Complex Poles 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.

Infrared gluon propagator in the refined Gribov-Zwanziger scenario at one-loop order in the Landau gauge

The refined Gribov-Zwanziger (RGZ) action in the Landau gauge provides a local and renormalizable framework to account for the existence of infinitesimal Gribov copies in the path integral together with other relevant infrared effects such as the formation of condensates. The properties of the tree-level gluon propagator obtained in this setup have been thoroughly investigated over the past decade. It accommodates important properties seen in lattice simulations such as a finite value at vanishing momentum and positivity violation. Yet a comprehensive study about the stability of such properties against quantum corrections was lacking. In this work, we compute the gluon propagator in the RGZ scenario at one-loop order and implement an appropriate renormalization scheme in order to compare our findings with lattice data. Remarkably, the qualitative properties of the tree-level gluon propagator are preserved. In particular, the fits with lattice data show evidence for positivity violation and the existence of complex poles for SU(2) and SU(3) gauge groups. We comment on the results for the ghost propagator as well. Published by the American Physical Society 2024

A wideband high-PSR OCL LDO using a gain-relaxed OTA featuring dynamic complex zeros frequency compensation

This article proposes an Output-Capacitor-Less (OCL) Low-Dropout (LDO) regulator with an assisted positive feedback loop technique, which mimics a negative resistance, along with a single common-gate stage. Conventional techniques utilize multistage high-gain OTA to achieve a high DC loop gain. However, such an OTA suffers from high power consumption and sophisticated frequency compensation mechanisms. Instead, the use of a single-stage relatively low-gain OTA helps to extend the bandwidth. Then, the overall DC loop gain is maximized by the proposal of a novel negative resistance circuit. To further improve the PSR, a bulk-driven ripple canceling path that is insensitive to process corners is proposed making the LDO suitable for high-PSR applications. Stability is another challenge in the design of OCL LDOs due to its associated complex poles. We propose a new frequency compensation technique by introducing two complex zeros to eliminate these complex poles. Hence, the overall stability is improved. Since these complex poles location vary from light to heavy loads, the proposed zeros dynamically change accordingly. Besides, this suggested mechanism has been analyzed using the generalized time-and-transfer constants (TTCs) circuit analysis technique. Under heavy load conditions, the suggested LDO has attained phase and gain margins of 62.8° and 29 dB, respectively. Moreover, Monte Carlo simulations along with process and temperature variations have been investigated to prove the reliability of such a frequency compensation technique. The proposed LDO has been implemented in 65 nm CMOS technology node with a short pass transistor length of 100nm. The simulation results reveals that the LDO draws 299.4μA of quiescent current under light load conditions and 296.8μA under heavy load conditions (including the bandgap voltage reference). The suggested LDO functions at 1.2V supply voltage, delivers 0.93V output voltage and can handle a load current up to 10mA with load regulation of 17μV/mA, line regulation of 2.22mV/V, and PSR of −48.7dB at low frequencies. The PSR at 1MHz is at least −32.5dB which is superior to the reported recent LDOs.

A global argument-based algorithm for finding complex zeros and poles to investigate plasma kinetic instabilities

Root-finding is a common problem in various fields of physics and mathematics. The basic version of this problem can be formulated as an equation f(z)=0 where z∈ℂ and f is a meromorphic function on a complex plane ℂ. In some cases, a conjugated problem has to be solved as well to investigate the properties of the inspected system: f(z)−1=0. Iterative Householder-like methods show high convergence rate, however, the convergence itself is strongly dependent on the input parameters such as an initial guess. If the function f is complicated enough, there can be no prior information about its zeros and poles, and thus, no way to correctly pick the initial guess. The aim of the algorithm proposed in this article is to find all zeros and poles inside a selected region without any information about the local behavior of the function f. Additionally, the method is generalized to a parametric problem with continuous solutions: f(z)→f(z;p) where p∈Rd, d∈N∪{0}. The basis of the algorithm consists of a triangulation process and an implementation of the Cauchy’s argument principle to inspect the constructed subregions. The refinement process is accompanied by an absolute value gradient ∇ln|f| analysis that significantly decreases the number of points needed to correctly identify the locations of all zeros and poles. The algorithm is presented as a hybrid class for d∈{0,1} that can be directly used to solve corresponding problems.

