Vacuum Polarization Research Articles

Extending Badger's rule. I. The relationship between energy and structure in hydrogen bonds.

We derive a new expression for the strength of a hydrogen bond (VHB) in terms of the elongation of the covalent bond of the donor fragment participating in the hydrogen bond (ΔrHB) and the intermolecular coordinates R (separation between the heavy atoms) and θ (deviation of the hydrogen bond from linearity). The expression includes components describing the covalent D-H bond of the hydrogen bond donor via a Morse potential, the Pauli repulsion, and electrostatic interactions between the constituent fragments using a linear expansion of their dipole moment and a quadratic expansion of their polarizability tensor. We fitted the parameters of the model using abinitio electronic structure results for six hydrogen bonded dimers, namely, NH3-NH3, H2O-H2O, HF-HF, H2O-NH3, HF-H2O, and HF-NH3, and validated its performance for extended parts of their potential energy surfaces, resulting in a mean absolute error ranging from 0.07 to 0.31 kcal/mol. The derived expression describes the energy-structure relationship in terms of a single structural parameter, namely, the elongation of the donor's covalent bond (ΔrHB), and suggests the novel relationship of 8.0 kcal/mol pm-1 (or 0.8 kcal/mol per 0.001Å elongation). This structural parameter is easily obtained from theory and can serve as the single descriptor of the strength of individual hydrogen bonds.

Refinement of Atomic Polarizabilities for a Polarizable Gaussian Multipole Force Field with Simultaneous Considerations of Both Molecular Polarizability Tensors and In-Solution Electrostatic Potentials.

Atomic polarizabilities are considered to be fundamental parameters in polarizable molecular mechanical force fields that play pivotal roles in determining model transferability across different electrostatic environments. In an earlier work, the atomic polarizabilities were obtained by fitting them to the B3LYP/aug-cc-pvtz molecular polarizability tensors of mainly small molecules. Taking advantage of the recent PCMRESPPOL method, we refine the atomic polarizabilities for condensed-phase simulations using a polarizable Gaussian Multipole (pGM) force field. Departing from earlier works, in this work, we incorporated polarizability tensors of a large number of dimers and electrostatic potentials (ESPs) in multiple solvents. We calculated 1565 × 4 ESPs of small molecule monomers and dimers of noble gas and small molecules and 4742 × 4 ESPs of small molecule dimers in four solvents (diethyl ether, ε = 4.24, dichloroethane, ε = 10.13, acetone, ε = 20.49, and water, ε = 78.36). For the gas-phase polarizability tensors, we supplemented the molecule set that was used in our earlier work by adding both the 4252 monomer and dimer sets studied by Shaw and co-workers and the 7211 small molecule monomers listed in the QM7b database to a combined total of 13,523 molecular polarizability tensors of monomers and dimers. The QM7b polarizability set was obtained from quantum-machine.org and was calculated at the LR-CCSD/d-aug-cc-pVDZ level of theory. All other polarizability tensors and all ESPs were calculated at the ωB97X-D/aug-cc-pVTZ level of theory. The atomic polarizabilities were developed using all polarizability tensors and the 1565 × 4 ESPs of small molecule monomers and were then assessed by comparing them to the 4742 × 4 ab initio ESPs of small molecule dimers. The predicted dimer ESPs had an average relative root-mean-square error (RRMSE) of 9.30%, which was only slightly larger than the average fitting RRMSE of 9.15% of the monomer ESPs. The transferability of the polarizability set was further evaluated by comparing the ESPs calculated using parameters developed in another dielectric environment for both tetrapeptide and DES monomer data sets. It was observed that the polarizabilities of this work retained or slightly improved the transferability over the one discussed in earlier work even though the number of parameters in the present set is about half of that in the earlier set. Excluding the gas-phase data, for the DES monomer set, the average transfer RRMSEs were 16.25% and 10.83% for pGM-ind and pGM-perm methods, respectively, comparable to the average fitting RRMSEs of 16.03% and 10.54%; for tetrapeptides, the average transfer RRMSEs were 5.62% and 3.95% for pGM-ind and pGM-perm methods, respectively, slightly larger than 5.41% and 3.61% of the fitting RRMSEs. Therefore, we conclude that the pGM methods with updated polarizabilities achieved remarkable transferability from monomer to dimer and from one solvent to another.

