Real Spectrum Research Articles

PT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr{P}\\mathscr{T}$$\\end{document}-symmetric KdV solutions and their algebraic extension with zero-width resonances

A class of complex breather and soliton solutions to both KdV and mKdV equations are identified with a Pöschl-Teller type PT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr{P}\\mathscr{T}$$\\end{document}-symmetric potential. However, these solutions represent only the unbroken-PT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr{P}\\mathscr{T}$$\\end{document} phase owing to their isospectrality to an infinite potential well in the complex plane having real spectra. To obtain the broken-PT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr{P}\\mathscr{T}$$\\end{document} phase, an extension of the potential satisfying the sl2,R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$sl\\left( 2,\\mathbb {R}\\right)$$\\end{document} potential algebra is mandatory that additionally supports non-trivial zero-width resonances.

Iterative robust peak-aware guided filter for signal smoothing

Due to the imperfection of experimental measurements, the measured spectrum signals are inevitably corrupted by random error (noise). It is very useful in applications to remove the noise in the measured data while preserving some significant features (such as peaks) by a smoothing filtering process. This paper presents a peak-preserving smoothing technique in the framework of guided filtering for spectrum signals, called robust peak-aware guided filter (RPAGF). Firstly, the robust peak-aware weight (RPAW) is introduced by means of hyperbolic tangent with threshold parameter, where the parameter is estimated by the median of absolute deviations from the median of local variances of the signal under consideration. Then the RPAGF is presented by incorporating the RPAW of a guidance signal into the cost function of guided filter as the regularization coefficient. The RPAGF uses the Gaussian-weighted averaging to deal with the problem of overlapping windows involved in computing filtering output, while the guidance signal is generated by a time fractional diffusion filtering from the input signal. Finally, the self-iteration scheme of RPAGF called iterative RPAGF (IRPAGF) is designed to provide a more faithful guidance signal for RPAGF at each iteration. The IRPAGF is evaluated by experiments on simulated and real spectrum signals, in comparison to the relevant state-of-the-art methods. Results show that the IRPAGF achieves higher performance in terms of peak-preserving smoothing of spectrum signals.

Ultrafast Modulations in Stellar, Solar and Galactic Spectra: Dark Matter and Numerical Ghosts, Stellar Flares and SETI

Background: - From new results presented in the literature we discuss the hypothesis, presented in an our previous work, that the ultrafast periodic spectral modulations at fS=0.607±0.08 THz found in the spectra of 236 stars of the Sloan Digital Sky Survey (SDSS) were due to oscillations induced by dark matter (DM) cores in their centers that behave as oscillating boson stars. Two other frequencies were found by Borra in the redshift-corrected SDSS galactic spectra, f1,G=9.71−0.19+0.20 THz and f2,G=9.17−0.16+0.18 THz; the latter was then shown by Hippke to be a spurious frequency introduced by the data analysis procedure. Results: - Within the experimental errors, the frequency f1,G is the beating of the two frequencies, the spurious one, f2,G and fS that was also independently detected in a real solar spectrum, but not in the Kurucz’s artificial solar spectrum by Hippke, suggesting that fS could actually be a real frequency. Independent SETI observations by Isaacson et al., taken at different epochs, of four of these 236 stars could not confirm with high confidence - without completely excluding - the presence of fS in their power spectra and with the same power initially observed. Instead, the radio SETI deep-learning analysis with artificial intelligence (AI) gave an indirect confirmation of the presence of fS through the detection of a narrowband Doppler drifting of the observed radio signals in two stars, over a sample of 7 with a high S/N. These two stars belong to the set of the 236 SDSS stars. Numerical simulations confirm that this drifting can be due to frequency and phase modulation in time of the observed frequencies (1.3–1.7 GHz) with fS. Conclusions: - Assuming the DM hypothesis, the upper mass limit of the axion-like DM particle is ma≃2.4×103μeV, in agreement with the results from the gamma ray burst GRB221009A, laser interferometry experiments, suggesting new physics with additional axion-like particle fields for the muon g-2 anomaly.

