Spectral Factor Research Articles

Correlation of Visible Reflectance Spectrometry and Portable Raman Data for Red Pigment Identification

The accurate identification of pigments is of principal relevance in the field of cultural heritage conservation and restoration practices. In this preliminary study, a first attempt to set up a procedure for accurate red pigment identification, based on the assessment of the correlations existing between visible reflectance spectrometry (vis-RS) and Raman data, is presented. The proposed approach involved the realization of a library consisting of data acquired on a set of 35 pure red historical pigments supplied by ©Kremer Pigmente. In particular, vis-RS data, collected through a Konica Minolta CM-2600d spectrophotometer, were registered, together with the position of the Extrema Points (E.P.s) encompassing both the maximum and minimum points of the first derivative of the % spectral reflectance factor (SRF%) curves. Portable Raman spectroscopy measurements were collected by a B&W Tek Inc. portable Raman spectrometer equipped with a 785 nm laser. For each tested pigment, the positions and relative intensities of the characteristic Raman peaks were considered. The library was then tested for the characterization of the red/reddish painted areas of the medieval wall painting located within The Norman Castle of Aci Castello (Catania, Italy), and was shown to be essential for the unambiguous identification of the pigment used. It is worth noting that this study represents the first novel attempt to establish a reliable and efficient methodology for pigment identification, offering promising prospects in reducing uncertainties and ambiguities arising from the application of a single stand-alone approach.

Implications of input ground-motion selection techniques on site response analyses for different tectonic settings

This study investigates how current practices of input ground-motion selection influence site response analysis results and their variability, when considering different tectonic settings. Study sites in Seattle and Boston are chosen to represent tectonic settings with contributions to the seismic hazard from shallow crustal and subduction events, as well as stable continental regions, respectively. Selected input ground-motion suites for one-dimensional site response analysis represent variations in the target spectrum definition, spectral period of interest, seismic source, and ground-motion database. When directly incorporating different types of seismic sources (e.g. shallow crustal versus subduction) into target spectrum definitions and selecting ground motions from the corresponding databases (i.e. consistent with such seismic sources), differences on the estimated site response and its variability are observed. These effects are captured by spectral amplification factors and nonspectral intensity measures (significant duration and Arias intensity) and become particularly apparent for subduction zones. The variability in spectral amplification factors stemming from ground-motion selection techniques is found to be also a function of the characteristics of the site, becoming higher near the fundamental period of the site. Estimated responses at stiffer sites are more significantly influenced by ground-motion selection techniques, whereas the onset of nonlinear soil behavior at softer sites can reduce such variability.

Towards interpretable machine learning for observational quantification of soil heavy metal concentrations under environmental constraints

Monitoring heavy metal concentrations in soils is central to assessing agricultural production safety. Satellite observations permit inferring concentrations from spectrum, thereby contributing to the prevention and control of soil heavy metal pollution. However, heavy metals exhibit weak spectral responses, particularly at low and medium concentrations, and are predominantly influenced by other soil components. Machine learning (ML)-driven modelling can produce predictions but lacks interpretability. Here, we present an interpretable ML framework for concentration quantification modelling and investigated the contributions of spectral and environmental factors—pH and organic carbon—to the estimation of metals with multiple concentration gradients, as analysed through SHAP (SHapley Additive exPlanations) data derived from four learning-based scenarios. The results indicated that scenarios SHC (spectral, pH, and organic carbon) and SH (spectral and pH) were the most optimal for chromium (Cr) [RPD = 1.42, Adj R2 = 0.62], and cadmium (Cd) [RPD = 1.80, Adj R2 = 0.80]. Under environmental constraints, the spectral predictability for Cr and Cd was improved by 67 % and 87 %, respectively. We concluded that interpretable modelling, utilising both spectral and soil environmental factors, holds significant potential for estimating heavy metals across concentration gradients. It is recommended that samples with higher organic carbon content and lower pH be selected to enhance Cr and Cd predictions. An advanced grasp of interpretable predictions facilitates earlier warning of heavy metal contamination and guides the formulation of robust sampling strategies.