Polarization tensor in spacetime of three dimensions and a quantum field-theoretical description of the nonequilibrium Casimir force in graphene systems

Polarization tensor in spacetime of three dimensions and a quantum field-theoretical description of the nonequilibrium Casimir force in graphene systems

Impact of background field localization on vacuum polarization effects

Impact of background field localization on vacuum polarization effects

Measurement of the tensor analyzing power T20 for incoherent π− photoproduction on a deuteron above the first resonance region

New measurements of the T20 component of tensor analyzing power in the reaction γd→ppπ− for photon energies 400−700 MeV are presented. The experiment was carried out on an internal tensor-polarized gas deuterium target of the VEPP-3 electron storage ring in 2023 with the use of tagged quasi-real photons and two-proton coincidence. For determination of T20, the asymmetry caused by a change of the sign of the tensor polarization of the deuteron target was measured. The new data are compared with the results of theoretical calculations based on the quasi-free approximation including πN and NN rescattering effects.

Propagation of surface waves on the vacuum-quantum plasma interface with vacuum polarization effects

Propagation of surface waves on the vacuum-quantum plasma interface with vacuum polarization effects

Plasmonic resonances in the chain of spheroidal metallic nanoparticles on the dielectric substrate

The optical and plasmonic properties of the chains of prolate metallic spheroids of the dielectric substrate are studied in the work using the local field approximation. The case when spheroids are arranged in such a way that their major semi-axis belongs to the substrate plane is considered. The relations for the transverse component of the chain polarizability tensor and the frequency of the transverse chain resonance are obtained. The comparative analysis of spectral shifts of the maxima of the imaginary part of the transverse chain polarizability and the polarizability of isolated prolate spheroid is performed. The influence of the variation of the material of particles in the chain and the dielectric environment on the location of the maxima of the imaginary part of the transverse polarizability is studied. The limits of applicability of the theory proposed in the paper are established.

The polarization tensor approach for Casimir effect

The polarization tensor approach for Casimir effect

Vacuum Polarization Energy of a Proca Soliton

We study an extended Proca model with one scalar field and one massive vector field in one space dimension and one time dimension. We construct the soliton solution and subsequently compute the vacuum polarization energy (VPE), which is the leading quantum correction to the classical energy of the soliton. For this calculation, we adopt the spectral methods approach, which heavily relies on the analytic properties of the Jost function. This function is extracted from the interaction of the quantum fluctuations with a background potential generated by the soliton. Particularly, we explore eventual non-analytical components that may be induced by mass gaps and the unconventional normalization for the longitudinal component of the vector field fluctuations. By numerical simulation, we verify that these obstacles do not actually arise and that the real and imaginary momentum formulations of the VPE yield equal results. The Born approximation to the The Jost function is crucial when implementing standard renormalization conditions. In this context, we solve problems arising from the Born approximation being imaginary for real momenta associated with energies in the mass gap.

A Study of the Structure of an Anion Exchange Resin with a Quaternary Ammonium Functional Group by Using Infrared Spectroscopy and DFT Calculations.

