Order Perturbation Research Articles

Reaching the precision limit with tensor-based wavefront shaping

Perturbations in complex media, due to their own dynamical evolution or to external effects, are often seen as detrimental. Therefore, a common strategy, especially for telecommunication and imaging applications, is to limit the sensitivity to those perturbations in order to avoid them. Here, instead, we consider enhancing the interaction between light and perturbations to produce the largest change in the output intensity distribution. Our work hinges on the use of tensor-based techniques, presently at the forefront of machine learning explorations, to study intensity-based measurements where its quadratic relationship to the field prevents the use of standard matrix methods. With this tensor-based framework, we can identify the maximum-information intensity channel which maximizes the change in its output intensity distribution and the Fisher information encoded in it about a given perturbation. We further demonstrate experimentally its superiority for robust and precise sensing applications. Additionally, we derive the appropriate strategy to reach the precision limit for intensity-based measurements, leading to an increase in Fisher information by more than four orders of magnitude compared to the mean for random wavefronts when measured with the pixels of a camera.

Second order perturbation theory of two-scale systems in fluid dynamics

In the present paper we study fast-slow systems of coupled equations from fluid dynamics, where the fast component is perturbed by additive noise. We prove that, under a suitable limit of infinite separation of scales, the slow component of the system converges in law to a solution of the initial equation perturbed by transport noise, and subject to the influence of an additional Itô–Stokes drift. The resulting limit equation is very similar to turbulent models derived heuristically. Our results apply to the Navier–Stokes equations in dimensions d=2,3 ; the surface quasi-geostrophic equations in dimension d=2 ; and the primitive equations in dimensions d=2,3 .

Inhibition of human epidermal growth factor receptor-2 protein by some alkaloid inhibitors

BackgroundHuman Epidermal Growth Factor Receptor-2 (HER2), a transmembrane tyrosine kinase receptor, has been associated with several types of cancer, including breast, lung, ovarian, etc. Therefore, this receptor is targeted by a variety of therapeutic approaches for cancer treatments. The alkaloid and lead compounds are among the selective and potent HER2 inhibitors that have been reported so far. MethodsThe present work involves molecular docking, molecular dynamics (MD) simulations, and density functional theory (DFT) calculations on alkaloid and lead compounds as HER2 inhibitors. Significant findingsThe docking results expressed that the alkaloids mainly interacted with Cys805, Val734, and Ala751 residues of HER2 protein. The MD simulation outcomes represented that all the complexes have adequate dynamic stability and flexibility based on the root mean square deviation, root mean square fluctuation, and radius of gyration. Furthermore, it is found that the strongest HER2 − ligand interaction belongs to the nocamycin I (NOI, ΔGbind = -12.84 kcal mol−1) molecule. The DFT calculations showed that electron density and the second − order perturbation stabilization energy values for HER2 − NOI interactions are higher than the other complexes. The molecular docking, MD simulation, and DFT calculation results are all in agreement and complementary. It is expected that the results obtained here can present very helpful information for the design of efficacious inhibitors for the treatment of HER2 − related cancer disease.

Observation and differential cross section measurement of neutral current DIS events with an empty hemisphere in the Breit frame

The Breit frame provides a natural frame to analyze lepton–proton scattering events. In this reference frame, the parton model hard interactions between a quark and an exchanged boson defines the coordinate system such that the struck quark is back-scattered along the virtual photon momentum direction. In Quantum Chromodynamics (QCD), higher order perturbative or non-perturbative effects can change this picture drastically. As Bjorken-x decreases below one half, a rather peculiar event signature is predicted with increasing probability, where no radiation is present in one of the two Breit-frame hemispheres and all emissions are to be found in the other hemisphere. At higher orders in αs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _{s}$$\\end{document} or in the presence of soft QCD effects, predictions of the rate of these events are far from trivial, and that motivates measurements with real data. We report on the first observation of the empty current hemisphere events in electron–proton collisions at the HERA collider using data recorded with the H1 detector at a center-of-mass energy of 319 GeV. The fraction of inclusive neutral-current DIS events with an empty hemisphere is found to be 0.0112±3.9%stat±4.5%syst±1.6%mod\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.0112 \\pm 3.9\\%_\ ext {stat} \\pm 4.5\\%_{\ ext {syst}} \\pm 1.6\\%_{\ ext {mod}}$$\\end{document} in the selected kinematic region of 150<Q2<1500GeV2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$150<Q^{2} <1500\\, \ extrm{GeV}^2 $$\\end{document} and inelasticity 0.14<y<0.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.14<y<0.7$$\\end{document}. The data sample corresponds to an integrated luminosity of 351.1 pb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{-1}$$\\end{document}, sufficient to enable differential cross section measurements of these events. The results show an enhanced discriminating power at lower Bjorken-x among different Monte Carlo event generator predictions.