Ensefgram: An optimal demodulation band selection method for the early fault diagnosis of high-speed train bearings

Early fault diagnosis of high-speed train bearings under road spectrum shocks is challenging. As a conventional narrowband demodulation method, the Fast Kurtogram (FK) class of algorithms have some drawbacks: the fixed-band segmentation strategy makes it difficult for the method to find the optimal demodulation frequency band (ODFB); other major limitations are the poor robustness of the statistical index of the blind algorithm and the poor adaptiveness of the target algorithm given the need to the know the bearing operating state in advance. To address these issues, this paper proposes Ensefgram, an early fault detection method for high-speed train bearings with the acoustic emission signal as an example. First, a filter bank is designed by combining the spectral trend with the median dichotomy strategy, which adaptively segments the frequency band and retains the integrity of the sub-band fault components to the maximum extent. In addition, a novel statistical index, termed the maximum weighted spectral energy frequency factor, is proposed, and it is combined with the envelope spectrum negentropy (ES-negentropy) to form a composite index ENSEF, which can select the ODFB blindly. Finally, the proposed method was validated by simulation and applying test signals close to the real working conditions of a high-speed train. Compared with FK, Infogram, and other methods, Ensefgram provides more accurate detection results for the early fault diagnosis of bearings.

Many-body quantum chaos in mixtures of multiple species.

We study spectral correlations in many-body quantum mixtures of fermions, bosons, and qubits with periodically kicked spreading and mixing of species. We take two types of mixing, namely, Jaynes-Cummings and Rabi, respectively, satisfying and breaking the conservation of a total number of species. We analytically derive the generating Hamiltonians whose spectral properties determine the spectral form factor in the leading order. We further analyze the system-size (L) scaling of Thouless time t^{*}, beyond which the spectral form factor follows the prediction of random matrix theory. The L dependence of t^{*} crosses over from lnL to L^{2} with an increasing Jaynes-Cummings mixing between qubits and fermions or bosons in a finite-size chain, and it finally settles to t^{*}∝O(L^{2}) in the thermodynamic limit for any mixing strength. The Rabi mixing between qubits and fermions leads to t^{*}∝O(lnL), previously predicted for single species of qubits or fermions without total-number conservation.

Effect of Zirconium Content on Defect Structure and Light Damage Resistance of Zr:Dy:LiNbO3 Crystals

AbstractIn this paper, Zr:Dy:LiNbO3 crystals are prepared by traditional pull‐up method, in which Zr4+ doping concentrations are 0, 1, 2, and 4 mol%, respectively. In this paper, the defective structure of Zr:Dy:LiNbO3 crystals and their resistance to photodamage under different Zr4+ concentration doping are studied. Firstly, the influence of Zr4+ doping concentration on the defective structure of Zr:Dy:LiNbO3 crystal and the occupancy of doped ions under different Zr4+ concentrations are tested and discussed by infrared (IR) absorption spectroscopy and ultraviolet‐visible near‐infrared (UV–vis–NIR) absorption spectroscopy. The Judd–Ofelt theoretical analysis results show that when the concentration of doped Zr4+ is 2 mol%, the spectral quality factor (X) of Dy3+ in lithium niobate crystals is significantly improved compared with that of Dy3+ in other crystals. Secondly, resistance to photodamage of Zr:Dy:LiNbO3 crystals is studied and analyzed by the light scattering exposure energy flow threshold method. The results show that when the concentration of doped Zr4+ ions reaches 4 mol%, the exposure energy value is increased by 210 times compared with the no doping, which greatly improves the anti‐photodamage performance of the crystal.

High spectral efficiency modulation scheme based on joint interaction of orthogonal compressed chirp division multiplexing and power superimposed code.

In this paper, we propose a high spectral efficiency modulation scheme based on joint interaction of orthogonal compressed chirp division multiplexing (OCCDM) and power superimposed code (PSC) under the intensity modulation and direct detection (IM/DD) system. OCCDM is a novel orthogonal chirp division multiplexing technology featuring spectral compression through the implementation of processing similar to a discrete Fourier transform, enhancing the spectral efficiency (SE) through bandwidth savings without loss of orthogonality of each chirp. Meanwhile, PSC technology enables multiple code words being transmitted superimposed on the same chirp. This technique involves allocating varying power levels to different users, thereby distinguishing them, increasing the transmission's net bit rate and substantially boosting the SE. The transmission has been performed experimentally using a 2 km 7-core fiber span. The impact of the above-mentioned technologies on the bit error rate (BER) performance is assessed in the power, frequency, and joint domain. The BER and enhancements in the SE can be balanced when the spectral bandwidth compression factor (α) and power distribution ratio are equal to 0.9 and 4, respectively. The observed outcome leads to the transmission's SE increase to more than double the baseline value, at 2.22 times. Based on the above analysis, we believe this structure is expected to become a potential for developing next-generation PON.

