Linear Spectrum Research Articles

Linear response of molecular polaritons.

In this article, we show that the collective light-matter strong coupling regime where N molecular emitters couple to the photon mode of an optical cavity can be mapped to a quantum impurity model where the photon is the impurity that is coupled to a bath of anharmonic transitions. In the thermodynamic limit where N ≫ 1, we argue that the bath can be replaced with an effective harmonic bath, leading to a dramatic simplification of the problem into one of the coupled harmonic oscillators. We derive simple analytical expressions for linear optical spectra (transmission, reflection, and absorption) where the only molecular input required is the molecular linear susceptibility. This formalism is applied to a series of illustrative examples, showing the role of temperature, disorder, vibronic coupling, and optical saturation of the molecular ensemble, explaining that it is useful even when describing an important class of nonlinear optical experiments. For completeness, we provide Appendixes A-C that include a self-contained derivation of the relevant spectroscopic observables for arbitrary anharmonic systems (for both large and small N) within the rotating-wave approximation. While some of the presented results herein have already been reported in the literature, we provide a unified presentation of the results as well as new interpretations that connect powerful concepts in open quantum systems and linear response theory with molecular polaritonics.

Extracting accurate light–matter couplings from disordered polaritons

Abstract The vacuum Rabi splitting (VRS) in molecular polaritons stands as a fundamental measure of collective light–matter coupling. Despite its significance, the impact of molecular disorder on VRS is not fully understood yet. This study delves into the complexities of VRS amidst various distributions and degrees of disorder. Our analysis provides precise analytical expressions for linear absorption, transmission, and reflection spectra, along with a “sum” rule, offering a straightforward protocol for extracting accurate collective light–matter coupling values from experimental data. Importantly, our study cautions against directly translating large VRS to the onset of ultrastrong coupling regime. Furthermore, for rectangular disorder, we witness the emergence of narrow side bands alongside a broad central peak, indicating an extended coherence lifetime even in the presence of substantial disorder. These findings not only enhance our understanding of VRS in disordered molecular systems but also open avenues for achieving prolonged coherence lifetimes between the cavity and molecules via the interplay of collective coupling and disorder.

High-frequency optimally windowed chirp rheometry for rapidly evolving viscoelastic materials: Application to a crosslinking thermoset

Knowledge of the evolution in the mechanical properties of a curing polymer matrix is of great importance in composite parts or structure fabrication. Conventional rheometry, based on small amplitude oscillatory shear, is limited by long interrogation times. In rapidly evolving materials, time sweeps can provide a meaningful measurement albeit at a single frequency. To overcome this constraint, we utilize a combined frequency- and amplitude-modulated chirped strain waveform in conjunction with a homemade sliding plate piezo-operated rheometer (PZR) and a dual-head commercial rotational rheometer (Anton Paar MCR 702) to probe the linear viscoelasticity of these time-evolving materials. The direct controllability of the PZR, resulting from the absence of any kind of firmware and the microsecond actuator-sensor response renders this device ideal for exploring the advantages of this technique. The high frequency capability allows us to extend the upper limits of the accessible linear viscoelastic spectrum and, most importantly, to shorten the length of the interrogating strain signal (OWCh-PZR) to subsecond scales, while retaining a high time-bandwidth product. This short duration ensures that the mutation number (NMu) is kept sufficiently low, even in fast-curing resins. The method is validated via calibration tests in both instruments, and the corresponding limitations are discussed. As a proof of concept, the technique is applied to a curing vinylester resin. The linear viscoelastic (LVE) spectrum is assessed every 20 s to monitor the rapid evolution in the time and frequency dependence of the complex modulus. Comparison of the chirp implementation, based on parameters such as duration of the experiment, sampling frequency, and frequency range, in a commercial rotational rheometer with the PZR provides further information on the applicability of this technique and its limitations. Finally, FTIR spectroscopy is utilized to gain insights into the evolution of the chemical network, and the gap dependence of the evolving material properties in these heterogeneous systems is also investigated.

