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At least 19 records

Scattering phase shift in quantum mechanics on quantum computers

Here, we investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in the work by Guo and Gasparian [Phys. Rev. D 108, 074504 (2023)] that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral. The system is first discretized in a finite box with periodic boundary conditions, and the formalism in real time is verified by employing a contact interaction potential with exact solutions. Quantum circuits are then designed and constructed to implement the formalism on current quantum computing architectures. To overcome the fast oscillatory behavior of the integrated correlation functions in real-time simulation, different methods of postdata analysis are proposed and discussed. Test results on IBM hardware show that good agreement can be achieved with two qubits, but complete failure ensues with three qubits due to two-qubit gate operation errors and thermal relaxation errors.

Guo, Peng [Dakota State Univ., Madison, SD (United↗

Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Role of effective mass and long-range interactions in the band-gap renormalization of photoexcited semiconductors

Understanding how to control changes in the electronic structure and related dynamical renormalizations by external driving fields is the key for understanding ultrafast spectroscopy and applications in electronics. Here, we focus on the band gap's modulation by external electric fields and uncover the effect of band dispersion on the gap renormalization. We employ the Green's function formalism using the real-time Dyson expansion to account for dynamical correlations induced by photodoping. The many-body formalism captures the dynamics of systems with long-range interactions, carrier mobility, and variable electron and hole effective mass. We also demonstrate that mean-field simulations based on the Hartree-Fock Hamiltonian, which lacks dynamical correlations, yields a qualitatively incorrect picture of band-gap renormalization. We find the trend that increasing effective mass, thus decreasing mobility, leads to as much as a 6% enhancement in band-gap renormalization. Further, the renormalization is strongly dependent on the degree of photodoping. As the screening induced by free electrons and holes effectively reduces any long-range and interband interactions for highly excited systems, we show that there is a specific turnover point with a minimal band gap. Here, we further demonstrate that the optical gap renormalization follows the same trend though its magnitude is altered by the Moss-Burstein effect.

Approximation methods for many-body systems↗

Thermal modifications of mesons and energy-energy correlators from real-time simulations of a 𝑈⁡(1) lattice gauge theory

We investigate thermal properties of a 𝑈⁡(1) lattice gauge theory in 1 + 1 dimensions through real-time simulations. We extract the spectral functions directly coupling to the pseudoscalar and scalar mesons, demonstrating the thermal modifications of these states with increasing temperatures. Introducing the notion of energy-flow operators, we quantify the temporal buildup of correlations in the energy flows across the lattice. We demonstrate that energy-energy correlators fail to factorize to products of energy flows, both in the vacuum and at nonzero temperature, indicating the presence of nontrivial correlations in the quantum states. Our results constitute a first real-time ab initio study of bound-state thermal broadening and finite temperature energy-flow correlations in a gauge theory, providing a benchmark for future studies of hadronic matter under extreme conditions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

radkit base v1.6

The radkit (base) software suite (python) consists of three primary libraries: stark, trajan, and curie. The trajan library provides the tools to analyze and manipulate data from lidar and inertial measurement unit (IMU) devices, cameras, as well as trajectories from algorithms such as simultaneous localization and mapping (SLAM). These components allow reading and writing standard data formats, performing rigid affine transformations, discretizing three-dimensional space, and visualizing data products. The curie library comprises a standard set of object-oriented tools for radiation data and analysis in the following modules: (1) listmode and binmode data classes with methods for manipulation, plotting, slicing and file IO; (2) radiological/nuclear source detection/identification analysis results; (3) source encounters of correlated analyses and (4) energy-dependent angular detector response functions. The stark package provides low-level tools that are leveraged by both curie and trajan. The tools are flexible for offline analysis as well as performant for real-time integrations.

Salathe, Marco [Lawrence Berkeley National Laborat↗

Electron Microscopy Approaches to Unraveling the Structure of Amorphous Materials

Determining atomic structures in crystalline materials—where atoms are arranged in rigid, periodic lattices—has been highly successful using probes such as electrons, X-rays, and neutrons. In contrast, amorphous materials, despite their ubiquity and technological importance, remain far more challenging to characterize with comparable accuracy and precision. This review highlights existing, emerging, and potential (scanning) transmission electron microscopy ((S)TEM) techniques for probing short- and medium-range order in amorphous materials. Approaches ranging from high-resolution (S)TEM imaging and selected electron diffraction pattern to four-dimensional STEM (4D-STEM) based pair distribution function, fluctuation electron microscopy, tomography, ptychography, and spectroscopic methods are discussed, emphasizing their ability to provide complementary insights across multiple length scales—from sub-angstrom local environments to nanometer-scale correlations. Here, we further explore the promise of multimodal and correlative strategies, as well as the growing role of machine learning and physics-informed AI in enabling real-time, quantitative interpretation of complex structural signatures. Together, these advances point toward a future where electron microscopy not only reveals the hidden order in amorphous systems but also establishes robust structure–property relationships, paving the way for materials innovation in disordered matter.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states

