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268 records · Page 9

Interface Design for High‐Performance All‐Solid‐State Lithium Batteries

All‐solid‐state batteries suffer from high interface resistance and lithium dendrite growth leading to low Li plating/stripping Coulombic efficiency (CE) of <90% and low critical current density at high capacity. Here, in this work, both challenges are simultaneously addressed and the Li plating/stripping CE is significantly increased to 99.6% at 0.2 mA cm −2 /0.2 mAh cm −2 , and critical current density (CCD) of > 3.0 mA cm −2 /3.0 mAh cm −2 by inserting a mixed ionic‐electronic conductive (MIEC) and lithiophobic LiF‐C‐Li 3 N‐Bi nanocomposite interlayer between Li 6 PS 5 Cl electrolyte and Li anode. The highly lithiophobic LiF‐C‐Li 3 N‐Bi interlayer with high ionic conductivity (10 −5 S cm −1 ) and low electronic conductivity (3.4×10 −7 S cm −1 ) enables Li to plate on the current collector (CC) surface rather than on Li 6 PS 5 Cl surface avoiding Li 6 PS 5 Cl electrolyte reduction. During initial Li plating on CC, Li penetrates into porous LiF‐C‐Li 3 N‐Bi interlayer and lithiates Bi nanoparticles into Li 3 Bi. The lithiophilic Li 3 Bi and Li 3 N nanoparticles in LiF‐C‐Li 3 N‐Li 3 Bi sub‐interlayer will move to CC along with plated Li, forming LiF‐C/Li 3 N‐Li 3 Bi lithiophobic/lithiophilic sublayer during the following Li stripping. This interlayer enables Co 0.1 Fe 0.9 S 2 /Li 6 PS 5 Cl/Li cell with an areal capacity of 1.4 mAh cm −2 to achieve a cycle life of >850 cycles at 150 mA g −1 . The lithiophobic/lithiophilic interlayer enables solid‐state metal batteries to simultaneously achieve high energy and long cycle life.

25 ENERGY STORAGE

Revealing key structures for reversible sulfur redox in amorphous polymeric sulfur

Amorphous polymeric sulfur cathodes, such as sulfurized polyacrylonitrile (SPAN), enable high-energy lithium-sulfur batteries without cobalt or nickel, leveraging abundant sulfur. However, the limited in situ understanding of their synthesis and electrochemistry has impeded targeted optimization. Here, in this study, we integrate operando high-energy total scattering with sulfur K-edge X-ray absorption spectroscopy to monitor SPAN's formation and cycling in real time. Our results show that S-C bond formation halts further fusion of cyclized polyacrylonitrile, fostering π-π stacking and a transition from long-chain to short-chain sulfur-critical for reversible sulfur redox. These features synergistically minimize polysulfide dissolution and charge-transfer resistance, enabling optimized SPAN to achieve high capacity retention over 1,000 cycles. Operando X-ray absorption spectroscopy reveals that residual protons drive thiol-thione tautomerism, with lithium replacement during the first discharge causing ~20% irreversible capacity loss. To enhance performance, minimizing -NH groups and expanding pyridine networks are key. These findings transform SPAN optimization from empirical tuning to mechanism‑guided engineering and point the way towards sulfur loadings and energy densities competitive with state‑of‑the‑art Li‑ion cathodes.