Durational and spectral factors in judgements of American Raising

Canadian Raising and its relatives in the USA can respond to underlying voicing of flapped /t/ (Raised “writer” vs. un-Raised “rider") from the earliest stages (Fruehwald 2016). How so, if Raising is phonologized from a phonetic precursor sensitive only to phonetic features? Proposal (Bermúdez-Otero 2019): Raising responds to duration, not voicing: diphthongs are shortened before underlyingly voiceless sounds by a pre-existing lexical phonological rule of Pre-Voiceless Clipping, after which postlexical Raising transparently affects the shortened diphthongs. Experiment: Participants (N = 141, US dialects) read wordlists with /ai/ and /ei/ in voiceless and voiced contexts, then sorted the words into groups judged to share a vowel (DiPaolo & Faber, 1990). Clipping and Raising were measured using duration, F1, and F2. Predictions: (1) across speakers, /ai/-Clipping and / ai/- Raising should be positively correlated. (2) /ai/-sorting should be better predicted by /ai/-Clipping than by /ai/-Raising, because lexical rules change phonemes, while postlexical ones are subphonemic. (3) /ei/-sorting should be positively correlated with /ai/-sorting, since Clipping affects all vocoids. Results: (1) /ai/-Clipping did *not* predict /ai/-Raising (r = −0.082); (2) / ai/-Clipping predicted word sorting marginally *worse* than /ai/-Raising (95% CI for rclipping-rraising = (−0.50, 0.03)). (3) /ei/ and /ai/ judgements *were* positively correlated (r = 0.37, 95% CI = (0.21, 0.51)).

Vegetation Type Mapping in Southern Patagonia and Its Relationship with Ecosystem Services, Soil Carbon Stock, and Biodiversity

Vegetation Type (VT) mapping using Optical Earth observation data is essential for the management and conservation of natural resources, as well as for the evaluation of the supply of provisioning ecosystem services (ESs), the maintenance of ecosystem functions, and the conservation of biodiversity in anthropized environments. The main objective of the present work was to determine the spatial patterns of VTs related to climatic, topographic, and spectral variables across Santa Cruz province (Southern Patagonia, Argentina) in order to improve our understanding of land use cover at the regional scale. Also, we examined the spatial relationship between VTs and potential biodiversity (PB), ESs, and soil organic content (SOC) across our study region. We sampled 59,285 sites sorted into 19 major categories of land cover with a reliable discrimination level from field measurements. We selected 31 potential predictive environmental dataset covariates, which represent key factors for the spatial distribution of land cover such as climate (four), topography (three), and spectral (24) factors. All covariate maps were generated or uploaded to the Google Earth Engine cloud-based computing platform for subsequent modeling. A total of 270,292 sampling points were used for validation of the obtained classification map. The main land cover area estimates extracted from the map at the regional level identified about 142,085 km2 of grasslands (representing 58.1% of the total area), 38,355 km2 of Mata Negra Matorral thicket (15.7%), and about 25,189 km2 of bare soil (10.3%). From validation, the Overall Accuracy and the Kappa coefficient values for the classification map were 90.40% and 0.87, respectively. Pure and mixed forests presented the maximum SOC (11.3–11.8 kg m−2), followed by peatlands (10.6 kg m−2) and deciduous Nothofagus forests (10.5 kg m−2). The potential biodiversity was higher in some shrublands (64.1% in Mata Verde shrublands and 63.7% in mixed shrublands) and was comparable to those values found for open deciduous forests (Nothofagus antarctica forest with 60.4%). The provision of ESs presented maximum values at pure evergreen forests (56.7%) and minimum values at some shrubland types (Mata Negra Matorral thicket and mixed shrubland) and steppe grasslands (29.7–30.9%). This study has provided an accurate land cover and VT map that provides crucial information for ecological studies, biodiversity conservation, vegetation management and restoration, and regional strategic decision-making.

Analysis of the Performance of mc-Si and CdTe Modules Under Soiling Conditions

In this work, we study the soiling impact on the performance of two PV technologies installed in the south of Spain. For this purpose, we include electrical measurements as well as spectral aspects such as dust transmittance, quantum efficiency and the local solar spectrum to analyse their response. The studied technologies were multicrystalline silicon (mc-Si) and cadmium telluride (CdTe) PV modules. The solar spectra representative for clear sky, clean glass cover and soiled glass as well as the spectral response of the PV modules were used for the calculation of the photogenerated current density and spectral mismatch factor. Two cloudless days were chosen for analysis. In terms of the solar resource, these days did not exhibit large differences. Nevertheless, soiling was present to a different extent. When comparing the corresponding power output of the technologies on day 1 and day 2, the power losses at 12 UTC were 3 times larger for mc-Si and nearly the same for CdTe. This result shows that the soiling impacts differently on PV modules having different spectral responses.

