Arbitrary Charge Research Articles

Building bases of loop integrands

We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of ‘power-counting’ for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all ‘leading-(transcendental-)weight’ contributions of any four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent all scattering amplitude integrands in the theory — for generic helicities and arbitrary multiplicity.

Anomalous Hall transport in tilted multi-Weyl semimetals

We study the effect of a perpendicular magnetic field B on a multinode Weyl semimetal (mWSM) of arbitrary integer monopole charge n, with the two Weyl multinodes separated in k-space. Besides type-I mWSMs, there exist type-II mWSMs which are characterized by the tilted minimal dispersion for low-energy excitations; the Weyl points in type-II mWSMs are still protected crossings but appear at the contact of the electron and hole pockets, after the Lifshitz transition. We find that the presence of a perpendicular magnetic field quantizes the occupation pockets due to the presence of Fermi tubes. In this theory, the Hilbert space is spanned by a set of n chiral degenerate ground states, and a countably infinite number of particle-hole symmetric Landau levels (LLs). We calculate the Hall conductivity for the tilt-symmetric case of type-I mWSM using the Kubo formula, in the zero-frequency (DC) limit, and recover the well-known vacuum contribution. We compute the Fermi surface corrections and show that the expression generalizes from the formula for elementary (n = 1) type-I WSMs. We derive an expression for the type-II mWSM Hall conductivity, which is bounded by a LL cutoff introduced on physical grounds. Interestingly, we find that the anomalous vacuum Hall conductivity is vanishing in the type-II phase at all temperatures. The corresponding thermal Hall and Nernst conductivities are evaluated and characterized for both phases. The qualitative and quantitative observations presented here may serve in the characterization of generic mWSMs of both types.

The use of oscillator-strength sum rules for evaluating the angular-momentum dependence of the blackbody-radiation-induced broadening and shift of Rydberg-state energy levels

First evaluations of the blackbody-radiation (BBR)-induced shift and broadening of highly excited Rydberg states were based on the account of only the first term of the expansion for the Planck’s distribution in powers of the ratio of the BBR-photon energy to the environmental thermal energy. The corresponding asymptotic expression for the shift is proportional to a sum rule for the oscillator strengths, which is identical for all states, independently of their principal and angular-momentum quantum numbers. The broadening appeared proportional to the sum of the oscillator-strength first moments, which is dependent on only the principal quantum number, being independent of the state’s angular momentum. In this article, we demonstrate that the account of higher-order terms of the Planck’s distribution expansion provides corrections revealing the dependence of asymptotic shift and broadening on the Rydberg-state principal and angular-momentum quantum numbers. The strongest corrections are observed for states with low angular momenta, in agreement with earlier performed numerical calculations. Sum rules for higher moments of oscillator strengths are used for evaluating the corrections for the BBR-induced broadening and shift of Rydberg-state energy levels in neutral atoms and ions of arbitrary nuclear charge Z.

Modeling the Transport of Nonthermal Particles in Flares Using Fokker–Planck Kinetic Theory

Abstract We describe a new approach for modeling the transport of high-energy particles accelerated during flares from the acceleration region in the solar corona until their eventual thermalization in the flare footpoint. Our technique numerically solves the Fokker–Planck equation and includes forces corresponding to Coulomb collisions in a flux loop with nonuniform ionization, synchrotron emission reaction, magnetic mirroring, and a return current electric field. Our solution to the Fokker–Planck equation includes second-order pitch angle and momentum diffusion. It is applicable to particles of arbitrary mass and charge. By tracking the collisions, we predict the bremsstrahlung produced as these particles interact with the ambient stellar atmosphere. This can be compared directly with observations and used to constrain the accelerated particle energy distribution. We have named our numerical code FP and distributed it for general use. We demonstrate its effectiveness in several test cases.

