Classical Amplitude Research Articles

Compton Amplitude for Rotating Black Hole from QFT.

We construct a candidate tree-level gravitational Compton amplitude for a rotating Kerr black hole, for any quantum spin s=0,1/2,1,…,∞, from which we extract the corresponding classical amplitude to all orders in the spin vector S^{μ}. We use multiple insights from massive higher-spin quantum field theory, such as massive gauge invariance and improved behavior in the massless limit. A chiral-field approach is particularly helpful in ensuring correct degrees of freedom, and for writing down compact off-shell interactions for general spin. The simplicity of the interactions is echoed in the structure of the spin-s Compton amplitude, for which we use homogeneous symmetric polynomials of the spin variables. Where possible, we compare to the general-relativity results in the literature, available up to eighth order in spin.

Tripartite entanglement in a detuned non-degenerate optical parametric oscillator

Continuous variable multipartite entanglement is an important resource in quantum optics and quantum information. Non-degenerate optical parametric oscillator (NOPO), generally working in a resonant regime, can generate high quality tripartite entanglement. However, the detuning in a real experiment is inevitable and sometimes necessary, for instance, in an optomechanical system. We calculate the tripartite entanglement from a detuned triply quasi-resonant NOPO. Unlike the previous literature using inseparability criterion, we use the positivity of partial transpose, a sufficient and necessary criterion, to characterize the tripartite entanglement with full inseparability generated from a detuned NOPO. We also consider the influence of the pump and signal/idler losses on the tripartite entanglement. The results show that, the tripartite entanglement could exist even with a large detuning of several times cavity linewidth, and may be better for a detuned regime than for the resonant one under some conditions. With a fixed non-zero loss which always exists in a real experiment, an appropriate value of non-zero detuning could lead to the best entanglement. What’s more, unlike the bipartite entanglement, which exists both below and above threshold, the tripartite entanglement only occurs for a nonzero classical amplitude of signal/idler field. The jumping between the tripartite and bipartite entanglement could make the NOPO become a quantum state switch element, which promises a potential application on the multiparty quantum secret sharing.

Efficiency of machine learning to predict gas accumulations

A growing number of research geophysicists are drawn to machine learning in geophysical applications. At the moment, direct applications of machine learning cover an expansive range of tasks related to the interpretation of seismic data. Beginning with computer-assisted seismic well tying, faults and horizons are automatically interpreted, velocity models are optimized, geobodies are extracted, and seismic facies are classified. Our goal is to demonstrate how artificial neural networks may be used to teach a computer to categorize seismic data and anticipate possible gas accumulations, starting from selecting training data, through filtering the best discriminating attributes, monitoring the learning process, and ending with running the predictions. This workflow was applied on a Dana Gas Messininan gas field in the Nile Delta province of Egypt. The network was trained on a few seismic points in the vicinity of one successful well as positive training examples. The network not only accurately predicted the gas accumulation near the training points but also the other nearby stratigraphically compartmentalized gas accumulations, aligning with production and pressure data of the hidden wells. Similar findings were obtained when the results were compared to classical amplitude variation with offset elastic inversion; however, the machine learning methodology is far faster and easier than the inversion in terms of procedural steps and required work.

Resummed spinning waveforms from five-point amplitudes

We compute the classical tree-level five-point amplitude for the two-to-two scattering of spinning celestial objects with the emission of a graviton. Using this five-point amplitude, we then turn to the computation of the leading-order time-domain gravitational waveform. The method we describe is suitable for arbitrary values of classical spin of Kerr black holes and does not require any expansion in powers of the spin. In this paper we illustrate it in the simpler case of the scattering of one Kerr and one Schwarzschild black hole. An important ingredient of our calculation is a novel form of the Compton amplitude with spinning particles including contact terms derived from matching to black-hole perturbation theory calculations. This ensures that our waveform is valid up to at least fourth order in the spin. Our method can be applied immediately to generate improved waveforms once higher-order contact terms in the Compton amplitude become available. Finally, we show the formula for the gravitational memory to all orders in the spin, which is in agreement with our results.