A precise symbolic emulator of the linear matter power spectrum

Computing the matter power spectrum, $P(k)$, as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used. We aim to construct an efficient, differentiable, interpretable, symbolic emulator for the redshift zero linear matter power spectrum which achieves sub-percent level accuracy. We also wish to obtain a simple analytic expression to convert $A_ s $ to $ given the other cosmological parameters. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and $ We learn the ratio between an existing low-accuracy fitting function for $P(k)$ and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2<!PCT!> between $k = 9 $ and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. Our analytic approximation is 950 times faster to evaluate than and 36 times faster than the neural network based matter power spectrum emulator We also provide a simple analytic approximation for $ with a similar accuracy, with a root mean squared fractional error of just 0.1<!PCT!> when evaluated across the same range of cosmologies. This function is easily invertible to obtain s $ as a function of $ and the other cosmological parameters, if preferred. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated.

Simulations of gravitational heating due to early matter domination

In cosmologies with an early matter-dominated era (EMDE) prior to Big Bang nucleosynthesis, the boosted growth of small-scale matter perturbations during the EMDE leads to microhalo formation long before halos would otherwise begin to form. For a range of models, halos can even form during the EMDE itself. These halos would dissipate at the end of the EMDE, releasing their gravitationally heated dark matter and thereby imprintinga free-streaming cut-off on the matter power spectrum.We conduct the first cosmological N-body simulations of the formation and evaporation of halos during and after an EMDE.We show that in these scenarios, the free-streaming cut-off after the EMDE can be predicted accurately from the linear matter power spectrum. Although the free streaming can erase much of the EMDE-driven boost to density perturbations, we use our findings to show that the (re-)formation of halos after the EMDE nevertheless proceeds before redshift ∼ 1000. Early-forming microhalos are a key observational signature of an EMDE, and our prescription for the impact of gravitational heating will allow studies of the observational status and prospects of EMDE scenarios to cover a much wider range of parameters.

Advantages of a synchrotron light source for fluorescence-detected linear dichroism.

Fluorescence-detected linear dichroism (FD-LD) enables one to collect linear dichroism spectra for oriented fluorophores in the presence of other absorbing species and light scattering. The experiment proceeds by scanning the excitation wavelength and using a filter to collect only emitted photons from the fluorophore. Thus, it has the potential to give data with enhanced selectivity and quality. By using a synchrotron radiation light source and fluorescence-detection, we show data for a range of fluorophores in different orienting environments. Film and flow-oriented FD-LD spectra were collected down to 170 nm. Even for flow-oriented liposomes, we have data collected down to 210 nm. For strongly scattering samples, for example, liposomes, FD-LD has the clear advantage that scattering is absent for the longer wavelength fluorescence photons. The collimated and smaller beam size of the synchrotron radiation also gives rise to sharper and more well-defined features in the spectra.

Machine learning models reveal distinct disease subgroups and improve diagnostic and prognostic accuracy for individuals with pathogenic SCN8A gain-of-function variants.

Distinguishing clinical subgroups for patients suffering with diseases characterized by a wide phenotypic spectrum is essential for developing precision therapies. Patients with gain-of-function (GOF) variants in the SCN8A gene exhibit substantial clinical heterogeneity, viewed historically as a linear spectrum ranging from mild to severe. To test for hidden clinical subgroups, we applied two machine learning algorithms to analyze a dataset of patient features collected by the International SCN8A Patient Registry. We utilized two research methodologies: a supervised approach that incorporated feature severity cutoffs based on clinical conventions, and an unsupervised approach employing an entirely data-driven strategy. Both approaches found statistical support for three distinct subgroups and were validated by correlation analyses utilizing external variables. However, distinguishing features of the three subgroups within each approach were not concordant, suggesting a more complex phenotypic landscape. The unsupervised approach yielded strong support for a model involving three partially-ordered subgroups rather than a linear spectrum. Application of these machine-learning approaches may lead to improved prognosis and clinical management of individuals with SCN8A GOF variants and provide insights into the underlying mechanisms of the disease.

Charge-Transfer-Induced Interfacial Ferromagnetism in Ferromagnet-Free Oxide Heterostructures.