3- and 6-degree-of-freedom analysis of the Magellan aerobraking experiment and planar aerobraking at Venus

The first non-Earth aerobraking experiment occurred in 1993 as part of the Magellan satellite's mission to Venus. Magellan reduced its orbit from elliptical to nearly circular over a span of 70 Earth days by leveraging the non-conservative force of aerodynamic drag to reduce its orbital energy via transiting the upper region of Venus' sensible atmosphere. First tested with the Hiten probe in the Earth-Moon system in 1991, the subsequent Magellan experiment helped prove the viability of aerobraking for planetary missions and paved the way for its implementation in Mars missions starting in the late 1990s and the 2014 Venus Express mission. This paper, for the first time in literature, investigates the Magellan aerobraking experiment from the perspective of both 3- and 6-degree-of-freedom analysis. Multiple atmospheric density models are considered, as well as J4 gravitational perturbations in order to understand the complexity and sensitivity of numerous aerobraking maneuvers in the thick Venusian atmosphere. Alternative satellites are also studied to ascertain their capability of maintaining the Magellan aerobraking flight profile. So as to examine a wide range of vehicle mass and drag reference area, the Hubble Space Telescope (HST) and Hiten satellites are modeled and their aerobraking performance analyzed for the hypothetical case of Venus orbital operations. When reconstructing the historical Magellan aerobraking maneuvers, 3DOF and 6DOF analysis yielded minimal trajectory deviation with the Magellan and Hiten models, while more significant deviation was experienced with the larger HST model. Both 3DOF and 6DOF analyses also reveal the sensitivity of the atmospheric density model and indicate a higher fidelity gravity model is necessary for Venusian aerobraking modeling, planning, and analysis.

Non-adiabatic dynamics of photoexcited cyclobutanone: Predicting structural measurements from trajectory surface hopping with XMS-CASPT2 simulations.

Over the years, theoretical calculations and scalable computer simulations have complemented ultrafast experiments, as they offer the advantage of overcoming experimental restrictions and having access to the whole dynamics. This synergy between theory and experiment promises to yield a deeper understanding of photochemical processes, offering valuable insights into the behavior of complex systems at the molecular level. However, the ability of theoretical models to predict ultrafast experimental outcomes has remained largely unexplored. In this work, we aim to predict the electron diffraction signals of an upcoming ultrafast photochemical experiment using high-level electronic structure calculations and non-adiabatic dynamics simulations. In particular, we perform trajectory surface hopping with extended multi-state complete active space with second order perturbation simulations for understanding the photodissociation of cyclobutanone (CB) upon excitation at 200nm. Spin-orbit couplings are considered for investigating the role of triplet states. Our simulations capture the bond cleavage after ultrafast relaxation from the 3s Rydberg state, leading to the formation of the previously observed primary photoproducts: CO + cyclopropane/propene (C3 products), ketene, and ethene (C2 products). The ratio of the C3:C2 products is found to be about 1:1. Within 700fs, the majority of trajectories transition to their electronic ground state, with a small fraction conserving the initial cyclobutanone ring structure. We found a minimal influence of triplet states during the early stages of the dynamics, with their significance increasing at later times. We simulate MeV-ultrafast electron diffraction (UED) patterns from our trajectory results, linking the observed features with specific photoproducts and the underlying structural dynamics. Our analysis reveals highly intense features in the UED signals corresponding to the photochemical processes of CB. These features offer valuable insights into the experimental monitoring of ring opening dynamics and the formation of C3 and C2 photoproducts.

