract the high order tune dependencies on the phase space amplitude and variation in the system parameters. As a specific example, a storage ring similar to the Storage Ring of the Muon g-2 Experiment at Fermilab (E989) is investigated.

43 PARTICLE ACCELERATORS↗

Discrimination of Anthropogenic Events and Tectonic Earthquakes in Utah Using a Quadratic Discriminant Function Approach with Local Distance Amplitude Ratios

Most of the commonly used seismic discrimination approaches are designed for teleseismic and regional data. To monitor for the smallest events, some of these discriminants have been adapted for local distances (< 200 km), with mixed level of success. For this, we take advantage of the variety of seismic sources, including nontraditionally studied anthropogenic sources and the existence of a dense regional seismic network in the Utah region to evaluate amplitude ratio seismic discrimination at local distances. First, we explored phase-amplitude Pg-to-Sg ratios for multiple frequency bands to classify events in a dataset that comprises populations of single-shot surface explosions, shallow and deep ripple-fired mining blasts, mining-induced events (MIEs), and tectonic earthquakes. We achieved a success rate of about 59%–83%. Then, for the same dataset, we combined the Pg-to-Sg phase-amplitude ratios with Sg-to-Rg spectral amplitude ratios in a multivariate quadratic discriminant function (QDF) approach. For two-category pairwise classification, seven of ten population pairs show misclassification rates of about 20% or less, with five pairs showing rates of about 10% or less. The approach performs best for the pair involving the populations of single-shot explosions and MIEs. By combining both Pg-to-Sg and Rg-to-Sg ratios in the multivariate QDFs, we are able to achieve an average improvement of about 4%–14% in misclassification rates compared with Pg-to-Sg ratios alone. When all five event populations are considered simultaneously, as expected, the potential for misclassification increases, and our QDF approach using both Pg-to-Sg and Rg-to-Sg ratios achieves an average success rate of about 74% compared with the rate of about 86% for two-category pairwise classification.

58 GEOSCIENCES↗

Natural boundaries for scattering amplitudes

Singularities, such as poles and branch points, play a crucial role in investigating the analytic properties of scattering amplitudes that inform new computational techniques. In this note, we point out that scattering amplitudes can also have another class of singularities called natural boundaries of analyticity. They create a barrier beyond which analytic continuation cannot be performed. More concretely, we use unitarity to show that 2 \to 2 2 → 2 scattering amplitudes in theories with a mass gap can have a natural boundary on the second sheet of the lightest threshold cut. There, an infinite number of ladder-type Landau singularities densely accumulates on the real axis in the center-of-mass energy plane. We argue that natural boundaries are generic features of higher-multiplicity scattering amplitudes in gapped theories.

97 MATHEMATICS AND COMPUTING↗

Efficient Hamiltonian encoding algorithms for extracting quantum control mechanism as interfering pathway amplitudes in the Dyson series

Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz \cite{abhra_1}, we define mechanism via pathways of eigenstates that describe the evolution of the system, where each pathway is associated with a complex-valued amplitude corresponding to a term in the Dyson series. The evolution of the system is determined by the constructive and destructive interference of these pathway amplitudes. Pathways with similar attributes can be grouped together into pathway classes. The amplitudes of pathway classes are computed by modulating the Hamiltonian matrix elements and decoding the subsequent evolution of the system rather than by direct computation of the individual terms in the Dyson series. The original implementation of Hamiltonian encoding was computationally intensive and became prohibitively expensive in large quantum systems. This paper presents two new encoding algorithms that calculate the amplitudes of pathway classes by using techniques from graph theory and algebraic topology to exploit patterns in the set of allowed transitions, greatly reducing the number of matrix elements that need to be modulated. These new algorithms provide an exponential decrease in both computation time and memory utilization with respect to the Hilbert space dimension of the system. To demonstrate the use of these techniques, they are applied to two illustrative state-to-state transition problems.

Abrams, Erez [Princeton University, Massachusetts ↗

Measurement of the light-field amplitude-correlation function through joint photon-count distributions.

When an amplitude-stabilized He-Ne laser beam is scattered by a rotating ground glass with small surface inhomogeneities, the probability density of the instantaneous scattered-wave amplitude is Gaussian. In this paper, we suggest the use of the joint photon-count probability distribution to measure the absolute value of the electric-field amplitude-correlation function for random Gaussian light fields, and report the results of an experiment in which the Gaussian field is produced by scattering a light beam through a rotating ground glass. This procedure offers an alternative to other conventional methods, such as self-beating spectroscopy and irradiance-correlation techniques. The correlation time of the scattered-field amplitude in the present experiment has been measured with an accuracy of approximately 0.8%.

Furcinitti, P.↗