Removing non-resonant background of CARS signal with generative adversarial network

Coherent anti-Stokes Raman scattering (CARS) microscopy requires the removal of non-resonant background (NRB) to ensure spectral accuracy and quality. This study introduces a deep-learning-based algorithm that leverages its enhanced capability for NRB removal and spectra retrieval. A generative adversarial network is trained using simulated noisy CARS data, enabling straightforward analysis of real CARS spectra obtained from pork belly and living mice brains. The results highlight the algorithm's ability to accurately extract vibrational information in the CH region. Importantly, this method eliminates the need for additional experimental measurements or extensive data preprocessing or postprocessing.

An indirect estimation of x-ray spectrum via convolutional neural network and transmission measurement

Objective. In this work, we aim to propose an accurate and robust spectrum estimation method by synergistically combining x-ray imaging physics with a convolutional neural network (CNN). Approach. The approach relies on transmission measurements, and the estimated spectrum is formulated as a convolutional summation of a few model spectra generated using Monte Carlo simulation. The difference between the actual and estimated projections is utilized as the loss function to train the network. We contrasted this approach with the weighted sums of model spectra approach previously proposed. Comprehensive studies were performed to demonstrate the robustness and accuracy of the proposed approach in various scenarios. Main results. The results show the desirable accuracy of the CNN-based method for spectrum estimation. The ME and NRMSE were −0.021 keV and 3.04% for 80 kVp, and 0.006 keV and 4.44% for 100 kVp, superior to the previous approach. The robustness test and experimental study also demonstrated superior performances. The CNN-based approach yielded remarkably consistent results in phantoms with various material combinations, and the CNN-based approach was robust concerning spectrum generators and calibration phantoms. Significance. We proposed a method for estimating the real spectrum by integrating a deep learning model with real imaging physics. The results demonstrated that this method was accurate and robust in estimating the spectrum, and it is potentially helpful for broad x-ray imaging tasks.

Anomalous dispersion, superluminality, and instabilities in two-flavor theories with local non-Hermitian mass mixing

Pseudo-Hermitian field theories possess a global continuous “similarity” symmetry, interconnecting the theories with the same physical particle content and an identical mass spectrum. In their regimes with real spectra, within this family of similarity transformations, there is a map from the non-Hermitian theory to its Hermitian similarity partner. We promote the similarity transformation to a local symmetry, which requires the introduction of a new vector similarity field as a connection in the similarity space of non-Hermitian theories. In the case of non-Hermitian two-flavor scalar or fermion mixing and by virtue of a novel IR/UV mixing effect, the effect of inhomogeneous non-Hermiticity then reveals itself via anomalous dispersion, instabilities, and superluminal group velocities at very high momenta, thus setting an upper bound on the particle momentum propagating through inhomogeneous backgrounds characterized by Lagrangians with non-Hermitian mass matrices. Such a non-Hermitian extension of the Standard Model of particle physics, encoded in a weak inhomogeneity of the non-Hermitian part of the fermion mass matrix, may nevertheless provide us with a low-energy particle spectrum consistent with experimentally observed properties. Published by the American Physical Society 2024

Quantization of second-order fermions

The quantization of a massive spin-1/2 field that satisfies the Klein-Gordon equation is studied. The framework is consistent, provided it is formulated as a pseudo-Hermitian quantum field theory by the redefinition of the dual field and the identification of an operator that modifies the inner product of states in Hilbert space to preserve a real energy spectrum and unitary evolution. Since the fermion field has mass dimension one, the theory admits renormalizable fermion self-interactions. Published by the American Physical Society 2024

From Pseudo to Real: Generalized Subspace Method for Power Spectrum Reconstruction

Subspace methods are widely used in statistical signal processing owing to their super-resolution. Conventional subspace methods, such as multiple signal classification (MUSIC) identify parameters containing frequency and direction of arrival by calculating pseudo-spectra without physical amplitudes. However, the real value of amplitude plays a significant role in fault diagnosis and condition monitoring. Additionally, due to hardware limitations and increased frequency, uniform (Nyquist) sampling becomes challenging. Nonuniform sampling, an alternative to high-rate sampling is common in practice. Consequently, Nonuniform (sub-Nyquist) signal processing methods are urgently required. In this paper, a generalized subspace method (GSM) is proposed to bridge the pseudo spectrum with the real spectrum. The proposed method is a supplement to the existing subspace methods and is applicable to both uniform and nonuniform sampling. In the GSM, the Fourier coefficient of the autocorrelation function is derived by signal subspace from the perspective of basis matching. Then, an alias-free real power spectrum is obtained by combining the power spectrum reconstructed by GSM with the classical pseudo spectrum. Finally, simulation and experiment demonstrate the performance of the proposed method in power spectrum reconstruction. Even under the dual influence of undersampled and nonuniform, the proposed method is still effective.