Due to the strong interlayer coupling between multiple degrees of freedom, oxide heterostructures have demonstrated exotic properties that are not shown by their bulk counterparts. One of the most interesting properties is ferromagnetism at the interface formed between "nonferromagnetic" compounds. Here we report on the interfacial ferromagnetic phase induced in the superlattices consisting of the two paramagnetic oxides CaRuO3 (CRO) and LaNiO3 (LNO). By varying the sublayer thickness in the superlattice period, we demonstrate that the ferromagnetic order has been established in both CaRuO3 and LaNiO3 sublayers, exhibiting an identical Curie temperature of ∼75 K. The X-ray absorption spectra suggest a strong charge transfer from Ru to Ni at the interface, triggering superexchange interactions between Ru/Ni ions and giving rise to the emergent ferromagnetic phase. Moreover, the X-ray linear dichroism spectra reveal the preferential occupancy of the d3z2-r2 orbital for the Ru ions and the dx2-y2 orbital for the Ni ions in the heterostructure. This leads to different magnetic anisotropy of the superlattices when they are dominated by CRO or LNO sublayers. This work clearly demonstrates a charge-transfer-induced interfacial ferromagnetic phase in the whole ferromagnet-free oxide heterostructures, offering a feasible way to tailor oxide materials for desired functionalities.

Machine learning unveils the linear matter power spectrum of modified gravity

Machine learning unveils the linear matter power spectrum of modified gravity

Electric Field Susceptibility of Chlorophyll c Leads to Unexpected Excitation Dynamics in the Major Light-Harvesting Complex of Diatoms.

Diatoms are one of the most abundant photosynthetic organisms on earth and contribute largely to atmospheric oxygen production. They contain fucoxanthin and chlorophyll-a/c binding proteins (FCPs) as light-harvesting complexes with a remarkable adaptation to the fluctuating light on ocean surfaces. To understand the basis of the photosynthetic process in diatoms, the excitation energy funneling within FCPs must be probed. A state-of-the-art multiscale analysis within a quantum mechanics/molecular mechanics framework has been employed. To this end, the chlorophyll (Chl) excitation energies within the FCP complex from the diatom Phaeodactylum tricornutum have been determined. The Chl-c excitation energies were found to be 5-fold more susceptible to electric fields than those of Chl-a pigments and thus are significantly lower in FCP than in organic solvents. This finding challenges the general belief that the excitation energy of Chl-c is always higher than that of Chl-a in FCP proteins and reveals that Chl-c molecules are much more sensitive to electric fields within protein scaffolds than in Chl-a pigments. The analysis of the linear absorption spectrum and the two-dimensional electronic spectra of the FCP complex strongly supports these findings and allows us to study the excitation transfer within the FCP complex.

The modulation of coherent structures by the near-wall motions of particles

Particle–wall interaction generates strong particle near-wall motion, including collision bounce and impact splashing. To distinguish the effect of particles and particle near-wall motions on the turbulent coherent structure, this study carried out three different cases of sand-laden two-phase flow measurements: a uniform sand release at the top, local-laying sand bed and global-laying sand bed (Liu et al., J. Fluid Mech., vol. 943, 2022, A8). Based on large field of view particle image velocimetry/particle tracking velocimetry measurements, we obtained the velocity field of a two-dimensional gas–solid two-phase dilute faction flow $(\varPhi _{v} \sim O(10^{-4}))$ with a friction Reynolds number $R e_{\tau }$ of 3950. Results indicate that particles weaken the high- and low-velocity iso-momentum zones and hairpin vortices, resulting in the increased length scale of the coherent structure. However, the collision bounce and impact splashing break up the inner iso-momentum zone and hairpin vortices while enhancing them in the outer region, thus reducing the structure scale. In addition, the upward-moving particles increase the large-scale structure inclination angle, while the downward-moving particles decrease it. The linear coherence spectrum analysis suggests that the particles themselves do not change the structural self-similarity, but their saltation motions disrupt the similarity of the near-wall structure, making the inclination angle decrease with the scale, and the generated ascending particles reduce the aspect ratio of the streamwise to wall-normal direction in the outer region.

Taming the third order cumulant approximation to linear optical spectroscopy.

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

A Quantum Chemistry Approach to Linear Vibro-Polaritonic Infrared Spectra with Perturbative Electron-Photon Correlation.