High-power quantum-limited 35 MHz photodiode and classical laser noise suppression

To benefit high-power interferometry and the creation of low-noise light sources, we develop a simple lead-compensated photodetector enabling quantum-limited readout from 0.3 to 10 mW and 10 kΩ gain from 85 Hz to 35 MHz, with a noise equivalent power of 9 pW/Hz. Feeding the detector output back to an intensity modulator, we suppress the classical amplitude noise of a commercial 1550 nm fiber laser to the shot noise limit over a bandwidth of 700 Hz–200 kHz, observing no degradation to its (nominally ∼100 Hz) linewidth.

Complementarity and entanglement in a simple model of inelastic scattering

A simple model coupling a one-dimensional beam particle to a one-dimensional harmonic oscillator is used to explore complementarity and entanglement. This model, well-known in the inelastic scattering literature, is presented under three different conceptual approaches, with both analytical and numerical techniques discussed for each. In a purely classical approach, the final amplitude of the oscillator can be found directly from the initial conditions. In a partially quantum approach, with a classical beam and a quantum oscillator, the final magnitude of the quantum-mechanical amplitude for the oscillator's first excited state is directly proportional to the oscillator's classical amplitude of vibration. Nearly the same first-order transition probabilities emerge in the partially and fully quantum approaches, but conceptual differences emerge. The two-particle scattering wavefunction clarifies these differences and allows the consequences of quantum entanglement to be explored.

A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections

By exploiting the Kerr-Schild gauge, we study the scattering of a massive (charged) scalar off a Kerr-Newman black hole. In this gauge, the interactions between the probe and the target involve only tri-linear vertices. We manage to write down the tree-level scattering amplitudes in analytic form, from which we can construct an expression for the eikonal phase which is exact in the spin of the black hole at arbitrary order in the Post-Minkowskian expansion. We compute the classical contribution to the cross-section and deflection angle at leading order for a Kerr black hole for arbitrary orientation of the spin. Finally, we test our method by reproducing the classical amplitude for a Schwarzschild black hole at second Post-Minkowskian order and outline how to extend the analysis to the Kerr-Newman case.

Entanglement maintenance of classically pumped qubits and calibration aspects with the resonator tomography under the Stark shift effect inside a coherent resonator

We present a scheme for the investigation of entanglement of a similar qubits-pair along with the coherent resonator tomography under two-photon processes. Our discussion is focusing on the effect of the classical power amplitude along with Stark shift width and the conditions under which they have a constructive role in protecting the initial-state entanglement and the corresponding field tomography evolution. We observe that the entanglement between the qubits does maximally peak below a critical value and can be determined by suitable measurements on the resonator tomography. Interestingly, above the critical value, the tomography profile either shows an annular structure or exhibits quantumness which could be largely diminished by controlling the driving power intensity as well as the shift width. Particularly and for a detuned interaction, the critical values can be largely exceeded for sufficiently large values of the driving intensity and Stark shift, hence, more regions in the plane of parameters can be occupied by the qubits correlation. In this case, the pronounced fluctuations exhibited by entanglement dynamics due to phase variations could be highly interrupted. Additionally, preserving the field tomography showing a multi-component Schrödinger cat state via field-field detuning, robust, periodical and close to unity entanglement between the qubits could be highly possible. Moreover, in particular situations, the field tomography dynamics show the Fourier transform of the original field wave packet one-quarter period after initial, accordingly, entanglement maxima are reached frequently per a quarter period of rotation.

Effect of fractional derivatives on amplitude chimeras and symmetry-breaking death states in networks of limit-cycle oscillators.

We study networks of coupled oscillators whose local dynamics are governed by the fractional-order versions of the paradigmatic van der Pol and Rayleigh oscillators. We show that the networks exhibit diverse amplitude chimeras and oscillation death patterns. The occurrence of amplitude chimeras in a network of van der Pol oscillators is observed for the first time. A form of amplitude chimera, namely, "damped amplitude chimera" is observed and characterized, where the size of the incoherent region(s) increases continuously in the course of time, and the oscillations of drifting units are damped continuously until they are quenched to steady state. It is found that as the order of the fractional derivative decreases, the lifetime of classical amplitude chimeras increases, and there is a critical point at which there is a transition to damped amplitude chimeras. Overall, a decrease in the order of fractional derivatives reduces the propensity to synchronization and promotes oscillation death phenomena including solitary oscillation death and chimera death patterns that were unobserved in networks of integer-order oscillators. This effect of the fractional derivatives is verified by the stability analysis based on the properties of the master stability function of some collective dynamical states calculated from the block-diagonalized variational equations of the coupled systems. The present study generalizes the results of our recently studied network of fractional-order Stuart-Landau oscillators.