Bubble Sensors for Temperature Measurements through a Colorimetric Approach.

This paper introduces an innovative sensor utilizing bubbles coated with thermochromic paint, aiming to facilitate temperature measurements in challenging-to-reach locations without the requirement of an external power source. The research conducted is innovative in terms of both methodology and application. The characterization of the thermochromic properties of paints was, in fact, performed using spectroradiometric measurements by selecting a temperature range useful for applications in various fields including preventive conservation. The study encompasses two main objectives: (1) analyzing the color characteristics of thermochromic paint and plastic resin that forms the bubbles, and (2) assessing a temperature sensor comprising a thermochromic paint-coated bubble subjected to temperature variations. The thermochromic paint exhibits reversible color modifications in response to temperature changes, making it an ideal candidate for applications of this nature. The color characterization phase involves measurements using a spectroradiometer to compare the spectral reflectance factor (SRF%) of the colored plastic resin spread on canvas with that of the inflated bubbles. The sensor characterization entails evaluating color changes of the thermochromic paint on the bubble surface with varying temperatures. Experimental results indicate that the combination of a red (R) bubble and blue (B) thermochromic paint produces quantifiable color variations suitable for the proposed applications, whereas the alternative combination under examination, namely a blue bubble and red thermochromic paint, yields less accurate results. Considering that for both thermochromic paints the color change temperature is 35 °C, it is possible to see how, for B bubble with R thermochromic paint, the chromatic coordinates change value: C* = 3.14 ± 0.14 and h = 289.54 ± 11.58 at room temperature, while C* = 2.96 ± 0.12 and h = 304.20 ± 12.17 at 35 °C. The same is true for R bubble with B thermochromic paint where C* = 25.31 ± 1.01 and h* = 285.05 ± 11.40 at room temperature, while C* = 20.87 ± 0.85 and h = 288.37 ± 11.53 at 35 °C. The study demonstrates the potential of the approach and suggests further investigations into reproducibility and expanded color combinations. The results provide a promising basis for future improvements in temperature monitoring with thermochromic bubble sensors.

Quantifying spectral albedo effects on bifacial photovoltaic module measurements and system model predictions

AbstractWe provide a comprehensive analysis of the effect of spectral albedo on photovoltaic (PV) module measurements and system model predictions. We demonstrate how to account for albedo in indoor bifacial device measurements by adjusting the applied irradiance using the scaled rear irradiance method, exemplified on fabricated silicon heterojunction (SHJ) modules. System model performance is studied using a detailed 3D finite‐element model, DUET, for fixed‐tilt and horizontal single‐axis tracked (SAT) arrays between 15 and 75°N. Spectral effects cause variations in measured SHJ module short‐circuit current up to 2% and efficiency variation up to 0.3% abs. We further demonstrate that rear‐side spectral mismatch factors (SMMs) resulting from including or omitting spectral albedo in PV system modeling vary between ±13%, while total (front+rear) SMMs vary up to 3%, depending on the deployment configuration and latitude. SAT array SMMs are weakly correlated with latitude, while fixed‐tilt array SMMs increase with latitude, driven by an increasing proportion of ground‐reflected light on the front‐side of modules. Ground‐reflections can constitute between 2% and 32% of total incident module irradiance, with notably high (>10%) contributions for fixed‐tilt arrays at high latitude. Effects of spectral albedo are most significant for: (1) fixed‐tilt deployments at high latitudes, (2) wide bandgap technologies such as perovskite and cadmium telluride cells, (3) albedos which vary steeply over the technology's absorption range, and (4) high albedo ground covers. Overall, we demonstrate that omitting spectral albedo effects can result in PV measurement and system‐level modeling uncertainties on the order of several percent in these cases.