Generation of arbitrary cylindrical vector vortex beams with cross-polarized modulation

Cylindrical vector vortex beams (CVVBs), possessing both spatially nonuniform phase and polarization distribution, have attracted research interests in many applications due to their unique optical properties. Although various methods have been previously demonstrated, the generation of CVVBs with arbitrary topological charge and polarization order remains elusive. We introduce cross-polarized modulation method to construct CVVBs via changing the phases of the orthogonal polarization components of light beams. Two cross-polarized modulation approaches are demonstrated for conjugate and consistent phase orthogonal circular polarization beams. The phases of the orthogonal circular polarization components of light beams can be flexibly manipulated by exploiting the polarization-sensitivity of spatial light modulators, which leads to changed topological charges and polarization orders, and a group of CVVBs with different topological charges and polarization orders are successfully generated. Because of the adjustable orders and the single light path, the CVVBs generation method possess not only flexibility but also high stability.

Generalized slab universal instability and its appearance in pair plasma

A generalized linear dispersion relation of electromagnetic slab universal modes is derived, taking into account arbitrary ion charge state, electron finite Larmor radius (FLR) effects, and Debye shielding effects. As a consequence, it provides more accurate predictions and is applicable to a wider range of plasmas. We find that electron FLR effects have a weakly stabilizing effect on the slab universal instability in electron–ion plasma, while Debye shielding strongly stabilizes this instability when λD approaches ρi (λD is the Debye length and ρi is the ion gyroradius). In particular, we examine the stability criterion for this instability in electron–positron pair plasmas and find that the instability persists in this simplest plasma system as long as the pair plasma number density exceeds the critical value nc=B2/(8πmec2).

Electrokinetic spectra of dilute surfactant-stabilized nano-emulsions

Abstract

Higher topological charge and the QCD vacuum

It is shown that gauge field configurations with higher topological charge modify the structure of the QCD vacuum, which is reflected in its dependence on the CP-violating topological phase $\theta$. To explore this, topological susceptibilities and the production of axion dark matter are studied here. The former characterize the topological charge distribution and are therefore sensitive probes of the topological structure of QCD. The latter depends on the effective potential of axions, which is determined by the $\theta$-dependence of QCD. The production of cold dark matter through the vacuum realignement mechanism of axions can therefore be affected by higher topological charge effects. This is discussed qualitatively in the deconfined phase at high temperatures, where a description based on a dilute gas of instantons with arbitrary topological charge is valid. As a result, topological susceptibilities exhibit a characteristic temperature dependence due to anharmonic modifications of the $\theta$-dependence. Furthermore, multi-instanton effects give rise to a topological mechanism to increase the amount of axion dark matter.

Spin-orbit and orbit-spin conversion in the sharp focus of laser light: Theory and experiment

Based on the Richards-Wolf theory, it is strictly shown that in the sharp focus of a linearly polarized laser beam, the flux of a spin vector has only transverse components (the effect of photonic wheels or a photonic helicopter). For a linearly polarized optical vortex, the orbit-spin conversion leads to the appearance of both longitudinal and transverse components of the spin angular momentum (SAM) vector in the focus. We show that in the strong focus of a circularly polarized Gaussian beam, the longitudinal component of the SAM is maximal on the optical axis, with the longitudinal component of the orbital angular momentum (OAM) being maximal on a ring. In this way, the effect of SAM and OAM on the motion of a trapped microparticle can be evaluated separately. Spin-orbit conversion is experimentally demonstrated for a circularly polarized Gaussian beam when transverse energy flux (orbital angular momentum) arises in the focus, which is transmitted to a microparticle and causes it to rotate. Switching the handedness of circular polarization (from left to right) switches the direction of microparticle rotation. It is also shown here that an azimuthally polarized vortex beam with an arbitrary integer topological charge generates in the focus a SAM vector with only an axial component (pure magnetization), whereas there is no transverse spin flux.