Scattering in black hole backgrounds and higher-spin amplitudes. Part II

We continue to investigate correspondences between, on the one hand, scattering amplitudes for massive higher-spin particles and gravitons in appropriate quantum-to-classical limits, and on the other hand, classical gravitational interactions of spinning black holes according to general relativity. We first construct an ansatz for a gravitational Compton amplitude, at tree level, constrained only by locality, crossing symmetry, unitarity and consistency with the linearized-Kerr 3-point amplitude, to all orders in the black hole’s spin. We then explore the extent to which a unique classical Compton amplitude can be identified by comparing with the results of the classical process of scattering long-wavelength gravitational waves off an exact Kerr black hole, determined by appropriate solutions of the Teukolsky equation. Up to fourth order in spin, we find complete agreement with a previously conjectured exponential form of the tree-level Compton amplitude. At higher orders, we extract tree-level contributions from the Teukolsky amplitude by an analytic continuation from a physical (a/GM < 1) to a particle-like (a/GM > 1) regime. Up to the sixth order in spin, we identify a unique conservative part of the amplitude which is insensitive both to the choice of boundary conditions at the black hole horizon and to branch choices in the analytic continuation. The remainder of the amplitude is determined modulo an overall sign from a branch choice, with the sign flipping under exchanging purely ingoing and purely outgoing boundary conditions at the horizon. Along the way, we make contact with novel applications of massive spinor-helicity variables pertaining to their relation to EFT operators and (spinning) partial amplitudes.

Recursion in the classical limit and the neutron-star Compton amplitude

We study the compatibility of recursive techniques with the classical limit of scattering amplitudes through the construction of the classical Compton amplitude for general spinning compact objects. This is done using BCFW recursion on three-point amplitudes expressed in terms of the classical spin vector and tensor, and expanded to next-to-leading-order in ћ by using the heavy on-shell spinors. Matching to the result of classical computations, we find that lower-point quantum contributions are, in general, required for the recursive construction of classical, spinning, higher-point amplitudes with massive propagators. We are thus led to conclude that BCFW recursion and the classical limit do not commute. In possession of the classical Compton amplitude, we remove non-localities to all orders in spin for opposite graviton helicities, and to fifth order in the same-helicity case. Finally, all possible on-shell contact terms potentially relevant to black-hole scattering at the second post-Minkowskian order are enumerated and written explicitly.

Scattering of gravitational waves off spinning compact objects with an effective worldline theory

We study the process, within classical general relativity, in which an incident gravitational plane wave, of weak amplitude and long wavelength, scatters off a massive spinning compact object, such as a black hole or neutron star. The amplitude of the asymptotic scattered wave, considered here at linear order in Newton's constant $G$ while at higher orders in the object's multipole expansion, is a valuable characterization of the response of the object to external gravitational fields. This amplitude coincides with a classical ($\ensuremath{\hbar}\ensuremath{\rightarrow}0$) limit of a quantum four-point (object and graviton in, object and graviton out) gravitational Compton amplitude, at the tree (linear-in-$G$) level. Such tree-level Compton amplitudes are key building blocks in generalized-unitary-based approaches to the post-Minkowskian dynamics of binaries of spinning compact objects. In this paper, we compute the classical amplitude using an effective worldline theory to describe the compact object, determined by an action functional for translational and rotational degrees of freedom, including couplings of spin-induced higher multipole moments to space-time curvature. We work here up to the levels of quadratic-in-spin quadrupole and cubic-in-spin octupole couplings, respectively involving Wilson coefficients ${C}_{2}$ and ${C}_{3}$. For the special case ${C}_{2}={C}_{3}=1$ corresponding to a black hole, we find agreement through cubic-in-spin order between our classical amplitude and previous conjectures arising from considerations of quantum scattering amplitudes. We also present new results for general ${C}_{2}$ and ${C}_{3}$, anticipating instructive comparisons with results from effective quantum theories.

