Spectral Function Research Articles

ABSTRACT Ships operating in complex seas exhibit pronounced six-degree-of-freedom motions—roll, pitch, yaw, heave, sway, and surge—complicating helicopter operations, search and rescue, and unmanned surface vessel autonomy. We construct a realistic prediction setting by synthesizing wave excitations from stochastic models driven by spectral density functions and coupling them with a ship response model to create a 6-DoF dataset. We then propose an attitude prediction framework that integrates empirical mode decomposition (EMD) with deep learning. EMD performs multi-scale decomposition and reconstruction to separate primary trends from high-frequency disturbances, simplifying the signals. A convolutional neural network extracts discriminative features from each intrinsic mode, while a long short-term memory network models temporal dependencies and forecasts future values. The predicted modal components are recombined to yield complete pose predictions. Experiments demonstrate high accuracy and strong generalization across motion modes, indicating the method’s potential to enhance operational safety and autonomy in maritime applications.

The Huanjing-2A/2B (HJ-2A/2B) satellites are China’s next-generation environmental monitoring satellites, equipped with four visible light wide-swath charge-coupled device (CCD) sensors. These sensors enable the acquisition of 16-m multispectral imagery (16m-MSI) with a swath width of 800 km through field-of-view stitching. However, traditional vicarious calibration techniques are limited by their calibration frequency, making them insufficient for continuous monitoring requirements. To address this challenge, the present study proposes a spectral-angle difference correction-based cross-calibration approach, using the Landsat 8/9 Operational Land Imager (OLI) as the reference sensor to calibrate the HJ-2A/2B CCD sensors. This method improves both radiometric accuracy and temporal frequency. The study utilizes cloud-free image pairs of HJ-2A/2B CCD and Landsat 8/9 OLI, acquired simultaneously at the Dunhuang and Golmud calibration sites between 2021 and 2024, in combination with atmospheric parameters from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) dataset and historical ground-measured spectral reflectance data for cross-calibration. The methodology includes spatial matching and resampling of the image pairs, along with the identification of radiometrically stable homogeneous regions. To account for sensor viewing geometry differences, an observation-angle linear correction model is introduced. Spectral band adjustment factors (SBAFs) are also applied to correct for discrepancies in spectral response functions (SRFs) across sensors. Experimental results demonstrate that the cross-calibration coefficients differ by less than 10% compared to vicarious calibration results from the China Centre for Resources Satellite Data and Application (CRESDA). Additionally, using Sentinel-2 MSI as the reference sensor, the cross-calibration coefficients were independently validated through cross-validation. The results indicate that the radiometrically corrected HJ-2A/2B 16m-MSI CCD data, based on these coefficients, exhibit improved radiometric consistency with Sentinel-2 MSI observations. Further analysis shows that the cross-calibration method significantly enhances radiometric consistency across the HJ-2A/2B 16m-MSI CCD sensors, with radiometric response differences between CCD1 and CCD4 maintained below 3%. Error analysis quantifies the impact of atmospheric parameters and surface reflectance on calibration accuracy, with total uncertainty calculated. The proposed spectral-angle correction-based cross-calibration method not only improves calibration accuracy but also offers reliable technical support for long-term radiometric performance monitoring of the HJ-2A/2B 16m-MSI CCD sensors.

Angle-resolved photoemission spectroscopy is the leading tool for studying the symmetry and structure of the order parameter in superconductors. The recent improvement of the technique made it possible to detect the superconducting energy gap at the surface of topological t- PtBi 2 via observation of the record-breaking narrow line shapes. The promising new physics uncovered requires further investigation of the spectral and gap functions of t- PtBi 2 , but the challenging experimental conditions severely limit the application of conventional ARPES setups. In this work, we use synchrotron-based measurements and show that the gap at the surface Fermi arc in t- PtBi 2 can be detected even with more relaxed experimental conditions than in our previous laser-based studies. At the same time, using simple model of ARPES spectra, we identify the minimum requirements to detect the gap and consider cases where the gap cannot be resolved.