Managing temperature in open quantum systems strongly coupled with structured environments.

In non-perturbative non-Markovian open quantum systems, reaching either low temperatures with the hierarchical equations of motion (HEOM) or high temperatures with the Thermalized Time Evolving Density Operator with Orthogonal Polynomials Algorithm (T-TEDOPA) formalism in Hilbert space remains challenging. We compare different ways of modeling the environment. Sampling the Fourier transform of the bath correlation function, also called temperature dependent spectral density, proves to be very effective. T-TEDOPA [Tamascelli et al., Phys. Rev. Lett. 123, 090402 (2019)] uses a linear chain of oscillators with positive and negative frequencies, while HEOM is based on the complex poles of an optimized rational decomposition of the temperature dependent spectral density [Xu et al., Phys. Rev. Lett. 129, 230601 (2022)]. Resorting to the poles of the temperature independent spectral density and of the Bose function separately is an alternative when the problem due to the huge number of Bose poles at low temperatures is circumvented. Two examples illustrate the effectiveness of the HEOM and T-TEDOPA approaches: a benchmark pure dephasing case and a two-bath model simulating the dynamics of excited electronic states coupled through a conical intersection. We show the efficiency of T-TEDOPA to simulate dynamics at a finite temperature by using either continuous spectral densities or only all the intramolecular oscillators of a linear vibronic model calibrated from abinitio data of a phenylene ethynylene dimer.

From pole parameters to line shapes and branching ratios

Resonances are uniquely characterized by their complex pole locations and the corresponding residues. In practice, however, resonances are typically identified experimentally as structures in invariant mass distributions, with branching fractions of resonances determined as ratios of count rates. To make contact between these quantities it is necessary to connect line shapes and resonance parameters. In this work we propose such a connection and illustrate the formalism with detailed studies of the ρ(770)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho (770)$$\\end{document} and f0(500)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0(500)$$\\end{document} resonances. Based on the line shapes inferred from the resonance parameters along these lines, expressions for partial widths and branching ratios are derived and compared to other approaches in the literature.

Toward the quark mass dependence of Tcc+ from lattice QCD

The DD* scattering phase shifts in the Tcc+=ccu¯d¯ channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to mπ≃280 MeV. The phase shifts are analyzed employing two approaches: effective range expansion and Lippmann-Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrized by contact terms and a slight repulsion at long range mediated by one-pion exchange with mπ>mD*−mD. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for mc close to the physical value. They turn into a pair of virtual states at the largest mc studied. With further increasing mc, one virtual pole representing Tcc+ is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the Tcc+ pole is briefly discussed using the data on DD* scattering from other lattice collaborations. Published by the American Physical Society 2024

Revisiting O(N) σ model at unphysical pion masses and high temperatures

Roy-equation analysis on lattice data of ππ scattering phase shifts at mπ=391 MeV reveals that the lowest f0 meson becomes a bound state under this condition. In addition, there is a pair of complex poles below threshold generated by crossing symmetry [X.-H. Cao , ]. We use the N/D method to partially recover crossing symmetry of the O(N) σ model amplitude at leading order of 1/N expansion, and qualitatively reproduce the pole structure and pole trajectories with varying pion masses as revealed by Roy-equation analyses. The σ pole trajectory with varying temperature is also discussed and found to be similar to its properties when varying mπ. As the temperature increases, the complex σ poles firstly move from the second Riemann sheet to the real axis becoming two virtual state poles, and then one virtual state pole moves to the first sheet turning into a bound state pole and finally tends to the pion pole position at high temperature which is as expected from the chiral symmetry restoration. Our results provide further evidence that the lowest f0 state extracted from experiments and lattice data plays the role of the σ meson in the spontaneous breaking of chiral symmetry. Finally, we also briefly discuss the problems of the effective potential in the situation when mπ and the temperature become large. Published by the American Physical Society 2024

Fully real-time configurable analogue implementation of continuous-time transfer function: Application on fractional controller