The large numbers of ion exchange resins used in various industries (food, pharmaceutitics, mining, hydrometallurgy), and especially in water treatment, are based on cross-linked polystyrene and divinylbenzene copolymers with functional groups capable of ion exchange. Their advantage, which makes them environmentally friendly, is the possibility of their regeneration and reuse. Taking into account the wide application of these materials, styrene-divinylbenzene resin with a quaternary ammonium functional group, Amberlite®IRA402, was characterized using a well-known and widely used method, FT-IR spectroscopy. As the infrared spectrum of the tested ion exchange resin was rich in bands, its detailed assignment was supported by quantum chemical calculations (DFT/B3LYP/6-31g** and DFT/PCM/B3LYP/6-31g**). Using appropriate 3D models of the resin structure, the optimization of geometry, the infrared spectrum and atomic charges from an atomic polar tensor (APT) were calculated. A detailed description of the infrared spectrum of Amberlite®IRA402 resin (Cl- form) in the spectral range of 4000-700 cm-1 was performed for the first time. The charge distribution on individual fragments of the resin structure in aqueous solution was also calculated for the first time. These studies will certainly allow for a better understanding of the styrene-divinylbenzene resin interaction in various processes with other substances, particularly in sorption processes.

Skin‐Inspired in‐Sensor Encoding of Strain Vector Using Tunable Quantum Geometry

AbstractHuman skin provides crucial tactile feedback, allowing to skillfully perceive various objects by sensing and encoding complex deformations through multiple parameters in each tactile receptor. However, replicating this high‐dimensional tactile perception with conventional materials' electronic properties remains a daunting challenge. Here, a skin‐inspired method is presented to encode strain vectors directly within a sensor. This is achieved by leveraging the strain‐tunable quantum properties of electronic bands in the van der Waals topological semimetal Td‐WTe2. Robust and independent responses are observed from the second‐order and third‐order nonlinear Hall signals in Td‐WTe2 when subjected to variations in both the magnitude and direction of strain. Through rigorous temperature‐dependent measurements and scaling law analysis, it is established that these strain responses primarily stem from quantum geometry‐related phenomena, including the Berry curvature and Berry‐connection polarizability tensor. Furthermore, the study demonstrates that strain‐dependent nonlinear Hall signals can efficiently encode high‐dimensional strain information using a single device. This capability enables accurate and comprehensive sensing of complex strain patterns in the embossed character “NJU”. The findings highlight the promising application of topological quantum materials in advancing next‐generation, bio‐inspired flexible electronics.

Measurement of the e+e−→π+π−π0 cross section in the energy range 0.62–3.50 GeV at Belle II

We report a measurement of the e+e−→π+π−π0 cross section in the energy range from 0.62 to 3.50 GeV using an initial-state radiation technique. We use an e+e− data sample corresponding to 191 fb−1 of integrated luminosity, collected at a center-of-mass energy at or near the ϒ(4S) resonance with the Belle II detector at the SuperKEKB collider. Signal yields are extracted by fitting the two-photon mass distribution in e+e−→π+π−π0γ events, which involve a π0→γγ decay and an energetic photon radiated from the initial state. Signal efficiency corrections with an accuracy of 1.6% are obtained from several control data samples. The uncertainty on the cross section at the ω and ϕ resonances is dominated by the systematic uncertainty of 2.2%. The resulting cross sections in the 0.62–1.80 GeV energy range yield aμ3π=[48.91±0.23(stat)±1.07(syst)]×10−10 for the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. This result differs by 2.5 standard deviations from the most precise current determination. Published by the American Physical Society 2024

Whispers from the quantum core: the ringdown of semiclassical stars

This investigation delves into the ringdown signals produced by semiclassical stars, which are ultra-compact, regular solutions of the Einstein equations incorporating stress-energy contributions from quantum vacuum polarization. These stars exhibit an approximately Schwarzschild exterior and an interior composed of a constant-density classical fluid and a cloud of vacuum polarization. By adjusting their compactness and density, we can alter the internal structure of these stars without modifying the exterior. This adaptability enables us to examine the sensitivity of the ringdown signal to the innermost regions of the emitting object and to compare it with similar geometries that differ substantially only at the core. Our results indicate that echo signals are intrinsically linked to the presence of stable light rings and can be very sensitive to the internal structure of the emitting object. This point was previously overlooked, either due to the imposition of reflective boundary conditions at the stellar surface or due to the assumption of low curvature interior geometries. Specifically, for stellar-sized semiclassical stars, we find that the interior travel time is sufficiently prolonged to render the echoes effectively unobservable. These findings underscore the potential efficacy of ultra-compact objects as black hole mimickers and emphasize that any phenomenological constraints on such objects necessitate a detailed understanding of their specific properties and core structure.