Understanding real-time dynamics of interacting quantum fields in curved space-time remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar λϕ 4 theory and the Schwinger model, i.e. a Dirac fermion coupled to a U(1) gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the λϕ 4 theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Correlation between infrared spectra features and coverage of different adsorption sites for the NO/Pd(111) system

This study investigates the adsorption of nitric oxide (NO) on Pd(111) surfaces at 200 K using infrared reflection absorption spectroscopy (IRRAS). Peak positions and areas are used as proxies for tracking coverage of different species, serving as groundwork for in-situ experiments that need real-time tracking of surface species. Here, we derived a mathematical model correlating NO coverage with dose, consistent with the Molecular Langmuir Model. Distinct correlations are observed between coverage and spectral features (peak position and peak area for the NO vibration): at lower coverages (θ<0.6), the total integrated peak areas are linearly corelated to coverage; at higher coverages (θ>0.6), the peak center for a compressed-hollow site becomes the primary coverage indicator, showing a linear relationship between wavenumber and coverage. Note that this study addresses coverages below saturation. These findings refine our understanding of NO adsorption and establish a foundation for real-time in situ transient kinetics studies of chemical reactions involving NO on Pd(111).

25 ENERGY STORAGE↗

Mesoporous Thin Film Architectures: Addressing Material Demands through Molecular Self-Assembly

Mesoporous thin films spark interest across a wide range of disciplines due to their tunable nanostructures, large internal surface areas, and strong compatibility with planar optical, electronic, and microfluidic devices. While attention in the porous materials community has shifted toward macroporous or disordered nanoporous systems, a resurgence in mesoporous thin film research is underway, driven by new molecular self-assembly methods, advanced materials chemistry, and improved characterization techniques. The integration of high-χN block copolymer design, kinetically persistent micelle templating, and postdeposition processing protocols now allows control over structural parameters such as pore size, wall thickness, porosity, and connectivity. These advances have overcome many of the thermodynamic and processing constraints that previously limited widespread adoption. Rather than serving only as high-surface-area supports, mesoporous thin films are engineered as active interfaces where responsive chemistries and nanoscale confinement act in tandem. Embedding switchable ligands, thermoresponsive polymers, redox mediators, or ion-selective groups directly within the pore walls enables real-time control over transport, optical, and electrochemical properties. These capabilities open up new directions in adaptive coatings, gated membranes, and fast-response biosensors. To further expand their functional scope, mesoporous films are integrated into hierarchical and multicomponent architectures. Techniques such as triblock terpolymer templating, crack-directed assembly, and nanoimprint lithography allow for control over spatial organization on the micron and submicron scale and pore system orientation. This enables programmable anisotropy, enhanced molecular diffusion, and wavelength-selective photonic behavior, essential for next-generation sensing, catalysis, and energy applications. Such structural and functional complexity requires equally sophisticated characterization. Multimodal and in situ techniques can track material dynamics under operational conditions. Recent progress includes extended-range ellipsometric porosimetry (EP) for hierarchical architectures, vacuum EP for interface energetics, time-resolved EP for diffusion kinetics, and correlative AFM-SAXS mapping. The introduction of advanced neutron-based spectroscopies, particularly quasielastic neutron scattering (QENS), promises to provide real-time access to ion transport dynamics and segmental motion under nanoscale confinement, offering a path toward deeper mechanistic understanding of structure-performance correlations in mesoporous systems. This Account reflects the technical advances made and the interdisciplinary collaborations that have shaped our collective vision. The particular dimensions of mesopores enable us to subtly tune interactions at the molecular, interfacial, and mesoscopic levels that permit us to harness nanoconfinement. What emerges is a versatile, modular platform capable of chemical gating, energy transduction, and sensing with a level of tunability unmatched by other porous materials. We highlight critical challenges including the need for more robust large-area processing, a deeper understanding of dynamic behavior under cycling, and better integration with device-level architectures. Our strategies support the transition of mesoporous thin films into active high-performance components in next-generation energy, environmental, and biomedical systems.