This paper proposes a new electronic analog circuit to realize real-time fully configurable continuous-time transfer function. The proposed circuit serves various purposes, including smart controllers, fractional-order controllers, optimal controllers, anti-aliasing filter, and programmable filters. The input signal of the transfer function is continuous and remains continuous throughout the circuit until the output signal is obtained. The proposed approach decomposes the transfer function into elementary first and/or second-order low-pass filters. A new analog first-order low-pass filter circuit is presented, offering advantages over conventional active first-order low-pass filters circuits. These benefits include DC gain and time constant independent of resistor ohmic values, enabling the use of smaller resistors and capacitors for low frequencies, and an expanded frequency working range. Similarly, a new analog circuit for a second-order low-pass filter is proposed, specifically used to obtain complex conjugate poles. The use of digital potentiometers and digital switches controlled by a micro-controller, makes this analog circuit configurable in real-time. As an application, the new circuit is used to realize fractional integrator controller. The circuit gives good similarity between theoretical and experimental measurements.

Complex choices: Pole selection for polarized projective mapping applied to a complex product set

AbstractPolarized projective mapping (PPM) employs reference samples called poles, positioned in the sensory space, to which samples are compared. This structure enables comparisons across sessions. Selecting the right poles is therefore critical for accurate and reliable comparisons. The current study examined whether simple poles (single fruit juices) or complex poles (fruit juice blends) better represented the sensory space in PPM using a trained panel (n = 12). Thirteen commercial fruit juices, including single juices and blends, were assessed using projective mapping to understand product diversity and select three simple and three complex poles. PPM was then conducted using simple poles in one session and complex poles in another. Six of the thirteen juices used in PPM and three new juices were evaluated to validate the results. Findings indicated that while both simple and complex poles described the product space, simple poles were more able to capture the diversity of the sensory space.Practical ApplicationsThe study's insights into appropriate pole selection in PPM for complex product sets contribute to the technique's usability and robustness. The guidance on pole selection ensures selected poles anchor the product space, enabling meaningful comparisons across sessions. The finding that simple poles are able to describe complex product sets may assist in minimizing fatigue, a common challenge in evaluating complex products like wine, spirits, and cider. By addressing the unique challenges of complex products, this research enhances the useability of PPM as a valuable tool for comprehensively evaluating sensory characteristics in product categories prone to fatigue and limited consumption.

On the quark spectral function in QCD

We calculate the spectral function of light quark flavours in 2+1 flavour vacuum QCD in the isospin-symmetric approximation. We employ spectral Dyson-Schwinger equations and compute the non-perturbative quark propagator directly in real-time, using recent spectral reconstruction results from Gaussian process regression of gluon propagator data in 2+1 flavour lattice QCD. Our results feature a pole-like peak structure at time-like momenta larger than the propagator’s gapping scale as well as a negative scattering continuum, which we exploit assuming an analytic pole-tail split during the iterative solution. The computation is augmented with a general discussion of the impact of the quark-gluon vertex and the gluon propagator on the analytic structure of the quark propagator. In particular, we investigate under which conditions the quark propagator shows unphysical complex poles. Our results offer a wide range of applications, encompassing the ab-initio calculation of transport as well as resonance properties in QCD.

The black hole behind the cut

We study the analytic structure of the heavy-heavy-light-light holographic correlators in the supergravity approximation of the AdS3 × S3/CFT2 duality. As an explicit example, we derive the correlator where the heavy operator is a classical microstate of the 5D supersymmetric black hole and its dual geometry interpolates as a function of a continuous parameter between global AdS3 and the extremal BTZ black hole. The simplest perturbation of this interpolating geometry by a light field is described by the Heun equation and we exploit the relation of its connection coefficients to the Liouville CFT to analytically compute the correlator in the two limits, focusing in particular on the black hole regime. In this limit we find that the real poles of the correlator become dense and can be approximated by a cut. We show that, when the charges of the heavy state are in the black hole regime, the discontinuity across the cut has complex poles corresponding to the quasi-normal modes of BTZ. This behaviour is qualitatively similar to what is expected for the large central charge limit of a typical black hole microstate.