Emerging ECG methods for acute coronary syndrome detection: Recommendations & future opportunities

Despite being the mainstay for the initial noninvasive assessment of patients with symptomatic coronary artery disease, the 12‑lead ECG remains a suboptimal diagnostic tool for myocardial ischemia detection with only acceptable sensitivity and specificity scores. Although myocardial ischemia affects the configuration of the QRS complex and the STT waveform, current guidelines primarily focus on ST segment amplitude, which constitutes a missed opportunity and may explain the suboptimal diagnostic performance of the ECG. This possible opportunity and the low cost and ease of use of the ECG provide compelling motivation to enhance the diagnostic accuracy of the ECG to ischemia detection. This paper describes numerous computational ECG methods and approaches that have been shown to dramatically increase ECG sensitivity to ischemia detection. Briefly, these emerging approaches can be conceptually grouped into one of the following four approaches: (1) leveraging novel ECG waveform features and signatures indicative of ischemic injury other than the classical ST-T amplitude measures; (2) applying body surface potentials mapping (BSPM)-based approaches to enhance the spatial coverage of the surface ECG to detecting ischemia; (3) developing an inverse ECG solution to reconstruct anatomical models of activation and recovery pathways to detect and localize injury currents; and (4) exploring artificial intelligence (AI)-based techniques to harvest ECG waveform signatures of ischemia. We present recent advances, shortcomings, and future opportunities for each of these emerging ECG methods. Future research should focus on the prospective clinical testing of these approaches to establish clinical utility and to expedite potential translation into clinical practice.

Reducing unitary coupled cluster circuit depth by classical stochastic amplitude prescreening

Unitary coupled cluster (UCC) approaches are an appealing route to utilizing quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared with the exponential scaling required on classical computers. Current noisy intermediate scale quantum computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the variational quantum eigensolver (VQE) approach. We present a combined classical-quantum approach where a stochastic classical UCC preprocessing step is used to determine the important excitations in the UCC Ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the ${\mathrm{CH}}_{2}, {\mathrm{N}}_{2}$, and ${\mathrm{N}}_{2}{\mathrm{H}}_{2}$ molecules giving submillihartree errors.

Improving the stability of frequency-dependent squeezing with bichromatic control of filter cavity length, alignment, and incident beam pointing

Frequency dependent squeezing is the main upgrade for achieving broadband quantum noise reduction in upcoming observation runs of gravitational wave detectors. The proper frequency dependence of the squeezed quadrature is obtained by reflecting squeezed vacuum from a Fabry-Perot filter cavity detuned by half of its linewidth. However, since the squeezed vacuum contains no classical amplitude, co-propagating auxiliary control beams are required to achieve the filter cavity's length, alignment, and incident beam pointing stability. In our frequency dependent squeezing experiment at the National Astronomical Observatory of Japan, we used a control beam at a harmonic of squeezed vacuum wavelength and found visible detuning variation related to the suspended mirrors angular drift. These variations can degrade interferometer quantum noise reduction. We investigated various mechanisms that can cause the filter cavity detuning variation. The detuning drift is found to be mitigated sufficiently by fixing the incident beam pointing and applying filter cavity automatic alignment. It was also found that there is an optimal position of the beam on the filter cavity mirror that helps to reduce the detuning fluctuations. Here we report a stabilized filter cavity detuning variation of less than 10$\,$Hz compared to the 113$\,$Hz cavity linewidth. Compared to previously published results [Phys. Rev. Lett. 124, 171101 (2020)], such detuning stability would be sufficient to make filter cavity detuning drift induced gravitational wave detector detection range fluctuation reduce from $11\%$ to within $2\%$.

Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G^{4}).

We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G^{4}) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight 2. Using the amplitude-action relation, weobtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.

Fermi-phase-induced interference in the reaction between Cl and vibrationally excited CH3D.