We have recently presented the multichannel Dyson equation as an alternative to the standard single-channel Dyson equation. While the latter involves a single many-body Green's function, the former uses a multichannel Green's function in which two or more many-body Green's functions are coupled. Quasiparticles and satellites are thus naturally treated on equal footing in the multichannel Dyson equation. To assess the accuracy of our approach, we apply it here to the ground- and excited-state properties of the extended Hubbard dimer, an exactly solvable model for H2. In particular, we focus on the potential energy surface as well as the corresponding spectral functions and HOMO-LUMO gaps, which are well-known challenges for many-body approximations such as second Born and GW. We show that the multichannel Dyson equation gives overall very good results for all properties considered and outperforms both GW and second Born. In particular, the multichannel Dyson equation yields the correct ground-state energy and HOMO-LUMO gap in the dissociation limit contrary to GW.

We introduce a framework for describing the real-time dynamics of quantum impurity models out of equilibrium which is based on the influence matrix approach. By replacing the dynamical map of a large fermionic quantum environment with an effective semigroup influence matrix (SGIM) which acts on a reduced auxiliary space, we overcome the limitations of previous proposals, achieving high accuracy at long evolution times. This SGIM corresponds to a uniform matrix-product state representation of the influence matrix and can be obtained by an efficient algorithm presented in this Letter. We benchmark this approach by computing the spectral function of the single impurity Anderson model with high resolution. Further, the spectrum of the effective dynamical map allows us to obtain relaxation rates of the impurity toward equilibrium following a quantum quench. Finally, for a quantum impurity model with on-site two-fermion loss, we compute the spectral function and confirm the emergence of Kondo physics at large loss rates.

ABSTRACT Harmonizing various satellite imagery could enhance Earth observation capabilities by facilitating the generation of dense time series of fine-resolution data, which is crucial for the monitoring of large-scale environmental changes. The Chinese Gaofen-6 Wide Field View (GF-6 WFV) and Sentinel-2 Multispectral Instrument (S2 MSI) are particularly suitable for such harmonization due to their similar spectral and spatial characteristics. Assessing the radiometric consistency of these instruments under various observation conditions is crucial for successful data integration. The objective of this study is to conduct a comprehensive cross-comparison analysis of WFV and MSI. In this paper, we assessed radiometric consistency across top-of-atmosphere (TOA) reflectance, bottom-of-atmosphere (BOA) reflectance, and nadir reflectance adjusted for bidirectional reflectance distribution function (BRDF) effects (BRDF-corrected) in near-contemporaneous observations for six bands between the MSI and WFV imagery. We evaluated differences using absolute difference metrics and reduced major axis regression (RMA) analysis between 16 image pairs across China in 2020, under various observation conditions, including different illumination angles, atmospheric conditions, and land cover types. RMA regression results indicate that simulated WFV and MSI surface reflectance derived using the sensor spectral response functions (SRFs) and laboratory spectra showed high radiometric agreement (R 2 > 0.9). However, the observed reflectance revealed significant discrepancies, primarily attributed to wider field-of-view of GF-6 WFV. Incorporating the pixel-level view zenith angle during atmospheric correction significantly improved the radiometric consistency of both products. Root-mean-square deviation (RMSD) values ranging from 0.0199 to 0.0390 were obtained between MSI and WFV TOA reflectance, and RMSD values ranging from 0.0202 to 0.0369 were obtained from BOA reflectance. The improvement was particularly pronounced in the red edge 2 band, evidenced by a 22% reduction in the RMSD and a 65% decrease in bias between the two instruments. This study also identifies the necessity of BRDF correction for wide field-of-view sensors like GF-6 WFV.

Based on a coupled-channel approach, we investigate the structures of four Pc states through compositeness criteria. Toward a more precise description of the states, we have obtained refined fit results of the LHCb data on the J/ψp invariant mass distribution of the Λb0→J/ψpK− decay. Allowing for the fact that each of the four Pc states couples strongly to a nearby S-wave channel, three criteria on the compositeness/elementariness are adopted in this study: the pole-counting rule, the spectral density function, and the Gamow wave function. Compositeness information is extracted from the scattering amplitudes and the pole parameters (pole positions and residues), without any preconceived assumptions on the nature of the Pc states and without any dependence on the model parametrization. Consistently within the framework of all the three methods, it has been found that the Pc(4312)1/2− is mainly composed by D¯Σc, Pc(4380)3/2− by D¯Σc*, while the Pc(4440)1/2− and Pc(4457)3/2− states both turn out as composite states of D¯*Σc. The upper limits of the values of their elementariness are estimated to be rather small. This paper provides an additional confirmation of the molecular interpretation for the Pc states in the literature.