25 ENERGY STORAGE

Solar Heat for Industrial Processes: Integration with Chemical Reactors

The integration of solar thermal systems with chemical reactors has been proposed as part of a larger effort to develop and deploy solar heat for industrial processes (SHIP) technologies. A strong motivation for SHIP processes and technologies is the potential for high thermal efficiency coupled with low-cost thermal energy storage (TES) which can enable commercial deployment of such systems. While there are different ways to categorize SHIP technologies, one important such distinction is between directly irradiated systems and indirect off-sun process driven by a SHIP system. While directly irradiated systems can provide high thermal efficiencies and high fluxes, they usually require complex engineering solutions due to the need for redesigning the established processes and unit operations. In most cases, it is also more challenging to couple such a process to a TES system, losing some of the benefits of SHIP. On the other hand, using a SHIP system to drive an industrial process off-sun can allow better integration with existing process chains, easier TES capabilities, and potential for more applications fitting a specific SHIP technology. However, the integration of SHIP systems with the industrial processes is not fully explored in detail, especially in the case of high-temperature processes such as reforming, cracking, cement manufacturing, and iron/steelmaking. Many of these systems require heating fluxes of >50 kW/m^2, supplied via combustion of hydrocarbons in a fire box and benefitting from radiative heat transfer between the flue gases and the reaction zones. As such, using SHIP systems for such processes is more complex than providing the same thermal input in the form of a heat transfer medium (HTM) entering the reactor, kiln, or furnace. Moreover, in case convective heat transfer using SHIP is envisioned, for example using supercritical CO2 as the HTM from a particle receiver, the thermal integration might be more challenging than initially envisioned: lower heat transfer coefficients and limited approach temperature might require large flow rates, causing a mismatch between the process thermal requirements and the thermal capacity of the SHIP system. In addition, even if the heat exchange between SHIP and reactor is effective, there is still a cold leg HTM at the reaction temperature or slightly below it. Chemical plants usually include a set of heat exchangers, heat recovery steam generators, and even power generation units - in a tightly integrated design - to recover the flue gases which are eventually vented. With SHIP systems mostly operating on a closed HTM loop, bottoming the cold leg is crucial. In this talk, we will present different modeling results for a variety of syngas production reactions, using catalytic and chemical looping processes, and discuss some of the challenges and design considerations for off-sun chemical reactors using SHIP systems.

14 SOLAR ENERGY

Self-generated electrokinetic flows from active-charged boundary patterns

We develop a hydrodynamic description of self-generated electrolyte flow in capillaries whose bounding walls feature nonuniform distributions of charge nonuniform active ionic fluxes. The hydrodynamic velocity arising in such a system has components that are forbidden by symmetry in the absence of charge and fluxes. However, when these two boundary mechanisms are simultaneously present, they can lead to a symmetry broken state where steady flows with both unidirectional and circulatory components emerge. We show that these flow states arise when modulated boundary patterns of charge and fluxes are offset by a flux-charge phase difference, which is associated with the separation between sites of their peak densities on the wall. Mismatch in diffusivity of cationic and anionic species can modify the flow states and becomes an enhancing factor when fluxes of both ion species are being produced together at the same site. We demonstrate that this mechanism can be realized with a microfluidic generator that is powered by enzyme-coated patches that catalyze reactants in the solution to produce fluxes of ions. The local ionic elevation or depletion, which disrupts a nonuniform double layer, promotes self-induced gradients yielding persistent body forces to generate bulk fluid motion. Our work quantifies a boundary-driven mechanism behind self-sustained electrolyte flow in confined environments that exists without any external bulk-imposed fields or gradients. It provides a theoretical framework for understanding the combined effect of active and charged boundaries that are relevant in biological or soft matter systems, and can be utilized in electrofluidic and iontronic applications.

active matter

Understanding Discharge‐Driven Growth of Cathode Impedance in Ni‐Rich NMC Cathodes

Degradation of LiNi x Mn y Co 1-x-y O 2 (NMC)-based lithium-ion batteries depends strongly on cut-off voltage ranges. In addition to the high upper cut-off voltage, a high depth of discharge (i.e., lower cut-off voltage) significantly worsens cathode impedance growth and capacity fade during long-term cycling. However, there is currently no consensus on the mechanism behind the negative role of a deep discharge. Here, this phenomenon was investigated in graphite||NMC cells with single-crystal cathodes (LiNi 0.6 Co 0.2 Mn 0.2 O 2 (NMC622) or LiNi 0.76 Co 0.14 Mn 0.10 O 2 (NMC76)) using targeted aging protocols (constant high-voltage holds vs. charge–discharge cycling), while monitoring transition-metal (TM) dissolution, cathode-electrolyte interface (CEI) impedance, and NMC surface composition. We demonstrate a correlation between discharge-driven CEI impedance growth and increased TM dissolution. Furthermore, this degradation pathway is more pronounced in lower-Ni NMC622 than in higher-Ni (NMC76) under comparable delithiation states at charge, with both compositions undergoing the H2→H3 phase transition. X-ray photoelectron spectroscopy (XPS) reveals NMC composition-dependent evolution of surface lattice oxygen and restructured surface layer composition between charged and discharged states. These findings add mechanistic depth to the role of discharge as an active driver of interfacial degradation and provide new insights into its composition dependence.