Влияние органического вещества и влажности на пересечение спектров диэлектрической проницаемости поч

The present study considers the crossover of the real part spectra of the complex dielectric constant obtained in the frequency range from 15 MHz to 15 GHz and temperature range from 0 to 25 °C for moist organic soils with the content of organic matter varying from 11 to 54 %. Based on the obtained experimental dependences, the empirical model is proposed to estimate the average value of the frequencies at which the crossover point of the soil dielectric constant spectra are observed with temperature changes. The proposed model also includes a formula for calculating the value of volumetric moisture at which the crossover point of the soil dielectric constant spectra appears.

Localization of overdamped bosonic modes and transport in strange metals

The strange metal phase of correlated electrons materials was described in a recent theory by a model of a Fermi surface coupled a two-dimensional quantum critical bosonic field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal were obtained for a wide range of intermediate temperatures, including the linear in temperature resistivity. The Harris criterion implies that spatial fluctuations in the local position of the critical point must dominate at lower temperatures. For an [Formula: see text]-component boson with [Formula: see text], we use multiple graphics processing units (GPUs) to compute the real frequency spectrum of the boson propagator in a self-consistent mean-field treatment of the boson self-interactions, but an exact treatment of multiple realizations of the spatial randomness from the random boson mass. We find that Landau damping from the fermions leads to the emergence of the physics of the random transverse-field Ising model at low temperatures, as has been proposed by Hoyos, Kotabage, and Vojta. This regime is controlled by localized overdamped eigenmodes of the bosonic scalar field, also has a resistivity which is nearly linear-in-temperature, and extends into a "quantum critical phase" away from the quantum critical point, as observed in several cuprates. For the [Formula: see text] Ising scalar, the mean-field treatment is not applicable, and so we use Hybrid Monte Carlo simulations running on multiple GPUs; we find a rounded transition and localization physics, with strange metal behavior in an extended region around the transition.

Spectrum of all multiplicative functions with application to powerfull numbers

Roughly speaking, the spectrum of multiplicative functions is the set of all possible mean values. In this paper, we are interested in the spectra of multiplicative functions supported over powerfull numbers. We prove that its real logarithmic spectrum takes values from −2/(4+2)=−0.26160... to 1 while it is known that the logarithmic spectrum of real multiplicative functions over all natural numbers takes values from 0 to 1. In the course of this study, we correct and complete the proof of Granville and Soundararajan on the spectrum of all multiplicative functions.

Time-Resolved Spectroscopy for Dynamic Investigation of Photoresponsive Metal-Organic Frameworks.

Photoresponsive MOFs with precise and adjustable reticular structures are attractive for light conversion applications. Uncovering the photoinduced carrier dynamics lays the essential foundation for the further development and optimization of the MOF material. With the application of time-resolved spectroscopy, photophysical processes including excimer formation, energy transfer/migration, and charge transfer/separation have been widely investigated. However, the identification of distinct photophysical processes in real experimental MOF spectra still remains difficult due to the spectral and dynamic complexity of MOFs. In this Perspective, we summarize the typical spectral features of these photophysical processes and the related analysis methods for dynamic studies performed by time-resolved photoluminescence (TR-PL) and transient absorption (TA) spectroscopy. Based on the recent understanding of excited-state properties of photoresponsive MOFs and the discussion of challenges and future outlooks, this Perspective aims to provide convenience for MOF kinetic analysis and contribute to the further development of photoresponsive MOF material.

