Pole Singularities Research Articles

Decoupled Dipole Arrays Empowered by Invisible Complex Poles in Epsilon‐Near‐Zero Metamaterials

AbstractEvanescent waves, characterized by an exponential decay in propagation, have witnessed significant advancements in far‐field imaging and near‐field sensing applications. However, incoming evanescent waves can excite guided resonance inside a dielectric slab, resulting in a rapid growth of transmission coefficient toward infinity at the pole points. Such evanescent‐wave excited resonance benefits super‐resolution applications yet causes severe crosstalk in highly integrated multi‐channel devices. Here, the invisible complex poles are discovered in the transmission spectra of epsilon‐near‐zero (ENZ) metamaterials and demonstrate the striking suppression of near‐field crosstalk enabled by the anomalous transmission beyond the critical angle. Equipped with an ENZ metamaterial spacer, collinear dipole arrays exhibit 9.2 dB improvement in near‐field isolation among interior dipoles at a distance of less than one wavelength. Experimental measurements show negligible influence on the intrinsic impedance matching and radiation patterns of the dipole antennas. The discovered field divergence effect from the disappearance of real‐valued pole singularity in ENZ metamaterials offers an alternative solution for highly compact arrays in full duplex communication and multiple‐input multiple‐output technology.

Scalar and Tensor Charmonium Resonances in Coupled-Channel Scattering from Lattice QCD

We determine JPC=0++ and 2++ hadron-hadron scattering amplitudes in the charmonium energy region up to 4100 MeV using lattice QCD, a first-principles approach to QCD. Working at mπ≈391 MeV, more than 200 finite-volume energy levels are computed and these are used in extensions of the Lüscher formalism to determine infinite-volume coupled-channel scattering amplitudes. We find that this energy region contains a single χc0 and a single χc2 resonance. Both are found as pole singularities on the closest unphysical Riemann sheet, just below 4000 MeV with widths around 70 MeV. The largest couplings are to kinematically closed D*D¯* channels in S-wave, and couplings to several decay channels consisting of pairs of open-charm mesons are found to be large and significant in both cases. Above the ground state χc0, no other scalar bound states or near-DD¯ threshold resonances are found, in contrast to several theoretical and experimental studies. Published by the American Physical Society 2024

Modulation Transfer between Microwave Beams: Asymptotic Evaluation of Integrals with Pole Singularities near a First-Order Saddle Point

Experimental results of delay-time measurements in the transfer of modulation between microwave beams, as reported in previous articles, were interpreted on a competition (interference) between two waves, one of which is modulated and the other is a continuous wave (c.w.). The creation of one of these waves was attributed to a saddle-point contribution, while the other was attributed to pole singularities. In this paper, such an assumption is justified by a quantitative field-amplitude analysis in order to make the modeling plausible. In particular, two ways of calculating field amplitudes are considered. These lead to results that are quantitatively markedly different, although qualitatively similar.

Renormalization group improved photon impact factors and the high energy virtual photon scattering

We perform the renormalization group improved collinear resummation of the photon-gluon impact factors. We construct the resummed cross section for virtual photon-photon (γ∗γ∗) scattering which incorporates the impact factors and BFKL gluon Green’s function up to the next-to-leading logarithmic accuracy in energy. The impact factors include important kinematical effects which are responsible for the most singular poles in Mellin space at next-to-leading order. Further conditions on the resummed cross section are obtained by requiring the consistency with the collinear limits. Our analysis is consistent with previous impact factor calculations at NLO, apart from a new term proportional to CF that we find for the longitudinal polarization. Finally, we use the resummed cross section to compare with the LEP data on the γ∗γ∗ cross section and with previous calculations. The resummed result is lower than the leading logarithmic approximation but higher than the pure next-to-leading one, and is consistent with the experimental data.

Temporal coupled-mode theory for PT-symmetric chiral metasurfaces.