[formula omitted], QCD power corrections and αs from e+e− → Hadrons

In this talk, I review the results obtained recently in Ref. [1]. First, we estimate the LO hadronic vacuum polarization contribution to the muon and τ anomalous magnetic moments to be: aμ|l.ohvp=(7036.5±38.9)×10−11, aτ|l.ohvp=(3494.8±24.7)×10−9 (see Table 1) leading to: Δaμ≡aμexp−aμSM=(143±42th±22exp)×10−11 which is about 3σ discrepancy between the SM predictions and experiment. One also finds: α(5)(MZ)|had=(2766.3±4.5)×10−5. Second, we estimate the QCD power corrections up to dimension 20 from the ratio of Laplace sum rule and from τ-like decay high moments (see Table 3). We do not observe any exponential growth of their size which may not favour a duality violation of the spectral function. We obtain 〈αsG2〉=(7.8±3.5)×10−2GeV4 in agreement with the more precise one from heavy quark sum rules, while ραs〈ψ¯ψ〉2=(5.98±0.64)×10−4GeV6 confirms a violation of the four-quark condensate factorization by a factor ρ≃6. Third, using the previous values of the condensates, we re-extract αs from the lowest τ-decay Braaten-SN-Pich (BNP) moment and find to order αs4:αs(Mτ)=0.3081(86)[resp.0.3260(79)]⟶∘αs(MZ)=0.1170(7)[resp.0.1192(7)] for Fixed Order (FO) [resp. Contour Improved (CI)] PT series. We also show that the contributions beyond the Shifman-Vainshtein-Zakharov (SVZ)-expansion are negligible.

Vacuum polarization effects in impulsive fields

Photons impinging on strong electromagnetic fields can change both momentum and helicity state, due to quantum vacuum polarization. We investigate these effects in the collision of photons with impulsive PP-waves, which describe e.g. the fields of ultraboosted charge distributions. We connect our results to vacuum birefringence and quantum reflection in both QED and SUSY QED. We also compare with helicity flip in plane wave backgrounds, exploring how and when known tree-level relations, relating amplitudes in PP-waves and in plane waves, extend to one-loop corrections. Published by the American Physical Society 2024

A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra.

The use of machine learning (ML) algorithms in molecular simulations has become commonplace in recent years. There now exists, for instance, a multitude of ML force field algorithms that have enabled simulations approaching ab initio level accuracy at time scales and system sizes that significantly exceed what is otherwise possible with traditional methods. Far fewer algorithms exist for predicting rotationally equivariant, tensorial properties such as the electric polarizability. Here, we introduce a kernel ridge regression algorithm for machine learning of the polarizability tensor. This algorithm is based on the bond polarizability model and allows prediction of the tensor components at the cost similar to that of scalar quantities. We subsequently show the utility of this algorithm by simulating gas phase Raman spectra of biphenyl and malonaldehyde using classical molecular dynamics simulations of these systems performed with the recently developed MACE-OFF23 potential. The calculated spectra are shown to agree very well with the experiments and thus confirm the expediency of our algorithm as well as the accuracy of the used force field. More generally, this work demonstrates the potential of physics-informed approaches to yield simple yet effective machine learning algorithms for molecular properties.