Domination of nonlinear semigroups generated by regular, local Dirichlet forms

AbstractIn this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. As a main result, we show that the semigroup generated by a local, regular, nonlinear Dirichlet form $${\mathcal {E}}$$ E dominates the semigroup generated by another local functional $${\mathcal {F}}$$ F if, and only if, $${\mathcal {F}}$$ F is a specific zero order perturbation of $${\mathcal {E}}$$ E . On the way, we prove a nonlinear version of the Riesz–Markov representation theorem, we define an abstract boundary of a topological measure space, and apply the notion of nonlinear capacity. The main result helps to classify the perturbations that lie between Neumann and Dirichlet boundary conditions.

Quadratic perturbations of the Schwarzschild black hole: the algebraically special sector

We investigate quadratic algebraically special perturbations (ASPs) of the Schwarzschild black hole. Their dynamics are derived from the expansion up to second order in perturbation of the most general algebraically special twisting vacuum solution of general relativity. Following this strategy, we present analytical expressions for the axial-axial, polar-polar and polar-axial source terms entering in the dynamical equations. We show that these complicated inhomogeneous equations can be solved analytically and we present explicit expressions for the profiles of the quadratic ASPs. As expected, they exhibit exponential growth both at the past and future horizons even in the non-linear regime. We further use this result to analyze the quadratic zero modes and their interpretation in terms of quadratic corrections to mass and spin of the Schwarzschild black hole. The present work provides a direct extension beyond the linear regime of the original work by Couch and Newman.

Analytical perturbations of relativistic images in Kerr space-time

Light rays passing very close to black holes may wind several times before escaping. For any given electromagnetic source around the black hole, a distant observer would thus observe two infinite sequences of images on either side of the black hole. These images are generated by light rays performing an increasing numbers of loops. The strong deflection limit provides a simple analytic formalism to describe such higher order images for spherically symmetric metrics, while for axially symmetric black holes one typically resorts to numerical approaches. Here we present the leading order perturbation to higher order images when the black hole spin is turned on. We show that the images slide around the black hole shadow as an effect of space-time dragging. We derive analytical formulae for their shifts and the perturbation of their time delays. We also discuss how such simple analytical formulae for images by Kerr black holes can be of great help in many applications.

Instabilities and self–organization in spatiotemporal epidemic dynamics driven by nonlinearity and noise

Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID–19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread–anchored in physical considerations–lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing–type instabilities, and the concomitant emergence of steady–state patterns under the interplay between three critical model parameters–the saturation parameter, the noise intensity, and the transmission rate. Employing a second–order perturbation analysis to investigate stability, we uncover both diffusion–driven and noise–induced instabilities and corresponding self–organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.

Metric perturbations in noncommutative gravity

We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a Drinfeld twist. The final result of the construction is a general formalism for obtaining NC corrections to the classical theory of gravity for a wide class of deformations and a general background. This also includes a novel proposal for noncommutative Einstein manifold. Moreover, the general construction is applied to the case of a linearized gravitational perturbation theory to describe a NC deformation of the metric perturbations. We specifically present an example for the Schwarzschild background and axial perturbations, which gives rise to a generalization of the work by Regge and Wheeler. All calculations are performed up to first order in perturbation of the metric and noncommutativity parameter. The main result is the noncommutative Regge-Wheeler potential. Finally, we comment on some differences in properties between the Regge-Wheeler potential and its noncommutative counterpart.

Quantum circuit for high order perturbation theory corrections

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which has led to a wide variety of applications. Over the past decades, advances in quantum computing provide opportunities for alternatives to classical methods. Recently, a general quantum circuit estimating the low order PT corrections has been proposed. In this article, we revisit the quantum circuits for PT calculations, and develop the methods for higher order PT corrections of eigenenergy, especially the 3rd and 4th order corrections. We present the feasible quantum circuit to estimate each term in these PT corrections. There are two the fundamental operations in the proposed circuit. One approximates the perturbation terms, the other approximates the inverse of unperturbed energy difference. The proposed method can be generalized to higher order PT corrections.