We have developed a temporal coupled-mode theory based on quasi-normal modes to investigate the chiroptical effects in parity-time (PT) symmetric metasurfaces. The PT symmetry enforces a different constraint for the direct scattering matrix and the coupling constants, which is verified by calculating the transmission spectra originating from the chiral quasi-bound states in the continuum. What's more, the scattering matrix can be analytically continued to the complex frequency plane. We find that the zero and pole singularities of the transmission coefficients and scattering matrix play an important role in the optical chirality. The pole singularities carry a quantized topological charge of -1. Our work paves the way for studying the enhanced optical chirality in non-Hermitian metasurfaces.

Modulation Transfer between Microwave Beams: Angular Dependence of the Delay-Time

Further measurements of delay time, in the transfer of modulation between microwave beams, are reported even considering the angular dependence in the orientation of the F1 c.w. launcher. The obtained results allow for a better interpretation of the observed phenomenology on the basis of a more sophisticated analysis, which takes into account the presence of pole singularities in field-amplitude evaluations according to the saddle point method. The model already presented in one of our previous publications, consisting of a photon–photon scattering mechanism as concomitant with a stochastic process, is then confirmed.

Highly sensitive gas optical sensing in a multicavity based quasi-parity-time-symmetric structure

A multicavity based quasi-parity-time (PT) symmetric structure is theoretically investigated for realizing highly sensitive gas detection. In the PT-symmetric broken phase, the singular pole effect can be achieved with much enhanced transmission, based on which low concentration of gas in the air can be efficiently sensed. In addition, the sensing signal is directly recorded by the change of the transmittance (T) of the sensor, real-time monitoring can be realized in our proposed structure. The sensitivities of -ΔT/ΔnD can reach 79437.2602 RIU−1 and 24753.7366 RIU−1 for benzene and methane, respectively. Such high sensitivity just occurs in the low concentration range. Our structures show great promise in constructing sensitive gas sensors to detect various harmful gases, such as volatile organic compounds (VOC) etc.

FIESTA5: Numerical high-performance Feynman integral evaluation

In this paper we present a new release of the FIESTA program (Feynman Integral Evaluation by a Sector decomposiTion Approach). FIESTA5 is performance-oriented — we implemented improvements of various kinds in order to make Feynman integral evaluation faster. We plugged in two new integrators, the Quasi Monte Carlo and Tensor Train. At the same time the old code of FIESTA4 was upgraded to the C++17 standard and mostly rewritten without self-made structures such as hash tables. There are also several essential improvements which are most relevant for complex integrations — the new release is capable of producing results where previously impossible. Program summaryProgram title: FIESTA5CPC Library link to program files:https://doi.org/10.17632/kyzw4zkwsd.2Developer's repository link:https://bitbucket.org/feynmanIntegrals/fiestaLicensing provisions: GPLv3Programming language:Wolfram Mathematica 8.0 or higher, C++Supplementary material: The article, usage instructions in the program package, https://bitbucket.org/feynmanIntegrals/fiestaJournal Reference of previous version: A.V. Smirnov, FIESTA4: Optimized Feynman integral calculations with GPU support, Comput. Phys. Commun. 204 (2016) 189–199, https://doi.org/10.1016/j.cpc.2016.03.013Does the new version supersede the previous version?: YesReasons for the new version: The code was not able to produce results in some cases where the competitive code, pySecDec could; moreover we were not happy with the performance of the algorithm having multiple inefficient parts of the code.Summary of revisions: New integrators, improved sector decomposition strategies, improvement of contour transformation algorithm, code optimization especially in physical regions (might be 100 times faster or more), possibility to work in some situations where previously impossible, update of the code to modern standard.Nature of problem: Sector decomposition is a well-known approach to the numerical evaluation of Feynman integrals. Feynman integrals in 4 space-time dimension are divergent and have to be regulated. Sector decomposition is used to resolve pole singularities and consists of different stages — sector decomposition itself, contour transformation (in case of physical kinematics meaning base functions changing sign therefore leading to integration in complex numbers), pole resolution, epsilon expansion and numerical integration.Solution method: Most stages are performed in Wolfram Mathematica [1] (required version is 8.0 or higher), this part is parallelized by the use of Mathematica subkelnels in shared memory. As a result a database on hard disk is produced with the use of the KyotoCabinet [2] database engine. The integration stage is written in C++ and can be run on personal computers as well as on supercomputers via MPI. It can make use of installed graphical processor units. As default integrator we use Vegas from the Cuba library [3], but also it can be switched to QMC [4] or Tensor Train [5]. The mimalloc memory allocator [6] can be used for improved performance.Additional comments including restrictions and unusual features: The complexity of the problem is mostly restricted by CPU time required to perform the integration and to obtain the desired precision.