Renal trauma during a rugby tackle

Rugby-related renal trauma is rare and identification of a young patient with renal trauma secondary to sports who requires observation versus further radiological evaluation in the emergency department (ED) poses a diagnostic challenge. We report a case of a 16-year-old girl who presented to the ED with abdominal pain after being tackled during a game of rugby. Examination revealed tenderness over the right lateral lower ribs and right flank. Blood tests were normal and bedside ultrasound did not show any free intraperitoneal fluid. Urinalysis showed gross hematuria. She was pain-free after analgesia but had a syncopal episode in the ED. A computed tomography (CT) scan of the abdomen and pelvis showed a complex right lower pole renal laceration and she was admitted to the Intensive Care Unit. She remained stable and was discharged. Assessment with urinalysis, hematocrit, and creatinine is required during the evaluation of a patient with suspected renal trauma. CT scan is the imaging modality for the diagnosis and grading of renal injury. Conservative treatment is the mainstay of therapy, but some patients require angioembolization of surgical intervention. Patients must discuss with their physician regarding the optimal timing of return to rugby. Rugby-related renal trauma is rare and poses a challenge for emergency physicians regarding their evaluation and management in the ED. AAST-OIS grading of renal trauma on CT imaging helps guide appropriate management decisions.

Scrutinizing the light scalar quarkonia from LSR at higher orders

We scrutinize, improve some determinations of the masses and couplings of light scalar quarkonia (q¯q and four-quark states) and present new results for the π+π−,K+K−,… molecules using QCD Laplace Sum Rule (LSR) truncated at the D=6 dimension vacuum condensates. We pay a special attention on the higher order perturbative (PT) corrections up to the (estimated) O(αs5) which improve the quality of the analysis. We request that the optimal results obey the rigorous constraint: Resonance ≥ QCD continuum contributions (RP/C≥1) in the LSR which excludes a Breit-Wigner/on-shell (not to be confused with a complex pole) scalar meson mass around (500-600) MeV obtained for values [tc≤(1∼1.5) GeV2] of the QCD continuum threshold. Mass-splittings due to SU(3) breakings are small. We discuss the different assignments of the observed scalar mesons below 2 GeV in the Conclusions where the I=0 states are compared with the scalar gluonia. The results are compiled in Tables 3 to 6. We hope that the systematic analysis done in this paper helps to clarify the complex spectra of the light scalar mesons.

Hardware Suitability of Complex Natural Resonances Extraction Algorithms in Backscattered Radar Signals

Complex natural resonances (CNRs) extraction methods such as matrix pencil method (MPM), Cauchy, vector-fitting Cauchy method (VCM), or Prony’s method decompose a signal in terms of frequency components and damping factors based on Baum’s singularity expansion method (SEM) either in the time or frequency domain. The validation of these CNRs is accomplished through a reconstruction of the signal based on these complex poles and residues and a comparison with the input signal. Here, we perform quantitative performance metrics in order to have an evaluation of each method’s hardware suitability factor before selecting a hardware platform using benchmark signals, simulations of backscattering scenarios, and experiments.

Sphenoparietal Sinus Transposition: Operative Technique for Optimizing Pretemporal Posterior Circulation Access While Preserving the Sylvian Venous Complex

Transsylvian approaches are a cornerstone of complex cranial operations, with wide applicability across cerebrovascular, skull base, and neuro-oncology operations. Deep lesions, especially those involving the basilar apex, midbrain, or interpeduncular fossa, require wide exposures that may be inhibited by the presence of a large complex of superficial sylvian veins (SSV) draining into the sphenoparietal sinus. This report describes technical and clinical aspects of the sphenoparietal sinus transposition (SPST) technique. Technical case report of the SPST technique, including a step-by-step neuroanatomic description, overview of common indications, clinical pearls and pitfalls, and illustrative case examples. Once the benefits of proceeding with SPST have been established, the maneuver is initiated with 2 stepwise dural incisions: an incision from lateral to medial along the lateral margin of the lesser sphenoid wing, followed by an orthogonal cut across the temporal pole down the middle fossa floor. The pretemporal dura is peeled off the lateral wall of the cavernous sinus, allowing mobilization of the SSV complex and temporal pole posteriorly without disrupting or straining the connection point at the sphenoparietal sinus. Illustrative case examples include a clip reconstruction of a basilar apex aneurysm for which earlier endovascular treatment had failed and microsurgical resection of a peduncular cavernous malformation. SPST is a simple but versatile technique with important applications in complex cranial surgery. By mobilizing the SSV complex together with its dural attachment, the transsylvian corridor can be markedly widened, allowing access to the basilar apex region and ventral midbrain.