Brickwall in rotating BTZ: a dip-ramp-plateau story

In this article, building on our recent investigations and motivated by the fuzzball-paradigm, we explore normal modes of a probe massless scalar field in the rotating BTZ-geometry in an asymptotically AdS spacetime and correspondingly obtain the Spectral Form Factor (SFF) of the scalar field. In particular, we analyze the SFF obtained from the single-particle partition function. We observe that, a non-trivial Dip-Ramp-Plateau (DRP) structure, with a Ramp of slope one (within numerical precision) exists in the SFF which is obtained from the grand-canonical partition function. This behaviour is observed to remain stable close to extremality as well. However, at exact extremality, we observe a loss of the DRP-structure in the corresponding SFF. Technically, we have used two methods to obtain our results: (i) An explicit and direct numerical solution of the boundary conditions to obtain the normal modes, (ii) A WKB-approximation, which yields analytic, semi-analytic and efficient numerical solutions for the modes in various regimes. We further re-visit the non-rotating case and elucidate the effectiveness of the WKB-approximation in this case, which allows for an analytic expression of the normal modes in the regime where a level-repulsion exists. This regime corresponds to the lower end of the spectrum as a function of the scalar angular momentum, while the higher end of this spectrum tends to become flat. By analyzing the classical stress-tensor of the probe sector, we further demonstrate that the back-reaction of the scalar field grows fast as the angular momenta of the scalar modes increase in the large angular momenta regime, while the back-reaction remains controllably small in the regime where the spectrum has non-trivial level correlations. This further justifies cutting the spectrum off at a suitable value of the scalar angular momenta, beyond which the scalar back-reaction significantly modifies the background geometry.

Effect of Broadness of Wave Spectrum on Significant Wave Height and Wave Power for Open Ocean Conditions of the Peru Basin

Abstract When estimating significant wave height and wave power, it is regularly assumed 4 for the spectral estimate factor. It means considering a narrowband wave spectrum. That approach is accurate enough when the spectral broadness parameter is near zero. Since the Peru Basin is an open ocean: swells and local wind waves can overlap; therefore, its wave spectrum should be considered broadband. This work aims to demonstrate that the wave spectrum in the Peru Basin has waves in a broad band of frequencies and also discuss how this characteristic affects estimating the significant wave height and wave power. The methodology comprises numerical methods, inferential statistics, and spectral analysis applied to ocean data. The paper's conclusions declare the Peru Basin wave spectrum as broadband. The estimated significant wave height for broadband wave spectrum is 7% lower than if the wave spectrum was considered narrowband. We propose 3.7 as the spectral estimate factor for calculating the significant wave height in the Peru Basin instead of the commonly used 4. The significant wave height error when assuming a narrowband wave spectrum slightly affects the spectral parametric wave power calculation, causing a maximum overestimation of 5%. Nevertheless, accurately estimating significant wave height is critical for diverse marine technologies.

What is the Simplest Linear Ramp?

We discuss conditions under which a deterministic sequence of real numbers, interpreted as the set of eigenvalues of a Hamiltonian, can exhibit features usually associated to random matrix spectra. A key diagnostic is the spectral form factor (SFF) — a linear ramp in the SFF is often viewed as a signature of random matrix behavior. Based on various explicit examples, we observe conditions for linear and power law ramps to arise in deterministic spectra. We note that a very simple spectrum with a linear ramp is En ~ log n. Despite the presence of ramps, these sequences do not exhibit conventional level repulsion, demonstrating that the lore about their concurrence needs refinement. However, when a small noise correction is added to the spectrum, they lead to clear level repulsion as well as the (linear) ramp. We note some remarkable features of logarithmic spectra, apart from their linear ramps: they are closely related to normal modes of black hole stretched horizons, and their partition function with argument s = β + it is the Riemann zeta function ζ(s). An immediate consequence is that the spectral form factor is simply −ζ|(it)|2. Our observation that log spectra have a linear ramp, is closely related to the Lindelöf hypothesis on the growth of the zeta function. With elementary numerics, we check that the slope of a best fit line through |ζ(it)|2 on a log-log plot is indeed 1, to the fourth decimal. We also note that truncating the Riemann zeta function sum at a finite integer N causes the would-be-eternal ramp to end on a plateau.

Spectral reflectance reconstruction based on wideband multi-illuminant imaging and a modified particle swarm optimization algorithm.