In the vibrational strong coupling (VSC) regime, molecular vibrations and resonant low-frequency cavity modes form light-matter hybrid states, vibrational polaritons, with characteristic infrared (IR) spectroscopic signatures. Here, we introduce a molecular quantum chemistry-based computational scheme for linear IR spectra of vibrational polaritons in polyatomic molecules, which perturbatively accounts for nonresonant electron-photon interactions under VSC. Specifically, we formulate a cavity Born-Oppenheimer perturbation theory (CBO-PT) linear response approach, which provides an approximate but systematic description of such electron-photon correlation effects in VSC scenarios while relying on molecular ab initio quantum chemistry methods. We identify relevant electron-photon correlation effects at the second order of CBO-PT, which manifest as static polarizability-dependent Hessian corrections and an emerging polarizability-dependent cavity intensity component providing access to transmission spectra commonly measured in vibro-polaritonic chemistry. Illustratively, we address electron-photon correlation effects perturbatively in IR spectra of CO2 and Fe(CO)5 vibro-polaritonic models in sound agreement with nonperturbative CBO linear response theory.

Tailoring Cu-rich surface spinel phase for high-performance O3-type layered cathode materials for sodium-ion batteries

O3-type layered oxide cathodes are primarily limited by complex phase transitions and sluggish kinetics resulting in rapid capacity drop and poor rate capability. Even worse, its inherent air sensitivity leads to spontaneous extraction of lattice Na-ions and the deactivation of the cathode. Simultaneous modification of both the bulk phase and the surface structure is promising to offset the above deficiencies. A spinel@O3 type layered composite structure Na0.9Mn0.5Ni0.5Cu0.1O2+x (NMNCO-SL) was constructed for the design of cathodes with higher cycling, rate and air stability. The atomic-level Cu-rich spinel structure on the surface was identified by scanning transmission electron microscopy, elemental linear scanning analysis and Raman spectra. In situ charge-discharge X-ray diffraction results show that the phase transition of NMNCO-SL is significantly suppressed. Finally, the material maintains good electrochemical properties after exposure to stringent humidity environments. The results indicate that the spinel structure at the surface plays a significant role in improving ion-diffusion dynamics, enhancing structural integrity, and increasing air stability. 1 Ah pouch cell based on NMNCO-SL showed 92% capacity retention after 500 cycles of charge/discharge cycling at 1 C, demonstrating the potential prospects of customizing the surface phase structure for materials engineering applications.

Comparison of Linear and Nonlinear Procedures for the Analysis of the Seismic Performance of Straight Multi-Span RC Bridges

Comparison of Linear and Nonlinear Procedures for the Analysis of the Seismic Performance of Straight Multi-Span RC Bridges

Linear analysis and crossphase dynamics in the CTEM fluid model

Collisionless trapped-electron mode (CTEM) turbulence is an important contributor to heat and particle transport in fusion devices. The ion-temperature gradient (ITG)/trapped-electron mode (TEM) fluid models are rarely treated analytically, due to the large number of transport channels involved, e.g., particle and ion/electron heat transport. The CTEM fluid model [Anderson et al., Plasma Phys. Controlled Fusion 48, 651 (2006)] provides a simplified model, in the regime where the density gradient drive (∇n) is negligible compared to the electron temperature gradient drive (∇Te). This provides a starting point to study mechanisms associated with linear waves, such as crossphase dynamics, and its possible role in the formation of E × B staircase. Here, an extended CTEM fluid model (with both ∇n and ∇Te drive) is derived from the more general ITG/TEM model, using a simplified ion density response, and its linear dynamics is first analyzed and compared with CTEM gyrokinetic simulations with bounce-averaged kinetic electrons, while nonlinear analysis is left for future work. The wave action density is derived for this CTEM model. Comparisons of linear ITG spectrum are also made with other analytical models.

Constraining Neutrino Cosmologies with Nonlinear Reconstruction

Nonlinear gravitational evolution induces strong nonlinearities in the observed cosmological density fields, leading to positive off-diagonal correlations in the power spectrum covariance. This has caused the information saturation in the power spectrum, e.g., the neutrino mass constraints from the nonlinear power spectra are lower than their linear counterparts by a factor of ∼2 at z = 0. In this paper, we explore how nonlinear reconstruction methods improve the cosmological information from nonlinear cosmic fields. By applying nonlinear reconstruction to cold dark matter fields from the Quijote simulations, we find that nonlinear reconstruction can improve the constraints on cosmological parameters significantly, nearly reaching the linear theory limit. For neutrino mass, the result is only 12% lower than the linear power spectrum, i.e., the theoretical best result. This makes nonlinear reconstruction an efficient and useful method to extract neutrino information from current and upcoming galaxy surveys.