Electromagnetic Debye mass within Gribov–Zwanziger action

Abstract In the present study we have investigated the electromagnetic Debye mass by computing the static limit of the temporal component of the one-loop photon polarization tensor involving effective quarks in the loop. These effective quarks have been considered within the Gribov–Zwanziger action, thereby incorporating the necessary non-perturbative effects. As an academic exercise, we have also shown one of the applications of this Gribov modified Debye mass by using it to evaluate the real and imaginary parts of the heavy quark potential in a Quantum Electrodynamics (QED) system. This computation of the electromagnetic Debye mass and the corresponding estimations of the heavy quark potential can be seen as stepping stones in the direction of further practical Quantum Chromodynamics (QCD) calculations in the non perturbative domain.

A discrete sine–cosine based method for the elasticity of heterogeneous materials with arbitrary boundary conditions

The aim of this article is to extend Moulinec and Suquet (1998)’s FFT-based method for heterogeneous elasticity to non-periodic Dirichlet/Neumann boundary conditions. The method is based on a decomposition of the displacement into a known term verifying the boundary conditions and a fluctuation term, with no contribution on the boundary, and described by appropriate sine–cosine series. A modified auxiliary problem involving a polarization tensor is solved within a Galerkin-based method, using an approximation space spanned by sine–cosine series. The elementary integrals emerging from the weak formulation of the equilibrium are approximated by discrete sine–cosine transforms, which makes the method relying on the numerical complexity of Fourier transforms. The method is finally assessed in several problems including kinematic uniform, static uniform and arbitrary Dirichlet/Neumann boundary conditions.

Efficient computation of magnetic polarizability tensor spectral signatures for object characterisation in metal detection

PurposeMagnetic polarizability tensors (MPTs) provide an economical characterisation of conducting magnetic metallic objects and their spectral signature can aid in the solution of metal detection inverse problems, such as scrap metal sorting, searching for unexploded ordnance in areas of former conflict and security screening at event venues and transport hubs. In this work, the authors aim to discuss methods for efficiently building large dictionaries for classification approaches.Design/methodology/approachPrevious work has established explicit formulae for MPT coefficients, underpinned by a rigorous mathematical theory. To assist with the efficient computation of MPTs at differing parameters and objects of interest, this work applies new observations about the way the MPT coefficients can be computed. Furthermore, the authors discuss discretisation strategies for hp-finite elements on meshes of unstructured tetrahedra combined with prismatic boundary layer elements for resolving thin skin depths and using an adaptive proper orthogonal decomposition (POD) reduced-order modelling methodology to accelerate computations for varying parameters.FindingsThe success of the proposed methodologies is demonstrated using a series of examples. A significant reduction in computational effort is observed across all examples. The authors identify and recommend a simple discretisation strategy and improved accuracy is obtained using adaptive POD.Originality/valueThe authors present novel computations, timings and error certificates of MPT characterisations of realistic objects made of magnetic materials. A novel postprocessing implementation is introduced and an adaptive POD algorithm is demonstrated.

Effective flexoelectric properties of inclusion-based composites based on strain gradient theory and homogenization technique

This study focuses on enhancing flexoelectricity in composites and develops a new micromechanical analytical framework to determine the effective electromechanical properties of inclusion-based flexoelectric composites within the context of SGE. Initially, we specialize in studying isotropic materials and derive the governing Navier equations for the problem. Subsequently, we streamline these differential equations by introducing a Laplacian-type gradient state variable, departing from higher-order gradient-enrichment treatments. The study employs Green’s functions and stress polarization tensors for spherical inhomogeneities, deriving homogenized material properties through volumetric averages of microscopic properties weighted by displacement localization operators. The analytical scheme’s relevance is validated against results from reference models and experimental data. Effective composite properties are evaluated using numerical methods, with an emphasis on assessing the impact of reinforcement on these properties. Our findings lay the foundation for developing a micromechanical method to predict the electromechanical behavior of composites. Specifically, we demonstrate the efficacy of our proposed theory by deriving effective flexoelectric properties of particulate composites.