The direct role of nuclear motion in spin-orbit coupling in strongly correlated spin systems.

The interaction between the magnetic moment of an electron and the magnetic field generated by a moving charge is one component of the spin-orbit interaction. The nuclei in a molecule or solid are charged, are generally in vibrational motion, and so contribute to this interaction, but the direct coupling between nuclear momentum and electron spin is normally ignored in discussions of spin-forbidden phenomena such as transitions between states of different spin, even when the nuclei are recognized as playing a fundamental role (spin-vibronic coupling). Here, we investigate the spin-orbit interaction in a Heisenberg model interacting with vibrating point charges representing nearby bridging ligands. To reach the model, we apply second order perturbation theory to the Hubbard model with the spin-orbit interaction. In contrast to the other components of the spin-orbit interaction, the part that directly couples the momentum of the charge and electron spin appears at first order as an effective magnetic field at each site. We find that the inclusion of this nuclear-motion induced spin-orbit coupling can increase the rate of otherwise spin-forbidden transitions between different spin states of the Heisenberg model by many orders of magnitude. This overlooked interaction may, therefore, play a significant role in spin-forbidden phenomena such as spin relaxation in coupled spin-qubits.

The photodissociation dynamics and ultrafast electron diffraction image of cyclobutanone from the surface hopping dynamics simulation

The comprehension of nonadiabatic dynamics in polyatomic systems relies heavily on the simultaneous advancements in theoretical and experimental domains. The gas-phase ultrafast electron diffraction (UED) technique has attracted significant attention as a unique tool for monitoring photochemical and photophysical processes at the all-atomic level with high temporal and spatial resolutions. In this work, we simulate the UED spectra of cyclobutanone using the trajectory surface hopping method at the extended multi-state complete active space second order perturbation theory (XMS-CASPT2) level and thereby predict the results of the upcoming UED experiments in the Stanford Linear Accelerator Laboratory. The simulated results demonstrate that a few pathways, including the C2 and C3 dissociation channels, as well as the ring opening channel, play important roles in the nonadiabatic reactions of cyclobutanone. We demonstrate that the simulated UED signal can be directly interpreted in terms of atomic motions, which provides a unique way of monitoring the evolution of the molecular structure in real time. Our work not only provides numerical data that help to determine the accuracy of the well-known surface hopping dynamics at the high XMS-CASPT2 electronic-structure level but also facilitates the understanding of the microscopic mechanisms of the photoinduced reactions in cyclobutanone.

Inverse scattering problems of the biharmonic Schrödinger operator with a first order perturbation

Inverse scattering problems of the biharmonic Schrödinger operator with a first order perturbation

Efficient Implementation of the Binary Common Neighbor Analysis for Platinum-Based Intermetallics

The common neighbor analysis (CNA) for binary systems is a powerful method used to identify chemical ordering in intermetallics by unique indices. The capability of binary CNA, however, is largely restricted by the availability of indices for various ordered phases. In this study, CNA indices of 11 ordered phases derived from a face-centered cubic structure were introduced on a case-by-case basis. These phases, common in intermetallics containing platinum-group metals, include C11b, MoPt2, C6, B11, AgZr, A2B2[111], A2B2[113], Pt3Tc, A3B[011], A3B[111], and A3B[113]. The chemical order in static chemical perturbation, dynamic phase competition, and experimentally reconstructed nanophase alloys were identified using binary CNA. The results indicated that the proposed version of binary CNA exhibited significantly higher accuracy and robustness compared to the short-range order, polyhedral template matching, and the original binary CNA method. Benchmarked against available methods, the formation, decomposition, and competition of specifically ordered phases in bulks and nanoalloys were well reflected by present CNA, highlighting its potential as a robust and widely adopted tool for deciphering chemical ordering at the atomic level.

Scalar perturbations in nonsingular universes from interacting vacuum

In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange between a nonrelativistic fluid and a vacuum component. In both scenarios it can be shown that closed models may furnish nonsingular orbits of physical interest in phase space once a decelerated past era is connected to a graceful exit to late-time acceleration. Regarding such configurations as background spacetimes we introduce scalar perturbations in order to examine the stability of these models in a high energy domain. We explicitly show that the vacuum perturbation is not an independent variable and diverges as dynamics approaches the bounce. This feature assigns a rather unstable signature to the dynamics making the choices for the energy transfer ill defined at least for nonsingular configurations at the bounce scale.