OpenSeismoMatlab: New Features, Verification and Charting Future Endeavors

To facilitate the precise design of earthquake-resistant structures, it is imperative to accurately evaluate the impact of seismic events on these constructions and predict their responses. OpenSeismoMatlab, a robust, free ground motion data processing software, plays a pivotal role in this endeavor. It empowers users to compute a wide array of outcomes using input acceleration time histories, encompassing time histories themselves, as well as linear and nonlinear spectra. These capabilities are instrumental in supporting structural design initiatives. This study provides a comprehensive exposition of the latest version (v 5.05) of OpenSeismoMatlab. It delves into intricate facets of the software, encompassing a detailed exploration of the input and output variables integral to each operational category. Comprehensive calculation flowcharts are presented to elucidate the software’s organizational structure and operational sequences. Furthermore, a meticulous verification assessment is conducted to validate OpenSeismoMatlab’s performance. This verification entails a rigorous examination of specific cases drawn from existing literature, wherein the software’s outcomes are rigorously compared against corresponding results from prior studies. The examination not only underscores the reliability of OpenSeismoMatlab but also emphasizes its ability to generate outcomes that closely align with findings documented in the established body of literature. Concluding the study, the paper outlines potential directions for future research, shedding light on avenues where further development and exploration can enhance the utility and scope of OpenSeismoMatlab in advancing seismic engineering and structural design practices.

Dielectric Response and Linear Absorption Spectroscopy of Ionic Systems.

Time-dependent electric fields applied to ionic systems can induce both a dielectric and a conductive response, leading to the generation of macroscopic polarization and current, respectively. It has long been recognized that it is not possible to determine the two types of responses separately. However, this aspect is often not adequately accounted for in dielectric and absorption spectroscopies of ionic systems. To clarify this, we theoretically investigate the dielectric and conductive responses of ionic systems containing polyatomic ions based on linear response theory. We derive general expressions for the frequency-dependent dielectric functions, conductivity, and absorption coefficient, including those measured experimentally. Furthermore, we show that the dielectric and conductive responses cannot be uniquely distinguished even at the theoretical level and, therefore, cannot represent experimentally measured quantities. Instead, dielectric and absorption spectra of ionic systems should be expressed in terms of the generalized dielectric function that encompasses both dielectric and conductive responses. We propose a computational method to calculate this generalized dielectric function reliably. Model calculations on concentrated aqueous solutions of NaCl, a monatomic salt, and LiTFSI, a polyatomic salt, show that the dielectric and linear absorption spectra of the two systems based on the generalized dielectric function are significantly different from purely dielectric counterparts in the far-IR, terahertz, and lower-frequency regions. Moreover, the spectra are mainly determined by the autocorrelations of total dipole and total current, but dipole-current cross-correlation can also significantly contribute to the spectra of the LiTFSI solution. The present theoretical approach could be extended to nonlinear spectroscopy of ionic liquids and electrolyte solutions.

Development and application of an optimised Bayesian shrinkage prior for spectroscopic biomedical diagnostics

Background and objectiveClassification of vibrational spectra is often challenging for biological substances containing similar molecular bonds, interfering with spectral outputs. To address this, various approaches are widely studied. However, whilst providing powerful estimations, these techniques are computationally extensive and frequently overfit the data. Shrinkage priors, which favour models with relatively few predictor variables, are often applied in Bayesian penalisation techniques to avoid overfitting. MethodsUsing the logit-normal continuous analogue of the spike-and-slab (LN–CASS) as the shrinkage prior and modelling, we have established classification for accurate analysis, with the established system found to be faster than conventional least absolute shrinkage and selection operator, horseshoe or spike-and-slab. These were examined versus coefficient data based on a linear regression model and vibrational spectra produced via density functional theory calculations. Then applied to Raman spectra from saliva to classify the sample sex. ResultsSubsequently applied to the acquired spectra from saliva, the evaluated models exhibited high accuracy (AUC>90 %) even when number of parameters was higher than the number of observations. Analyses of spectra for all Bayesian models yielded high-classification accuracy upon cross-validation. Further, for saliva sensing, LN–CASS was found to be the only classifier with 100 %-accuracy in predicting the output based on a leave-one-out cross validation. ConclusionsWith potential applications in aiding diagnosis from small spectroscopic datasets and are compatible with a range of spectroscopic data formats. As seen with the classification of IR and Raman spectra. These results are highly promising for emerging developments of spectroscopic platforms for biomedical diagnostic sensing systems.