oxides↗

Improving Trustworthiness of Data-Driven Power Grid Contingency Analysis With Bayesian Residual Graph Neural Networks

The evolving energy landscape requires novel tools to efficiently perform contingency analysis and reliability assessment of power grids, potentially in real-time. The high computational cost of traditional power flow solvers limits their applicability in practice. Machine learning (ML) surrogates such as deep neural networks (NNs) accelerate power flow solvers computations, enabling high-order contingency analysis and real-time decision-making by learning highly nonlinear functions and integrating grid topology via graph architectures. However, (graph) NNs lack predictive power away from training data and do not provide predictive confidence estimates. Here, we present a Bayesian residual graph NN that integrates knowledge from low-fidelity data via residual training and embeds granular quantification of uncertainties, improving trustworthiness critical for high-consequence decision-making. Applying Bayesian concepts to NNs is challenging due to the high-dimensionality of both the parameter space, complicating derivation of a meaningful prior, and the output space in large grid systems, requiring enhanced techniques to assess the predicted high-dimensional uncertainties. Our contributions include: (1) Deriving a prior for fully connected and graph NNs that leverages low-fidelity data to guide mean predictions and appropriately control prior predictive uncertainty. (2) Integrating this prior within an ensembling with anchoring scheme for efficient approximate posterior inference. (3) Deriving enhanced metrics to assess accuracy of both the mean and uncertainty predictions in high dimensions, appropriately accounting for correlations propagated through graph layers. The resulting Bayesian residual graph NN is tested on a contingency analysis task for 14-bus and 118-bus grids.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

Deciphering supramolecular and polymer-like behavior in metallogels: real-time insights into temperature-modulated gelation and rapid self-assembly dynamics

Bis(pyridyl) urea-based gelators, namely L2 and its isomeric mixture ( L1 + L2 ), are known to self-assemble into 1D architectures capable of inducing supramolecular gelation. Coordination with metal ions such as Ag( I ), Cu( II ), and Fe( III ) introduces structural reinforcement, enabling the formation of distinct 3D networks governed by metal-specific coordination geometries. Here, we present a comprehensive investigation into the temperature-responsive behavior (20–60 °C) of L2 and L1 + L2 , both in the absence and presence of Ag( I ), Dy( III ), Fe( III ), Cu( II ), and Ho( III ), using real-time small-angle neutron scattering (SANS). To probe long-term structural evolution/kinetics of self-assembly, real-time small-angle X-ray scattering (SAXS) was employed on L2 + Ag gels, complemented by differential scanning calorimetry (DSC) to evaluate thermal transitions. Our results reveal strikingly divergent gelation behaviors: L2 forms a highly rigid, covalent polymer-like network, while L1 + L2 exhibits remarkable thermal adaptability. Upon metal coordination, the assemblies exhibit pronounced crystallinity and exceptional thermal stability, as evidenced by persistent Bragg reflections and invariant d-spacings. Intriguingly, L2 : Fe (2 : 1) and L1 : L2 : Fe (0.5 : 0.5 : 1) in acetonitrile-d 3 (ACN-d 3 ) deviate from this trend, forming thermally labile amorphous gels. These systems show a complete loss of crystalline order, reduced Porod exponents—indicative of collapsed or branched fiber morphologies—and prominent melting and glass transition events in DSC. Fitting SANS and SAXS data to the correlation length model unveiled insightful nanostructural features. While most systems displayed minimal temperature-induced variation in mesh size or surface morphology, L2 : Ag in dimethyl sulfoxide-d 6 (DMSO-d 6 )/D 2 O and L2 : Fe (1 : 1) in ACN-d 3 exhibited a rare combination of thermally stable correlation lengths and increasing high- q exponents—strongly suggesting progressive fiber densification or surface smoothing within a robust gel framework. These findings highlight the tunability and structural resilience of supramolecular gels through precise control of ligand architecture, metal coordination, and temperature, offering valuable design principles for functional soft materials.