Modeling the BAO feature in bispectrum

Abstract We investigate how well a simple leading order perturbation theory model of the bispectrum can fit the BAO feature in the measured bispectrum monopole of galaxies. Previous works showed that perturbative models of the galaxy bispectrum start failing at the wavenumbers of k ∼ 0.1h Mpc−1. We show that when the BAO feature in the bispectrum is separated it can be successfully modeled up to much higher wavenumbers. We validate our modeling on GLAM simulations that were run with and without the BAO feature in the initial conditions. We also quantify the amount of systematic error due to BAO template being offset from the true cosmology. We find that the systematic errors do not exceed 0.3 per cent for reasonable deviations of up to 3 per cent from the true value of the sound horizon.

Gauge invariance, gauge field quantization, and renormalization in autoregularization

Autoregularization, a new divergence-free framework for calculating scattering amplitudes, uses a Lorentz-invariant scale harvested from the kinematics of a scattering process to regularize the amplitude of the process [N. Prabhu, .]. Preliminary validation studies show that autoregularization’s predictions are in good agreement with experimental data—across several scattering processes and a wide range of energy scales. Further, tree-level calculation of the vacuum energy density of the free fields in the Standard Model, using autoregularization, is shown to yield a value that is smaller than the current estimate of the cosmic critical density. In this paper, we prove that the scattering amplitudes in QED, calculated using autoregularization, are gauge invariant. Our proof, which is valid both for autoregularization and current theory, is stronger in that it shows the amplitude of every Feynman diagram is gauge invariant in contrast to previous proofs, which establish gauge invariance only for sum of amplitudes of Feynman diagrams of a process. Next, we show that—unlike in the standard quantization framework, which requires modification of both the quantization framework itself as well as the Lagrangian in order to quantize gauge fields in covariant gauge—in autoregularization the gauge field in QED can be quantized, in covariant gauge, without modifying the standard quantization procedure or the Lagrangian and without introducing the ghost field. Finally, we illustrate renormalization based on autoregularization up to 1-loop in φ4 theory. Since perturbative corrections are finite in autoregularization, the counterterms are not designed to remove divergences but to implement renormalization prescriptions at every order of perturbation. We also derive the renormalization group equation (RGE). Unlike in some regularization schemes (such as dimensional regularization), in which the physical meaning of the fictitious scale introduced by regularization is unclear, in autoregularization the scale in RGE has a transparent physical meaning—it is the Lorentz-invariant kinematic scale of the scattering process of interest. The increasing simplifications resulting within autoregularization and the agreement between its predictions and experimental data, together with the underlying thermodynamic argument, which shows that the framework is essential for a complete description of quantum fields, all converge to suggest that autoregularization provides the proper framework for the description of quantum fields. Published by the American Physical Society 2024

Analyzing coherent and incoherent optical susceptibilities in four-wave mixing: stochasticity, symmetry, and intramolecular coupling

The nonlinear optical susceptibilities are analyzed in their optical propagation length considering the incoherent-coherent contributions with the dependence on the relaxation times. In addition, some symmetry properties of the Four-Wave mixing (FWM) signal concerning the frequency detuning exchange are used in the study, without restricting ourselves to the maxima of population oscillations. We analyze the behaviors of these optical responses in a vibronic coupling scheme using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in position and nuclear energies. The solvent effect in our model is treated through the natural Bohr frequency shift to a time-dependent function, with explicit manifestations in its comparison as if the upper state were broadened. Our results for both FWM signal propagation and nonlinear optical susceptibilities are sensitive to the intramolecular coupling parameters, solvent stochasticity, and perturbation order for the treatment of the weak probe beam. The consideration of a second-order probe beam in FWM would not represent a significant contribution to the predicted results, since its percentage contribution is negligible within the model development framework; however, this contribution becomes important when increasing the ratio between longitudinal and transverse relaxation times.