A method for spectral reflectance factor reconstruction based on wideband multi-illuminant imaging was proposed, using a programmable LED lighting system and modified Bare Bones Particle Swarm Optimization algorithms. From a set of 16 LEDs with different spectral power distributions, nine light sources with correlated color temperatures in the range of 1924 K - 15746 K, most of them daylight simulators, were generated. Samples from three color charts (X-Rite ColorChecker Digital SG, SCOCIE ScoColor paint chart, and SCOCIE ScoColor textile chart), were captured by a color industrial camera under the nine light sources, and used in sequence as training and/or testing colors. The spectral reconstruction models achieved under multi-illuminant imaging were trained and tested using the canonical Bare Bones Particle Swarm Optimization and its proposed modifications, along with six additional and commonly used algorithms. The impacts of different illuminants, illuminant combinations, algorithms, and training colors on reconstruction accuracy were studied comprehensively. The results indicated that training colors covering larger regions of color space give more accurate reconstructions of spectral reflectance factors, and combinations of two illuminants with a large difference of correlated color temperature achieve more than twice the accuracy of that under a single illuminant. Specifically, the average reconstruction error by the method proposed in this paper for patches from two color charts under A + D90 light sources was 0.94 and 1.08 CIEDE2000 color difference units. The results of the experiment also confirmed that some reconstruction algorithms are unsuitable for predicting spectral reflectance factors from multi-illuminant images due to the complexity of optimization problems and insufficient accuracy. The proposed reconstruction method has many advantages, such as being simple in operation, with no requirement of prior knowledge, and easy to implement in non-contact color measurement and color reproduction devices.

Narrow–linewidth tunable laser source for long-wavelength optical coherence tomography at 1700 nm

We present a widely tunable laser source with narrowed linewidths at the level of 0.4 – 1.1 nm. The laser source incorporates a comb-profile fiber (CPF) which allows for spectral compression of the tunable optical pulses to the linewidths below 1 nm. The spectral compression factor is as high as 37.2 and is the highest obtained for this wavelength range. With the use of an electro-optic modulator (EOM), the laser system ensures rapid tuning up to 10 GHz. Together with the wide spectral range of 1600-1900 nm, and compressed spectral width, the source meets the requirements of the optical coherence tomography (OCT).

Double-Factor Tensor Cascaded-Rank Decomposition for Hyperspectral Image Denoising

Hyperspectral image (HSIs) denoising is a preprocessing step that plays a crucial role in many applications used in Earth observation missions. Low-rank tensor representation can be utilized to restore mixed-noise HSIs, such as those affected by mixed Gaussian, impulse, stripe, and deadline noises. Although there is a considerable body of research on spatial and spectral prior knowledge concerning subspace, the correlation between the spectral continuity and the nonlocal sparsity of the spectral and spatial factors is not yet fully understood. To address this deficiency, in the present study, we determined the correlation between these factors using a cascaded technique, and we describe in this paper the double-factor tensor cascaded-rank (DFTCR) minimization method that was used. The information existing in the nonlocal sparsity property of the spatial factor was employed to promote a geometrical feature representation, and a tensor cascaded-rank minimization approach was introduced as a nonlocal self-similarity to promote restoration quality. The continuity between the difference and nonlocal gradient sparsity constraints of the spectral factor was also introduced to learn the basis. Furthermore, to estimate the solutions of the proposed model, we developed an algorithm based on the alternating direction method of multipliers (ADMM). The performance of the DFTCR method was tested by a comparison with eleven established denoising methods for HSIs. The results showed that the proposed DFTCR method exhibited superior performance in the removal of mixed noise from HSIs.

Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos

We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental domain. The focus of this paper is on the discrete part of the spectrum, which consists of the Maass cusp forms. Both their eigenvalues and Fourier coefficients are sporadic discrete numbers with interesting statistical properties and relations to analytic number theory; this is referred to as ‘arithmetic chaos’. We show that the near-extremal spectral form factor at late times is only sensitive to a statistical average over these erratic features. Nevertheless, complete information about their statistical distributions is encoded in the spectral form factor if all its spin sectors exhibit universal random matrix eigenvalue repulsion (a ‘linear ramp’). We ‘bootstrap’ the spectral correlations between the cusp form basis functions that correspond to a universal linear ramp and show that they are unique up to theory-dependent subleading corrections. The statistical treatment of cusp forms provides a natural avenue to fix the subleading corrections in a minimal way, which we observe leads to the same correlations as those described by the [torus]×[interval] wormhole amplitude in AdS3 gravity.

Long-ranged spectral correlations in eigenstate phases

We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the spectral form factor and the density of all spectral gaps, and show that they furnish unique signatures that can be used to sharply identify the two phases. We demonstrate this by numerically studying three one-dimensional quantum spin chain models with (i) quenched disorder, (ii) periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in what ways the signatures are universal and in what ways they are not. More generally, this thorough analysis is expected to play a useful role in classifying phases of disorder systems.