Pajoubpong, Jinnipha [Univ. of Cincinnati, OH (Uni↗

Transformative Impacts of Laser-Induced Breakdown Spectroscopy on Environmental and Biological Research at Oak Ridge National Laboratory

This manuscript will present an advancement of transformative research that has been conducted at Oak Ridge National Laboratory (ORNL) over a 25-year period (2000–2025) on a variety of environmental and biological matrices. These investigations derived a fundamental understanding of how elemental detection and analysis of these matrices led to the knowledge and discovery of natural processes in plants and the environment. Each project led to the initiation of a new research area which unearthed awesome and novel breakthroughs. Highlights are listed below: 1. The preliminary research at ORNL centered on the detection of aerosols utilizing Laser-induced Breakdown Spectroscopy (LIBS) technology. The Clean Air Act Amendment (CAAA) of 1990 highlighted the importance of identifying hazardous air pollutants (HAPs) due to their impact on environmental and human health, thereby underscoring the need to detect various toxic elements. Research in aerosol chemistry aimed to identify these harmful elements released by factories during periods of increased emissions in their manufacturing processes. LIBS emerged as the most effective method for real-time, in situ measurements of metal species in both gaseous and aerosol phases. 2. An understanding of the presence of total carbon in soils gives perspective on how to develop carbon sequestration strategies. The recognition that carbon sinks can evolve back to carbon sources to emit back to the atmosphere was an important consideration. Also, the concentration of carbon in soil indicates the health of land areas for growing crops successfully. 3. The direct detection of most of the elements in a wood sample in a single emission spectrum, without sample preparation, encouraged the research to use the LIBS technique for preservative treated wood coupled with use of multivariate statistical methodology. Additionally, it encouraged the researchers to try to differentiate natural woods from different parts of the country, and it was successfully demonstrated that LIBS coupled with MVA analysis could differentiate wood of different species from each other and of similar species grown in different environments based on their elemental spectra. This was a breakthrough since it revealed a systematic approach to connect elemental scarcity and abundance to either drought or typical rainfall conditions for the hardwood trees grown in specific areas. 4. Furthermore, the research progressed to reveal physiological and developmental processes contributing to biomass production such that the variation in leaf elemental composition increases our understanding of terrestrial nutrient cycles, as well as tracking the transfer of toxic elements from soils to living organisms. 5. Recently another breakthrough viz., ionomics initiated the correlation of elements to specific genes, uncovering the function that the element performed in the plant. More recently, this has been extended from plants to fungi as well as fungi growing in symbiotic relations with plants.

09 BIOMASS FUELS↗

Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model

Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present an ancilla-based framework for implementing trigonometric gates with arguments given by arbitrary Hermitian functions of qumode quadratures. The protocol yields unitary gates deterministically, and non-unitary gates through probabilistic post-selection. As a concrete application, we develop a hybrid qubit-qumode quantum simulation of the lattice sine-Gordon model. Using these gates, we prepare ground states via quantum imaginary-time evolution, simulate real-time dynamics, compute time-dependent vertex two-point correlation functions, and extract quantum kink profiles under topological boundary conditions. Our results demonstrate that trigonometric continuous-variable gates provide a physically natural framework for simulating interacting field theories on near-term hybrid quantum hardware, while establishing a parallel route to universality beyond polynomial gate constructions. We expect that the trigonometric gates introduced here to find broader applications, including quantum simulations of condensed matter systems, quantum chemistry, and biological models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Correlation of Surface Acoustic Wave (SAW) force myography sensor output with elbow joint torque

Accurate assessment of skeletal muscle forces and net joint torque is essential for preventing fatigue-related injuries, optimizing physical training, and monitoring disease progression in neuromuscular conditions. However, existing joint torque evaluation techniques are hindered by limited portability and high operational costs, confining their use to controlled laboratory or clinical settings. Despite substantial advances in wearable joint torque estimation systems, ongoing challenges such as power constraints, bulky wired setups, and susceptibility to environmental or motion artifacts underscore the urgent need for truly batteryless, wireless solutions deployable in real-world settings. This paper proposes a novel surface acoustic wave (SAW)-based force myography (FMG) system for noninvasive measurement of joint torque, validated against a gold-standard electromechanical dynamometer. The approach uses a single SAW sensor embedded in an armband to detect volumetric biceps brachii changes, with a second-order polynomial mapping sensor output and elbow angle to torque. Seven participants were tested in both isometric (15°–90°) and isokinetic (10°/s and 20°/s) supinated elbow flexion tasks. Under isometric conditions, subject-specific calibration achieved a normalized root-mean-square error (NRMSE) of 13.6% ± 6.0% and R 2 = 0.834 ± 0.180, while a group-level model yielded 14.4% ± 6.8% and 0.808 ± 0.208, respectively. For isokinetic trials, the group model produced an NRMSE of 24.1% ± 6.6% at 10°/s and 24.9% ± 08.9% at 20°/s, highlighting the feasibility of using a single-sensor SAW-FMG setup across different speeds. Because SAW devices support wireless, battery-free operation, the proposed system offers a pathway to portable, real-time monitoring for sports medicine, rehabilitation, and clinical diagnostics.