Self-Adaptive Mesh Generator for Global Complex Roots and Poles Finding Algorithm

In any global method of searching for roots and poles, increasing the number of samples increases the chances of finding them precisely in a given area. However, the global complex roots and poles finding algorithm (GRPF) (as one of the few) has direct control over the accuracy of the results. In addition, this algorithm has a simple condition for finding all roots and poles in a given area: it only requires a sufficiently dense initial grid. However, in practice, this requirement may turn out to be very difficult to implement. For a complex and sophisticated function, the use of a regular high-density mesh may be ineffective or even impossible due to limited computational resources. In this article, a method for creating a self-adaptive initial mesh for this algorithm is presented. The proposed solution uses gradient calculation to identify areas that require mesh refinement, including areas where a zero and a pole are in close proximity. The adaptive mesh allows for faster and more accurate analysis of functions with a much smaller number of samples. As shown in the numerical examples, this approach reduces the number of function calls by several orders of magnitude, and thus significantly reduces the computational time.

Nonlinear swing-down control of the Acrobot: Analysis and optimal gain design

In this paper, we address the swing-down control of the Acrobot, a two-link planar robot operating in a vertical plane with only the second joint being actuated. The control objective is to rapidly stabilize the Acrobot around the downward equilibrium point, with both links in the downward position, from almost all initial states. Under the conditions of no friction and measurability of only the angle and angular velocity of the actuated joint, we present a sinusoidal-derivative (SD) controller. This controller consists of a linear feedback of the sinusoidal function of the angle of the actuated joint and a linear feedback of its angular velocity. We prove that the control objective is achieved if the sinusoidal gain is greater than a negative constant and the derivative gain is positive. We establish crucial relationships between the relative stability of the Acrobot under the SD controller and its physical parameters, presenting analytically all optimal control gains. These gains minimize the real parts of the dominant poles of the linearized model of the resulting closed-loop system around the downward equilibrium point. We demonstrate that the resulting dominant closed-loop poles can be double complex conjugate poles, or a quadruple real pole, or a triple real pole, depending on the Acrobot’s physical parameters. Simulation studies indicate that the proposed SD controller outperforms the derivative (D) controller in rapidly stabilizing the Acrobot at the downward equilibrium point.

Analytic solutions of linear neutral and non-neutral delay differential equations using the Laplace transform method: featuring higher order poles and resonance

In this article, we extend the Laplace transform method to obtain analytic solutions for linear RDDEs and NDDEs which have real and complex poles of higher order. Furthermore, we present first-order linear DDEs that feature resonance phenomena. The procedure is similar to the one where all of the poles are order one, but requires one to use the appropriate modifications when using Cauchy’s residue theorem for the poles of higher order. The process for obtaining the solution relies on computing the relevant infinite sequence of poles and then determining the Laplace inverse, via the Cauchy residue theorem. For RDDEs, the poles can be obtained in terms of the Lambert W function, but for NDDEs,the complex poles, in most cases, must be computed numerically. We found that an important feature of first-order linear RDDES and NDDES with poles of higher order is that it is possible to incite the resonance phenomena, which in the counterpart ordinary differential equation cannot occur. We show that despite the presence of higher order poles or resonance phenomena, the solutions generated by the Laplace transform method for linear RDDEs and NDDEs that have higher order poles are still accurate.

Collective excitations of a charged Fermi superfluid in the BCS-BEC crossover

We consider collective excitations in the superfluid state of Fermi condensed charged gases. The dispersion and damping of collective excitations at nonzero temperatures are examined, and the coexistence and interaction of different branches of collective excitations: plasma oscillations, pair-breaking Higgs modes, and Carlson–Goldman phonon-like excitations are taken into account. The path integral methods for superfluid Fermi gases and for Coulomb gas are combined into a unified formalism that extends the Gaussian fluctuation approximation to account for plasmonic modes. This approximation of Gaussian pair and density fluctuations is able to describe all branches of collective excitations existing in a charged superfluid. The spectra of collective excitations are determined in two ways: from the spectral functions and from the complex poles of the fluctuation propagator. A resonant avoided crossing of different modes is shown. It is accompanied by resonant enhancement of the response provided by the pair-breaking modes due to their interaction with plasma oscillations. This may facilitate the experimental observation of the pair-breaking modes.