Enhanced parametric pulse amplification in a comparable-mass plasma affected by charge state

Enhanced stimulated Brillouin scattering and stimulated Raman scattering are shown in comparable-mass plasma by considering charge state through a simplified theoretical model and particle-in-cell simulations. We present a more general dispersion relation of plasma wave with arbitrary mass ratio and charge state compared to the previous electron–positron plasma study. Further, the ion-bulk mode is responsible for Brillouin amplification from kinetic analysis. Higher intensities of seed laser pulse amplification through stimulated Brillouin scattering are observed in βZ = 1 type plasmas and β = 1 type plasmas as Z increases; the former is caused by kinetic effects, while the latter is due to the higher growth rates of instability. Our results will have potential application in pulse amplification in the comparable-mass plasmas with charge state Z > 1, such as plasma of .

Multifunctional Geometric Metasurfaces Based on Tri‐Spectral Meta‐Atoms with Completely Independent Phase Modulations at Three Wavelengths

AbstractMetasurface has drawn much attention due to its unprecedented wave‐front manipulation abilities with an ultrathin flat profile. However, the metasurface as a diffractive device usually suffers from chromatic aberrations, which greatly hinders the design freedom at different wavelengths. In this work, it is demonstrated that this limitation can be overcome by a multifunctional metasurface with completely independent phase modulations at three arbitrarily wavelengths. Specifically, a novel single‐layer tri‐spectral meta‐atom composed of three alternatively arranged slot and metallic resonators is proposed to operate at three distinct wavelengths, where 2π geometric phase modulations under the circularly polarized incidence can be achieved independently by rotating the corresponding resonators. As proof of concept demonstrations, a tri‐wavelength vortex beam generator and a meta‐hologram are designed to verify the proposed method. First, a vortex beam generator with arbitrary topological charge numbers at three wavelengths is designed and verified through theoretical calculation and full‐wave simulation. Moreover, a meta‐hologram generated by the computer‐generated holography is designed to display three frequency selective holographic images on the same image plane. The tri‐wavelength meta‐hologram is validated through theoretical calculation, full‐wave simulation, and experiment. The experimental results agree very well with the numerical ones, demonstrating the attractive capabilities of multifunctionalities at three wavelengths.

Electric multipole fields of higher-dimensional massive bodies

It was shown in a recent paper [J. Math. Phys. 60, 102502 (2019)] that slowly lowering an electric charge into a Schwarzschild-Tangherlini (ST) black hole endows the final state with electric multipole fields, which implies the final state geometry is not Reissner-Nordstr\"om-Tangherlini in nature. This conclusion departs from the four-dimensional case in which the no-hair theorem (NHT) requires the final state to be a Reissner-Nordstr\"om black hole. To better understand this discrepancy clearly requires a deeper understanding of the origin of the multipole hair in the higher-dimensional case. In this paper, we advance the conjecture that charged, static, and asymptotically-flat higher-dimensional black holes can acquire electric multipole hair only after they form. This supposition derives from studying the asymptotic behavior of the field of a multipole charge onto which a massive and hyperspherical shell with an exterior ST geometry is collapsing. In the mathematical limit as the shell approaches its ST radius, we find that the multipole fields (except the monopole) vanish. This implies that the only information of an arbitrary (but finite) charge distribution inside the collapsing shell that is available to an asymptotic observer is the total electric charge. Our results yield considerable insight into how higher-dimensional black holes acquire electric multipole hair, and also imply that, in four dimensions, the fadeaway of multipole moments during gravitational collapse is not strictly because of the NHT.