36 MATERIALS SCIENCE↗

Perspective on Many-Body Methods for Molecular Polaritonic Systems

Recent advances in strong light–matter interactions have revealed a wealth of new physical phenomena in molecules embedded in optical cavities, including modified chemical reactivity, altered excitation spectra, and novel quantum correlations. To describe these effects from first-principles, the field of ab initio quantum electrodynamics (QED) has emerged as a compelling extension of quantum chemistry that treats electronic and photonic degrees of freedom on equal footing. In this Perspective, we review the growing landscape of many-body QED methods, including Hartree–Fock, density functional theory (QEDFT), time-dependent DFT (QED-TDDFT), configuration interaction (QED-CI), complete active space (QED-CASSCF), coupled cluster (QED-CC), quantum Monte Carlo (QED-QMC), and density matrix renormalization group (QED-DMRG), highlighting recent developments and implementations. We further explore real-time methods, gradient and Hessian formalisms, and the integration of nonadiabatic nuclear dynamics. Applications range from benchmark simulations of polaritonic chemistry to quantum simulations on emerging quantum hardware. We conclude by outlining future directions for theory development and interdisciplinary efforts at the interface of quantum chemistry, condensed matter, and quantum optics.

36 MATERIALS SCIENCE↗

Current-Driven Symmetry Breaking and Spin–Orbit Polarization in Chiral Wires

The spin dynamics of electrons in chiral molecular systems remains a topic of intense interest, particularly regarding whether geometric chirality inherently induces spin polarization in current-carrying electrons. In this work, we employ ab initio real-time time-dependent density functional theory (rt-TDDFT) to directly simulate the interplay among charge current, spin, and orbital. This realtime tracking extends beyond perturbative treatments, and we analyze how nonequilibrium currents effectively lift the symmetry constraints of screw rotation and time-reversal symmetry. We find that the emergence of spin and orbital angular momenta is dynamically correlated with a concomitant loss of translational (linear) momentum, which we interpret as an intrinsic consequence of current-driven symmetry lowering. The implications of this mechanism for chirality-induced spin selectivity and spintronics device design are discussed.

chiral wire↗

Improving Spectral Resolution from Real-time Evolution for Correlated Systems

Abstract The quality of numerically simulated spectra using real-time evolution methods for strongly correlated systems is affected by both the length of simulation time and the system size, limiting resolution in both frequency and momentum. In this work, we propose a computationally cheap, linear autoregressive machine learning-based framework to extend short-time and short-distance results over a wider range. We use the proposed method to extend the lesser Green’s function for both the Hubbard model and the much more computationally challenging Hubbard-extended Holstein model. This technique significantly improves both the frequency and momentum resolution of the single-particle removal spectrum $${\mathcal{A}}(k,\omega )$$ A ( k , ω ) , allowing the observation of otherwise obscured spectral features due to electron-phonon coupling.

Tang, Ta↗

Influence of Markovianity and self-consistency on time-resolved spectral functions of driven quantum systems

We present a systematic comparison of the real-time Dyson expansion (RTDE) with established nonequilibrium Green's function (GF) approaches for simulating driven, interacting quantum systems. Focusing on density matrix dynamics, time-off-diagonal GFs, and time-resolved photoemission spectra, we benchmark RTDE against fully self-consistent Kadanoff-Baym equation (KBE) calculations, the generalized Kadanoff-Baym ansatz, and exact diagonalization for small systems using second-order many-body perturbation theory. Using a driven two-band Hubbard model, we show that mean-field single-particle density matrix trajectories provide a reliable baseline for RTDE across a broad range of interaction strengths and excited-carrier populations. Further, RTDE accurately captures correlation effects in the GFs, including long-lived oscillations and revivals that are strongly suppressed by the overdamping inherent to self-consistent KBE schemes. As a consequence, RTDE resolves rich nonequilibrium spectral structure in time-resolved photoemission, such as interaction- and population-dependent quasiparticle splittings and band gap renormalization, which are largely washed out in self-consistent approaches yet are present in exact solutions. Furthermore, our results demonstrate that RTDE bridges the gap between mean-field propagation and full two-time KBE simulations, retaining favorable linear scaling while capturing essential dynamical correlations relevant for ultrafast spectroscopy.

Electronic structure↗