Mode selectivity is a well-established concept in chemical dynamics. A polyatomic molecule possesses multiple vibrational modes and the mechanical couplings between them can result in complicated anharmonic motions that defy a simple oscillatory description. A prototypical example of this is Fermi-coupled vibration, in which an energy-split eigenstate executes coherent nuclear motion that is comprised of the constituent normal modes with distinctive phases. Will this vibrational phase affect chemical reactivity? How can this phase effect be disentangled from more classical amplitude effects? Here, to address these questions, we study the reaction of Cl with a pair of Fermi states of CH3D(v1-I and v1-II). We find that the reactivity ratio of (v1-I)/(v1-II) in forming the CH2D(v = 0) + HCl(v) products deviates significantly from that permitted by the conventional reactivity-borrowing framework. Based on a proposed metric, this discrepancy can only be explained when the scattering interferences mediated by the CH3D vibrational phases are explicitly considered, which expands the concept of vibrational control of chemical reactivity into the quantum regime.

Radiated momentum in the post-Minkowskian worldline approach via reverse unitarity

We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton’s contant G and at all orders in the velocities, using the Effective Field Theory worldline approach. Following [1], we derive the conserved stress-energy tensor linearly coupled to gravity generated by localized sources, at leading and next-to-leading order in G, and from that the classical probability amplitude of graviton emission. The total emitted momentum is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude. We recast this as a two-loop integral that we solve using techniques borrowed from particle physics, such as reverse unitarity, reduction to master integrals by integration-by-parts identities and canonical differential equations. The emitted momentum agrees with recent results obtained by other methods. Our approach provides an alternative way of directly computing radiated observables in the post-Minkowskian expansion without going through the classical limit of scattering amplitudes.

Novel ECG features and machine learning to optimize culprit lesion detection in patients with suspected acute coronary syndrome

BackgroundNovel temporal-spatial features of the 12‑lead ECG can conceptually optimize culprit lesions' detection beyond that of classical ST amplitude measurements. We sought to develop a data-driven approach for ECG feature selection to build a clinically relevant algorithm for real-time detection of culprit lesion. MethodsThis was a prospective observational cohort study of chest pain patients transported by emergency medical services to three tertiary care hospitals in the US. We obtained raw 10-s, 12‑lead ECGs (500 s/s, HeartStart MRx, Philips Healthcare) during prehospital transport and followed patients 30 days after the encounter to adjudicate clinical outcomes. A total of 557 global and lead-specific features of P-QRS-T waveform were harvested from the representative average beats. We used Recursive Feature Elimination and LASSO to identify 35/557, 29/557, and 51/557 most recurrent and important features for LAD, LCX, and RCA culprits, respectively. Using the union of these features, we built a random forest classifier with 10-fold cross-validation to predict the presence or absence of culprit lesions. We compared this model to the performance of a rule-based commercial proprietary software (Philips DXL ECG Algorithm). ResultsOur sample included 2400 patients (age 59 ± 16, 47% female, 41% Black, 10.7% culprit lesions). The area under the ROC curves of our random forest classifier was 0.85 ± 0.03 with sensitivity, specificity, and negative predictive value of 71.1%, 84.7%, and 96.1%. This outperformed the accuracy of the automated interpretation software of 37.2%, 95.6%, and 92.7%, respectively, and corresponded to a net reclassification improvement index of 23.6%. Metrics of ST80; Tpeak-Tend; spatial angle between QRS and T vectors; PCA ratio of STT waveform; T axis; and QRS waveform characteristics played a significant role in this incremental gain in performance. ConclusionsNovel computational features of the 12‑lead ECG can be used to build clinically relevant machine learning-based classifiers to detect culprit lesions, which has important clinical implications.

Gravitational Bremsstrahlung in the post-Minkowskian effective field theory

We study the gravitational radiation emitted during the scattering of two spinless bodies in the post-Minkowskian Effective Field Theory approach. We derive the conserved stress-energy tensor linearly coupled to gravity and the classical probability amplitude of graviton emission at leading and next-to-leading order in the Newton's constant $G$. The amplitude can be expressed in compact form as one-dimensional integrals over a Feynman parameter involving Bessel functions. We use it to recover the leading-order radiated angular momentum expression. Upon expanding it in the relative velocity between the two bodies $v$, we compute the total four-momentum radiated into gravitational waves at leading-order in $G$ and up to an order $v^8$, finding agreement with what was recently computed using scattering amplitude methods. Our results also allow us to investigate the zero frequency limit of the emitted energy spectrum.