Thermoelectric transport properties of Floquet multi-Weyl semimetals

We discuss the circularly polarized light (of amplitude $A_0$ and frequency $\omega$) driven thermo-electric transport properties of type-I and type-II multi-Weyl semimetals (mWSMs) in the high frequency limit. Considering the low energy model, we employ the Floquet-Kubo formalism to compute the thermal Hall and Nernst conductivities for both types of mWSMs. We show that the anisotropic nature of the dispersion for arbitrary integer monopole charge $n>1$ plays an important role in determining the effective Fermi surface behavior; interestingly, one can observe momentum dependent corrections in Floquet mWSMs in addition to momentum independent contribution as observed for Floquet single WSMs. Apart from the non-trivial tuning of the Weyl node position $\pm Q \to \pm Q- A_0^{2n}/\omega$, our study reveals that the momentum independent terms result in leading order contribution in the conductivity tensor. This has the form of $n$ times the single WSMs results with effective chemical potential $\mu \to \mu -A_0^{2n}/\omega$. On the other hand, momentum dependent corrections lead to sub-leading order terms which are algebraic function of $\mu$ and are present for $n>1$. Remarkably, this analysis further allows us to distinguish type-I mWSMs from their type-II counterparts. For type-II mWSMs, we find that the transport coefficients for $n\geq 2$ exhibit algebraic dependence on the momentum cutoff in addition to the weak logarithmic dependence as noticed for $n=1$ WSMs. We demonstrate the variation and qualitative differences of transport coefficients between type-I and type-II mWSM as a function of external driving parameter $\omega$.

New integrable two-centre problem on sphere in Dirac magnetic field

We present a new family of integrable versions of the Euler two-centre problem on two-dimensional sphere in the presence of the Dirac magnetic monopole of arbitrary charge. The new systems have very special algebraic potential and additional integral quadratic in momenta, both in classical and quantum versions.

Better in theory than in practise? Challenges when applying the luck egalitarian ethos in health care policy

Luck egalitarianism, a theory of distributive justice, holds that inequalities which arise due to individuals’ imprudent choices must not, as a matter of justice, be neutralized. This article deals with the possible application of luck egalitarianism to the area of health care. It seeks to investigate whether the ethos of luck egalitarianism can be operationalized to the point of informing health care policy without straying from its own ideals. In the transition from theory to practise, luck egalitarianism encounters several difficulties. We argue that the charge of moral arbitrariness can, at least in part, be countered by our provided definition of “imprudent actions” in the health area. We discuss the choice for luck egalitarianism in health care between ex ante and ex post policy approaches, and show how both approaches are flawed by luck egalitarianism’s own standards. We also examine the problem of threshold setting when luck egalitarianism is set to practise in health care. We argue that wherever policy thresholds are set, luck egalitarianism in health care risks pampering the imprudent, abandoning the prudent or, at worst, both. Furthermore, we claim that moves to mitigate these risks in turn diminish the normative importance of the ethos of luck egalitarianism to policy. All in all, our conclusion is that luck egalitarianism cannot be consistently applied as a convincing and relevant normative principle in health care policy.

Multi-instanton contributions to anomalous quark interactions

In quantum chromodynamics (QCD), the role which topologically nontrivial configurations play in splitting the singlet pseudo-Goldstone meson, the ${\ensuremath{\eta}}^{\ensuremath{'}}$, from the octet is familiar. In addition, such configurations contribute to other processes which violate the axial $U(1{)}_{A}$ symmetry. While the nature of topological fluctuations in the vacuum is still unsettled, at temperatures above that for the chiral phase transition, they can be described by a dilute gas of instantons. We show that instantons of arbitrary topological charge $Q$ generate anomalous interactions between $2{N}_{f}|Q|$ quarks, which for $Q=1$ make the ${\ensuremath{\eta}}^{\ensuremath{'}}$ heavy. For two flavors we compute an anomalous quartic meson coupling and discuss its implications for the phenomenology of the chiral phase transition. A dilute instanton gas suggests that for cold, dense quarks, instantons do not evaporate until very high densities, when the baryon chemical potential is $\ensuremath{\gtrsim}2\text{ }\text{ }\mathrm{GeV}$.

Bi-channel near- and far-field optical vortex generator based on a single plasmonic metasurface

With the recent development of the metasurface, generating an optical vortex in optical far or near fields is realized in various ways. However, to generate vortices in both the near and far fields simultaneously is still a challenge, although it has great potential in the future compact and versatile photonic system. Here, a bi-channel optical vortex generator in both the near and far fields is proposed and demonstrated within a single metasurface, where the surface plasmon vortex and the far-field optical vortex can be simultaneously generated under circularly polarized light. The ability of generating vortices with arbitrary topological charges is experimentally demonstrated, which agrees well with simulations. This approach provides great freedom to integrate different vortex generators in a single device and offers new opportunities for integrated optical communications, trapping, and other related fields.