Note on solutions of scattering equations

In the CHY-frame for the amplitudes, there are two kinds of singularities we need to deal with. The first one is the pole singularities when the kinematics is not general, such that some of $S_A\to 0$. The second one is the collapse of locations of points after solving scattering equations (i.e., the singular solutions). These two types of singularities are tightly related to each other, but the exact mapping is not well understood. In this paper, we have initiated the systematic study of the mapping. We have demonstrated the different mapping patterns using three typical situations, i.e., the factorization limit, the soft limit and the forward limit.

Regularity for a Class of Singular Complex Hessian Equations

In this paper, we study the regularity of the complex Hessian equation when the right hand has pole singularity. We show the Holder continuity of the solution to the Dirichlet problem. In particular, for the complex Monge-Ampere equation, we improve a result of [7].

Decays of an exotic 1−+ hybrid meson resonance in QCD

We present the first determination of the hadronic decays of the lightest exotic ${J}^{PC}={1}^{\ensuremath{-}+}$ resonance in lattice QCD. Working with SU(3) flavor symmetry, where the up, down and strange-quark masses approximately match the physical strange-quark mass giving ${m}_{\ensuremath{\pi}}\ensuremath{\sim}700\text{ }\text{ }\mathrm{MeV}$, we compute finite-volume spectra on six lattice volumes which constrain a scattering system featuring eight coupled channels. Analytically continuing the scattering amplitudes into the complex-energy plane, we find a pole singularity corresponding to a narrow resonance which shows relatively weak coupling to the open pseudoscalar--pseudoscalar, vector--pseudoscalar and vector--vector decay channels, but large couplings to at least one kinematically closed axial-vector--pseudoscalar channel. Attempting a simple extrapolation of the couplings to physical light-quark mass suggests a broad ${\ensuremath{\pi}}_{1}$ resonance decaying dominantly through the ${b}_{1}\ensuremath{\pi}$ mode with much smaller decays into ${f}_{1}\ensuremath{\pi}$, $\ensuremath{\rho}\ensuremath{\pi}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}$ and $\ensuremath{\eta}\ensuremath{\pi}$. A large total width is potentially in agreement with the experimental ${\ensuremath{\pi}}_{1}(1564)$ candidate state observed in $\ensuremath{\eta}\ensuremath{\pi}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}$, which we suggest may be heavily suppressed decay channels.

Quadratic differentials, measured foliations, and metric graphs on punctured surfaces

A meromorphic quadratic differential on a punctured Riemann surface induces horizontal and vertical measured foliations with pole singularities. In a neighborhood of a pole, such a foliation comprises foliated strips and half-planes, and its leaf space determines a metric graph. We introduce the notion of an asymptotic direction at each pole and show that for a punctured surface equipped with a choice of such asymptotic data, any compatible pair of measured foliations uniquely determines a complex structure and a meromorphic quadratic differential realizing that pair. This proves the analogue of a theorem of Gardiner–Masur for meromorphic quadratic differentials. We also prove an analogue of the Hubbard–Masur theorem; namely, for a fixed punctured Riemann surface there exists a meromorphic quadratic differential with any prescribed horizontal foliation, and such a differential is unique provided we prescribe the singular flat geometry at the poles.