Non-Hermitian Systems with a Real Spectrum and Selective Skin Effect

In this work, we first show a simple approach to constructing non-Hermitian Hamiltonians with a real spectrum, which are not obtained by a non-unitary transformation such as the imaginary gauge transformation. They are given, instead, by the product of a Hermitian Hamiltonian H0 and a positive semi-definite matrix A. Depending on whether A has zero eigenvalue(s), the resulting H can possess an exceptional point at zero energy. When A is only required to be Hermitian instead, the resulting H is pseudo-Hermitian that can have real and complex conjugate energy levels. In the special case where A is diagonal, we compare our approach to an imaginary gauge transformation, which reveals a selective non-Hermitian skin effect in our approach, i.e., only the zero mode is a skin mode and the non-zero modes reside in the bulk. We further show that this selective non-Hermitian skin mode has a much lower lasing threshold than its counterpart in the standard non-Hermitian skin effect with the same spatial profile, when we pump at the boundary where they are localized. The form of our construction can also be found, for example, in dynamical matrices describing coupled frictionless harmonic oscillators with different masses.

Exceptional Entanglement and Quantum Sensing with a Parity‐Time‐Symmetric Two‐Qubit System

AbstractParity‐time (PT) symmetric systems with gain‐loss balanced structures can have entirely real eigenenergy spectra despite their non‐Hermitian nature, leading to peculiar discoveries such as single‐mode lasers, wireless power transfer, and non‐reciprocal light propagation. Recently, the study of PT‐symmetry has extended to the quantum realm, inspiring a search for PT‐symmetric quantum effects as well as their unique applications. Here, quantum entanglement and sensing with a PT‐symmetric system of two qubits are studied with Ising‐type interaction. It is shown that exceptional points (EPs) can induce exceptional entanglement phenomena such as collapse‐revival and steady‐state entanglement on the two sides of EPs. The entanglement in the PT‐symmetric system is also found to be generated more quickly than that in the Hermitian counterpart. In addition, a scheme for realizing EP‐enhanced quantum sensing is proposed by calculating the quantum Fisher information to estimate the parameters of the system. The work provides new insights into EP‐engineered quantum effects and can benefit a wide range of applications based on non‐Hermitian quantum devices.

Kinematic analysis and bearing capacity optimization of fully decoupled two-rotation mechanisms

Abstract. The existing vehicle durability test platform has low accuracy in reproducing the road spectrum and cannot meet the demand for high-accuracy road spectrum reproduction. In order to meet the need for high accuracy in road spectrum reproduction of vehicle durability tests, this paper is based on an analysis of the factors affecting the accuracy of the test platform. From the perspective of mechanism innovation, a fully decoupled two-rotation parallel mechanism with large load-bearing capacity for vehicle durability testing is proposed in this paper. A new solution is provided to improve the road spectrum reproduction accuracy of the test platform. Based on the requirement of reproduction accuracy of a real road spectrum, inverse kinematics, velocity Jacobians, and workspaces of mechanisms are analyzed. The inverse kinematics and velocity Jacobian analysis of parallel mechanisms can lay a research foundation for the subsequent calculation of load-bearing capacity indexes. The design of the parallel mechanism is based on the performance requirements of large load capacity and complete decoupling. A new index for evaluating the global average carrying capacity of a mechanism is proposed. Based on this index and the atlas method, the dimensional parameters of the mechanism have been optimized. A finite-element simulation study is carried out, and it is proved that the optimized fully decoupled two-rotation parallel mechanism can satisfy the bearing capacity requirements of the platform test. The large load capacity and fully decoupled mechanism proposed in the research work of this paper can improve the road spectrum reproduction accuracy of the vehicle durability test platform and has good application prospects in the field of vehicle durability tests.

Geometric Origin of Non-Bloch PT Symmetry Breaking.