We study dynamical properties of strongly coupled chiral matter by using the holographic method. We demonstrate, at both linear and nonlinear levels, that perturbations on thermodynamically unstable backgrounds within the spinodal region of chiral first-order phase transitions exhibit dynamic instability. The corresponding magnitude of dynamic instability can be characterized by the critical momentum. Furthermore, we found that, within a certain temperature range, the quasinormal-mode spectrum contains purely imaginary diffusive modes. As spatial momentum increases, a transition occurs in the system’s long-time dynamics. The dominant contribution shifts from diffusive mode to propagating mode. When the diffusive mode becomes dominant, the spectral function exhibits a transport peak structure in the low-frequency region. A heuristic argument suggests that this particular transition can be related to the chiral symmetry breaking and restoration.

The spin polarization for a baryon in a hydrodynamic medium has been extensively studied in the weakly coupled regime using quantum kinetic theory. As a first study of this problem in the strongly coupled regime, we investigate holographically the spectral function of a probe baryon in the fluid-gravity background. This is done by carefully performing gradient expansion of the Dirac equation in the fluid-gravity background. Different contributions in the expansion are understood in terms of density matrices of the probe baryon and the medium. The resulting spectral functions indicate that the holographic baryon is polarized as responses to fluid acceleration, shear stress, and vorticity. The structures of the responses are similar to those found in weakly coupled studies.

The multipoint numerical renormalization group (mpNRG) is a powerful impurity solver that provides accurate spectral data useful for computing local, dynamic correlation functions in imaginary or real frequencies nonperturbatively across a wide range of interactions and temperatures. It gives access to a local, nonperturbative four-point vertex in imaginary and real frequencies, which can be used as input for subsequent computations such as diagrammatic extensions of dynamical mean-field theory. However, computing and manipulating the real-frequency four-point vertex on large, dense grids quickly becomes numerically challenging when the density and/or the extent of the frequency grid is increased. In this paper, we compute four-point vertices in a strongly compressed quantics tensor train format using quantics tensor cross interpolation, starting from discrete partial spectral functions obtained from mpNRG. This enables evaluations of the vertex on frequency grids with resolutions far beyond the reach of previous implementations. We benchmark this approach on the four-point vertex of the single-impurity Anderson model across a wide range of physical parameters, both in its full form and in its asymptotic decomposition. For imaginary frequencies, the full vertex can be represented to an accuracy on the order of 2×10−3 with maximum bond dimensions not exceeding 120. The more complex full real-frequency vertex requires maximum bond dimensions not exceeding 170 for an accuracy of ≲2%. Our work marks another step toward tensor-train-based diagrammatic calculations for correlated electronic lattice models starting from a local, nonperturbative mpNRG vertex.

The simulation of quantum many-body systems, relevant for quantum chemistry and condensed matter physics, is one of the most promising applications of near-term quantum computers before fault-tolerance. However, since the vast majority of quantum computing technologies are built around qubits and discrete gate-based operations, the translation of the physical problem into this framework is a crucial step. This translation will often be device specific, and a suboptimal implementation will be punished by the exponential compounding of errors on real devices. The importance of an efficient mapping is already revealed for models of spinful fermions in two or three dimensions, which naturally arise when the relevant physics relates to electrons. Using the most direct and well-known mapping, the Jordan-Wigner transformation, leads to a nonlocal representation of local degrees of freedom, and necessities efficient decompositions of nonlocal unitary gates into a sequence of hardware accessible local gates. In this paper, we provide a step-by-step recipe for simulating the paradigmatic two-dimensional Fermi-Hubbard model on a quantum computer using only local operations. To provide the ingredients for such a recipe, we briefly review the plethora of different approaches that have emerged recently but focus on the Derby-Klassen compact fermion mapping to make our discussion concrete. We provide a detailed recipe for an end-to-end simulation including embedding on a physical device, preparing initial states such as ground states, simulation of unitary time evolution, and measurement of observables and spectral functions. We explicitly compute the resource requirements for simulating a global quantum quench and conclude by discussing the challenges and future directions for simulating strongly correlated fermionic matter on quantum computers.