The myth of ivory tower versus practice-oriented research: A systematic review of randomised studies in medical education.

A long-standing myth in medical education research is a divide between two different poles: research aiming to advance theory with little focus on practical applications ('ivory tower' research) and practically oriented research aiming to serve educators and decision-makers with little focus on advancing theory ('in-the-trenches' practice). We explored this myth in a sample of randomised medical education studies using Stokes' four-quadrant framework for the classification of research perspective. We searched MEDLINE, Embase, CINAHL, PsychINFO, ERIC, Web of Science and Scopus for studies in medical education using a randomised design that were published between 1 January 2018 and 31 December 2018. We used Stokes' four-quadrant framework to categorise the studies according to their use of theory, concepts and their justification for practical use. We compared medical education research published in medical education journals and clinical journals. A total of 150 randomised studies were included in the analysis. The largest segment of studies (46.7%) was categorised as use-inspired basic research (Pasteur's Quadrant), closely followed by pure applied research (40.7%, Edison's Quadrant). Only a few studies were categorised as aiming to advance knowledge with no thought for practical educational application (2.0%, Bohr's Quadrant). The proportion of studies that included educational concepts and theory differed according to publication in clinical journals or medical education journals: 40.5% vs 71.8%, respectively, P<.001. There were no differences between journals with regard to the proportion of studies that included a practical educational or clinical rationale (P=.99). In a large sample of studies using randomised designs, we found no evidence to support the myth that medical education research divides between two singular poles represented by 'ivory tower research' and 'in-the-trenches practice'. We did confirm prevailing assumptions regarding an emphasis on non-theoretical medical education research in clinical journals.

Landau-Fermi liquids without quasiparticles

Landau-Fermi liquid theory is conventionally believed to hold whenever the interacting single-particle density of states develops a $\delta$-like component at the Fermi surface, which is associated with quasiparticles. Here we show that a microscopic justification can be actually achieved under more general circumstances, even in case coherent quasiparticles are totally missing and the interacting single-particle density of states vanishes at the chemical potential as consequence of a pole singularity in the self-energy.

Review: The Sociology of Identity: The Dialectics of Consciousness, Deconstruction and Reconstruction, by Abdulghani Imad

Review: The Sociology of Identity: The Dialectics of Consciousness, Deconstruction and Reconstruction, by Abdulghani Imad

Langer Modification, Quantization Condition and Barrier Penetration in Quantum Mechanics

The WKB approximation plays an essential role in the development of quantum mechanics and various important results have been obtained from it. In this paper, we introduce another method, the so-called uniform asymptotic approximations, which is an analytical approximation method to calculate the wave functions of the Schrödinger-like equations, and it is applicable to various problems, including cases with poles (singularities) and multiple turning points. A distinguished feature of the method is that in each order of the approximations the upper bounds of the errors are given explicitly. By properly choosing the freedom introduced in the method, the errors can be minimized, which significantly improves the accuracy of the calculations. A byproduct of the method is to provide a very clear explanation of the Langer modification encountered in the studies of the hydrogen atom and harmonic oscillator. To further test our method, we calculate (analytically) the wave functions for several exactly solvable potentials of the Schrödinger equation, and then obtain the transmission coefficients of particles over potential barriers, as well as the quantization conditions for bound states. We find that such obtained results agree with the exact ones extremely well. Possible applications of the method to other fields are also discussed.

Propagation of time-resolved fluorescence in a diffuse medium: complex analytical derivation.