The parity-time (PT) symmetry of a non-Hermitian Hamiltonian leads to real (complex) energy spectrum when the non-Hermiticity is below (above) a threshold. Recently, it has been demonstrated that the non-Hermitian skin effect generates a new type of PT symmetry, dubbed the non-Bloch PT symmetry, featuring unique properties such as high sensitivity to the boundary condition. Despite its relevance to a wide range of non-Hermitian lattice systems, a general theory is still lacking for this generic phenomenon even in one spatial dimension. Here, we uncover the geometric mechanism of non-Bloch PT symmetry and its breaking. We find that non-Bloch PT symmetry breaking occurs by the formation of cusps in the generalized Brillouin zone (GBZ). Based on this geometric understanding, we propose an exact formula that efficiently determines the breaking threshold. Moreover, we predict a new type of spectral singularities associated with the symmetry breaking, dubbed non-Bloch van Hove singularity, whose physical mechanism fundamentally differs from their Hermitian counterparts. This singularity is experimentally observable in linear responses.

Hilbert space fragmentation imposed real spectrum of non-Hermitian systems

Hilbert space fragmentation imposed real spectrum of non-Hermitian systems

Parity–time-symmetric photonic topological insulator

Topological insulators are a concept that originally stems from condensed matter physics. As a corollary to their hallmark protected edge transport, the conventional understanding of such systems holds that they are intrinsically closed, that is, that they are assumed to be entirely isolated from the surrounding world. Here, by demonstrating a parity–time-symmetric topological insulator, we show that topological transport exists beyond these constraints. Implemented on a photonic platform, our non-Hermitian topological system harnesses the complex interplay between a discrete coupling protocol and judiciously placed losses and, as such, inherently constitutes an open system. Nevertheless, even though energy conservation is violated, our system exhibits an entirely real eigenvalue spectrum as well as chiral edge transport. Along these lines, this work enables the study of the dynamical properties of topological matter in open systems without the instability arising from complex spectra. Thus, it may inspire the development of compact active devices that harness topological features on-demand.

Nirdust: probing hot dust emission around type 2 AGN using K-band spectra

ABSTRACT Hot dust in the proximity of active galactic nuclei (AGNs) strongly emits in the near-infrared producing a red excess that, in type 2 sources, can be modelled to measure its temperature. In the era of high spatial resolution multiwavelength data, mapping the hot dust around supermassive black holes is important for the efforts to achieve a complete picture of the dust’s role and distribution around these compact objects. In this work, we propose a methodology to detect the hot dust emission in the proximity of type 2 AGNs and measure its temperature using K-band spectra (λc = 2.2 µm). To achieve this, we have developed nirdust, a python package for modelling K-band spectra, estimating the dust temperature, and characterizing the involved uncertainties. We tested synthetic and real spectra in order to check the performance and suitability of the physical model over different types of data. Our tests on synthetic spectra demonstrated that the obtained results are influenced by the signal-to-noise ratio (S/N) of the input spectra. However, we accurately characterized the uncertainties, which remained below ∼150 K for an average S/N per pixel exceeding 20. Applying nirdust to NGC 5128 (Centaurus A), observed with the Gemini South Telescope, we estimated a dust temperature of 662 and 667 K from Flamingos-2 spectra and 697 and 607 K from Gemini Near-Infrared Spectrograph (GNIRS) spectra using two different approaches.

Floristic diversity of plant communities in sandy wadis of the northern Algerian Sahara (Ghardaïa region)

Plant species diversity was studied in 20 sandy wadis of the northern Algerian Sahara (Ghardaïa region). Based on subjective sampling, 20 floristic surveys were carried out in the various sandy biotopes in February-April 2022. Through an ascending hierarchical analysis, we distinguished 3 phytoecological groups and assessed their functional, biogeographic, and abundance characteristics. The recorded plants represented 15 species (296 individuals) belonging to 15 genera of 10 botanical families. The most represented families were the Fabaceae, Anacardiaceae, Brassicaceae, and Poaceae. In terms of the real plant-life spectrum, hemicryptophytes (51.7% of individuals) dominated the sandy wadis, followed by chamaephytes (33.1%) and phanerophytes (15.2%). In the real dispersal spectrum, the barochores prevailed (60%). The real phytogeographic spectrum shows that the Saharan endemic element reached the highest share (32.7%). In terms of abundance, an analysis of the real spectrum revealed that very common species (52%) dominate in the Ghardaïa region, but some fairly rare plants were also found. Indeed, the sandy biotopes of the wadis of the Ghardaïa region are valuable habitats for the conservation of plant species in the northern Algerian Sahara.