Abstract We study real-time finite-temperature correlators for free scalars of any mass in a dS d+1 static patch in any dimension. We show that whenever the inverse temperature is a rational multiple of the inverse de Sitter temperature, certain Matsubara poles of the symmetric Wightman function disappear. At the de Sitter temperature, we explicitly show how the Lorentzian thermal correlators can all be obtained by analytic continuations from the round S d+1. We establish the precise relation between the Harish-Chandra character for SO(1, d + 1) and the integrated spectral function, providing a novel dynamical perspective on the former and enabling generalizations. Furthermore, we study scalars with exceptional non-positive masses. We provide a physical picture for the distinctive structures of their characters. For the massless case, we perform a consistent static patch quantization, and find the unique S d+1 correlator that analytically continues to the correlators in the quantum theory.

Abstract This paper deals with a method for quantitative assessment of damage severity in composite laminates by an in-field inspection technique known as acousto-ultrasonics (AU). In this technique, Lamb waves are transmitted through a damage zone in composite laminates and the received waves are analysed by transforming them from time domain to frequency domain. From the frequency domain description of the signals, certain factors, called stress wave factors, defined on the power spectral density function, are then correlated with the measures of damage that has interacted with the transmitted waves. The application of the AU technique is described here for the case of transverse cracking and delamination in cross ply laminates.

Research on the construction of power spectral density function on the core barrel surface of pressurized water reactor

This study presents a novel methodology for estimating Suspended Sediment Concentration (SSC) in the Mula Dam reservoir, Maharashtra, by integrating in-situ hyperspectral reflectance with Sentinel-2 satellite imagery. While conventional remote sensing techniques or field-based spectroscopy have been employed independently for SSC monitoring, this research introduces a spectral integration framework that bridges these two data sources through a transitive relation model. Field data collection was conducted from October 2021 to February 2022, during which 121 surface water samples were obtained and their spectral signatures recorded using an SVC HR-1024i Spectroradiometer. Simultaneously, Sentinel-2 MSI Level 2A images were processed to extract spectral reflectance at corresponding sampling points. Strong correlations were observed between SSC and reflectance in the Green, Red, and Red Edge 1 bands. Multiple spectral indices and band ratios were evaluated to identify optimal SSC estimators, with the combination (Green × Red Edge 1)/Red demonstrating the highest predictive capability. A spectral integration function was developed using a two-stage regression approach: first, linking observed SSC to Spectroradiometer-derived indices; second, connecting these indices to Sentinel-2 reflectance data. The resulting models were validated using linear regression, Student’s t-test, residual analysis, and k-fold cross-validation. Among all models, the (Green × Red Edge 1)/Red function achieved superior performance with an R2 of 0.80, RMSE of 8.58 mg/L, and MAPE of 19.41%. The approach was further tested for temporal SSC mapping using past Sentinel-2 imagery, revealing seasonal sediment trends. The study concludes that the proposed spectral integration method provides a robust, scalable, and transferable framework for accurate SSC monitoring in large water bodies. This advancement holds significant implications for sediment management, water quality assessment, and hydrological research.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-15719-w.

ABSTRACTThis article explores the solvability and approximate controllability of a new class of neutral impulsive stochastic integro‐differential systems. These systems are uniquely characterized by their use of fractional calculus to model real‐world behavior, the inclusion of hemivariational inequalities and impulsive terms to capture nonlinearities and sudden changes, and a history‐dependent operator to account for memory effects. The research demonstrates solvability through a fixed‐point framework that combines stochastic analysis, the generalized Clarke subdifferential, and fractional calculus. A numerical example illustrates the practical application of these findings, incorporating a comprehensive framework that uses fractional finite differences for the Caputo derivative, Monte Carlo sampling for stochastic forcing, and finite difference methods for spatial derivatives. The study highlights the effectiveness of selecting a Gaussian spectral decay function in the Monte Carlo approximation for enhancing numerical stability and accuracy, thereby advancing numerical techniques for these complex stochastic models.