The spatiotemporal evolution of fluorescence in an optically diffusive medium following ultrashort laser pulse excitation is evaluated using complex analytical methods. When expressed as a Fourier integral, the integrand of the time-resolved diffuse fluorescence with embedded fluorophores is shown to exhibit branch points and simple pole singularities in the lower-half complex-frequency plane. Applying Cauchy's integral theorem to solve the Fourier integral, we calculate the time-resolved signal for fluorescence lifetimes that are both shorter and longer compared to the intrinsic absorption timescale of the medium. These expressions are derived for sources and detectors that are in the form of localized points and wide-field harmonic spatial patterns. The accuracy of the expressions derived from complex analysis is validated against the numerically computed, full time-resolved fluorescence signal. The complex analysis shows that the branch points and simple poles contribute to two physically distinct terms in the net fluorescence signal. While the branch points result in a diffusive term that exhibits spatial broadening (corresponding to a narrowing with time in the spatial Fourier domain), the simple poles lead to fluorescence decay terms with spatial/spatial-frequency distributions that are independent of time. This distinct spatiotemporal behavior between the diffuse and fluorescence signals forms the basis for direct measurement of lifetimes shorter than the intrinsic optical diffusion timescales in a turbid medium.

The extended Bogomolny equations and generalized Nahm pole boundary condition

In this paper we develop a Kobayashi-Hitchin type correspondence between solutions of the extended Bogomolny equations on $\Sigma\times \RP$ with Nahm pole singularity at $\Sigma \times \{0\}$ and the Hitchin component of the stable $SL(2,\mathbb{R})$ Higgs bundle; this verifies a conjecture of Gaiotto and Witten. We also develop a partial Kobayashi-Hitchin correspondence for solutions with a knot singularity in this program, corresponding to the non-Hitchin components in the moduli space of stable $SL(2,\mathbb{R})$ Higgs bundles. We also prove existence and uniqueness of solutions with knot singularities on $\mathbb{C}\ti\RP$.

Simple Analytical Solution of Čerenkov-Type Terahertz Wave Generation via Difference Frequency Generation in Dielectric Waveguides

We newly analyze the Cerenkov-type terahertz wave generation via the optical difference frequency generation in nonlinear dielectric waveguides based on the coupled-mode theory. The nonlinear coupled equations are derived, and the simple analytical solution for the terahertz wave is obtained in a closed form. The validity of our solution is also checked by the nonlinear beam propagation method. The analytical solution shows that for planar waveguides, the coupling coefficient has pole singularities at the propagation constants of the leaky modes at the terahertz frequency of the waveguides, and thus, the terahertz wave generation can be significantly enhanced as the phase-matching point approaches to the propagation constant of the lowest order leaky mode, whose imaginary part is very small compared to the real part of that.

Gaussian Unitary Ensembles with Pole Singularities Near the Soft Edge and a System of Coupled Painlevé XXXIV Equations

In this paper, we study the singularly perturbed Gaussian unitary ensembles defined by the measure $$\begin{aligned} \frac{1}{C_n} \mathrm{e}^{- n\text {tr}\, V(M;\lambda ,\mathbf {t}\;)}\mathrm{d}M, \end{aligned}$$ over the space of $$n \times n$$ Hermitian matrices M, where $$V(x;\lambda ,\mathbf {t}\;):= 2x^2 + \sum _{k=1}^{2m}t_k(x-\lambda )^{-k}$$ with $$\mathbf {t}= (t_1, t_2, \ldots , t_{2m})\in {\mathbb {R}}^{2m-1} \times (0,\infty )$$ , in the multiple scaling limit, where $$\lambda \rightarrow 1$$ together with $$\mathbf {t} \rightarrow \mathbf {0}$$ as $$n\rightarrow \infty $$ at appropriate related rates. We obtain the asymptotics of the partition function, which is described explicitly in terms of an integral involving a smooth solution to a new coupled Painlevé system generalizing the Painlevé XXXIV equation. The large n limit of the correlation kernel is also derived, which leads to a new universal class built out of the $$\Psi $$ -function associated with the coupled Painlevé system.