Transfer of spin angular momentum to a dielectric particle

We show here that in the sharp focus of a linearly polarized laser beam the spin vector flux has only transverse components (the effect of photonic wheels or photonic helicopter). For a linearly polarized optical vortex, the orbit-spin conversion leads to the appearance of both longitudinal and transverse components of the spin density vector in the focus. Spin-orbit conversion is experimentally demonstrated for a circularly polarized Gaussian beam when a transverse energy flux (orbital angular momentum) arises in the focus, which is transmitted to a microparticle and makes it rotate. Switching the handedness of circular polarization (from left to right) switches the microparticle rotation direction. It is also shown here that an azimuthally polarized vortex beam with an arbitrary integer topological charge generates in the focus a spin density vector that only has an axial component (pure magnetization), while the transverse spin flux is absent.

Data-driven smart charging for heterogeneous electric vehicle fleets

The ongoing electrification of mobility comes with the challenge of charging electric vehicles (EVs) sufficiently while charging infrastructure capacities are limited. Smart charging algorithms produce charge plans for individual EVs and aim to assign charging capacities fairly and efficiently between vehicles in a fleet. In practice, EV charging processes follow nonlinear charge profiles such as constant-current, constant-voltage (CCCV). Smart charging must consider charge profiles in order to avoid gaps between charge plans and actual EV power consumption. Generally valid models of charge profiles and their parameters for a diverse set of EVs are not publicly available. In this work we propose a data-driven approach for integrating a machine learning model to predict arbitrary charge profiles into a smart charging algorithm. We train machine learning models with a dataset consisting of charging processes from the workplace gathered in 2016–2018 from a heterogeneous EV fleet of 1001 EVs with 18 unique models. Each charging process includes the time series of charging power. After preprocessing, the dataset contains 10.595 charging processes leading to 1.2 million data points in total. We then compare different machine learning models for charge profile predictions finding that XGBoost yields the most accurate predictions with a mean absolute error (MAE) of 126W and a relative MAE of 0.06. Simulations show that smart charging with the integrated XGBoost model leads to a more effective infrastructure usage with up to 21% more energy charged compared to smart charging without considering charge profiles. Furthermore, an ablation study on regression model features shows the EV’s model is not a necessary attribute for accurate charge profile predictions. However, charging features are required including the number of phases used for charging.

Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping amplitude $-t$ ($t>0$) and on-site interaction $U$. This chiral phase is stabilized in the Mott phase with one particle per site in the presence of a uniform $\pi$-flux per plaquette, and in the Mott phase with two particles per site without any flux. Our approach relies on effective spin models derived in the strong-coupling limit in powers of $t/U$ for general SU$(N)$ and arbitrary uniform charge flux per plaquette, which are subsequently studied using exact diagonalizations and variational Monte Carlo simulations for $N=3$, as well as exact diagonalizations of the SU($3$) Hubbard model on small clusters. Up to third order in $t/U$, and for the time-reversal symmetric cases (flux $0$ or $\pi$), the low-energy description is given by the $J$-$K$ model with Heisenberg coupling $J$ and real ring exchange $K$. The phase diagram in the full $J$-$K$ parameter range contains, apart from three already known, magnetically long-range ordered phases, two previously unreported phases: i) a lattice nematic phase breaking the lattice rotation symmetry and ii) a spontaneous time-reversal and parity symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an investigation that includes higher-order itinerancy effects supports the presence of a phase transition inside the insulating region, occurring at $(t/U)_{\rm c}\approx 0.07$ [$(U/t)_{\rm c} \approx 13$] between the three-sublattice magnetically ordered phase at small $t/U$ and this Abelian chiral spin liquid.