The properties of bound states are fundamental to hadronic spectroscopy and play a central role in the transition from hadronic matter to a quark-gluon plasma (QGP). In a strongly coupled QGP (sQGP), the interplay of temperature, binding energy, and large collisional widths of the partons poses formidable challenges in evaluating the in-medium properties of hadronic states and their eventual melting. In particular, the existence of heavy quarkonia in the QGP is a long-standing problem that is hard to solve by considering their spectral properties on the real-energy axis. We address this problem by analyzing in-medium thermodynamic quarkonium T matrices in the complex energy plane. We first validate this method in vacuum, where the T-matrix poles of observed states are readily identified. When deploying this approach to recent self-consistently calculated T matrices in the QGP, we find that poles in the complex energy plane can persist to surprisingly large temperatures, depending on the strength of the in-medium interactions. While the masses and widths of the pole positions are precisely defined, the notion of a binding energy is not due to the absence of thresholds caused by the (large) widths of the underlying quark or anti-quark spectral functions. Our method thus provides a new and definitive quantum-mechanical criterion to determine the melting temperature of hadronic states in the sQGP while increasing the accuracy in the theoretical determination of transport parameters.

The design of carbon allotropes that simultaneously exhibit mechanical robustness and quantum functionalities remains a longstanding challenge. Here, we report a comprehensive first-principles study of cT16, a three-dimensional sp2-hybridized carbon network with topologically interlinked graphene-like sheets. The structure features high ideal tensile and shear strengths, with pronounced anisotropy arising from strain-induced bond rehybridization and interlayer slipping mechanisms. Electronic structure calculations reveal that cT16 is intrinsically metallic, with dispersive π-bands crossing the Fermi level. Phonon dispersion confirms its dynamical stability, and analysis of the Eliashberg spectral function yields a moderate electron-phonon coupling constant (λ = 0.481) and a logarithmic average frequency of 696.2 K. The superconducting transition temperature is estimated to reach 7.2 K at via the Allen-Dynes formula, without requiring any external doping or intercalation. Compared to existing carbon superconductors such as CaC6 or boron-doped diamond, cT16 uniquely combines chemical purity, structural resilience, and intrinsic superconductivity. These findings position cT16 as a promising lightweight carbon superconductor and expand the functional landscape of three-dimensional sp2-carbon frameworks.

Remote sensing imaging satellites play a vital role in Intelligence, Surveillance, and Reconnaissance (ISR) missions, as they enable the acquisition of information from virtually any location on the Earth’s surface. To ensure the reliability of the provided information, it is essential to calibrate the onboard sensors on these satellites. This paper aims to present a methodology for spectral and radiometric calibration of a Parrot Sequoia camera in laboratory settings. This camera features four monochromatic sensors and one RGB sensor, similar to those onboard orbital platforms. The methodology described employs equipment available at the Laboratory of Radiometry and Characterization of Electro-Optical Sensors (LaRaC) at the Institute for Advanced Studies (IEAv). The paper presents the Spectral Response Functions (SRFs) of the camera sensors, as well as the Radiometric Calibration data. It is worth noting that the proposed methodology can be replicated for any other orbital electro-optical imaging sensor.

In this work, using two distinct semiclassical approaches-namely, the mean-field Ehrenfest method and the mapping approach to surface hopping-we investigate the spectral function of a single charge interacting with phonons on a lattice. This quantity is relevant for the description of angle-resolved photoemission experiments. Focusing on the one-dimensional Holstein model, we compare the performance of these approaches across a range of coupling strengths and lattice sizes, exposing the relative strengths and weaknesses of each. We demonstrate that these approaches can be efficiently applied with reasonable accuracy to abinitio polaron models. Our work provides a route to the calculation of spectral properties in realistic electron-phonon-coupled systems in a computationally inexpensive manner with encouraging accuracy.