25 ENERGY STORAGE

Market participation strategy of hybrid energy resources: A New York ISO case study

Drawing on existing market designs with independent resource participation in electricity markets, this study analyzes participation models for hybrid resources combining renewable generation and storage. Two models are considered: in the first, the components operate independently, with the Independent System Operator (ISO) managing the storage state of charge (SoC); in the second, the hybrid resource acts as an integrated unit, submitting offers as a “black box” and managing its SoC internally. Using a production cost model for the zonal New York Bulk Power System, we evaluate trade-offs in system reliability, market efficiency, and asset profitability. Our results provide several key insights for policymakers, showing that the ISO-managed granular model enhances social welfare through explicit SoC management, while the simpler integrated model is more computationally efficient, but may cause more real-time violations and lower overall profits.

Bansal, Rajni Kant

Underground Test Area Activity Waste Management Plan; and Attachment 1 Fluid Management Plan for the Underground Test Area Activity

The U.S. Department of Energy, National Nuclear Security Administration Nevada Field Office initiated the Underground Test Area Activity to characterize the risk posed to human health and the environment as a result of underground nuclear testing activities at the Nevada National Security Site. The UGTA Activity is now administered by the DOE Environmental Management Nevada Program. This document is a revision to NNSA/NSO (2009). The new document and revision number reflect EM Nevada Program as the current UGTA Activity administrator.

54 ENVIRONMENTAL SCIENCES

Decorated Honeycomb Lattice and Successive Magnetic Transitions of the Delafossite Derivative K 4 Ni 5 Te 3 O 16

Here, we report the synthesis and characterization of the delafossite derivative K 4 Ni 5 Te 3 O 16 , which hosts a decorated honeycomb Ni 2+ lattice. Single-crystal X-ray diffraction, electron microscopy, and neutron diffraction establish a noncentrosymmetric Pmm2 crystal structure that combines regular honeycomb units with elongated motifs formed by Ni 2+ trimers along extended edges. Magnetic susceptibility reveals strong antiferromagnetic interactions, while heat capacity measurements identify two successive magnetic transitions at 30 and 12 K. Neutron diffraction shows that these transitions correspond to a progression from partial to full long-range magnetic order on distinct Ni sites, reflecting competition among the various exchange interactions. The resulting magnetic point group, mm2.1′, inherits the lattice polarity and permits high-order magnetoelectric coupling. Consistent with this symmetry, a quadratic magnetic-field-induced polarization is experimentally observed below the magnetic ordering temperature, likely arising from exchange-driven magnetostriction coupled to the polar lattice. These results establish K 4 Ni 5 Te 3 O 16 as an interesting platform for engineering B-site ordering in delafossite derivatives to realize complex quantum magnetism and functional responses.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Localizing the non-thermal X-ray emission of PSR J2229+6114 from its multi-wavelength pulse profiles

Context.Pulsars are detected over the whole electromagnetic spectrum, from radio wavelengths up to very high energies, in the GeV-TeV range. While the radio emission site for young pulsars is well constrained to occur at altitudes about several percent of the light-cylinder radius andγ-ray emission is believed to be produced in the striped wind, outside the light cylinder, the non-thermal X-ray production site remains unknown. Aims.The aim of this Letter is to localize the non-thermal X-ray emission region based on a multi-wavelength pulse profile fitting for PSR J2229+6114, which stands as a particularly good candidate given its high X-ray brightness. Methods.Based on the geometry deduced from the joint radio andγ-ray pulse profiles, we fixed the magnetic axis inclination angle and the line-of-sight (LoS) inclination angle. However, we left the region of X-ray emission unlocalized, setting it somewhere between the surface and the light cylinder. We localized this region and its extension by fitting the X-ray pulse profile as observed by the NICER,NuSTAR, and RXTE telescopes in the ranges of 2–7 keV, 3–10 keV, and 9.4–22.4 keV, respectively. Results.We constrained the non-thermal X-ray emission to arise from altitudes between 0.2 r L and 0.55 r L wherer L is the light-cylinder radius. The magnetic obliquity is approximatelyα ≈ 45° −50° and the LoS inclination angle isζ ≈ 32° −48°. Conclusions.This Letter is among the first works to offer a tight constraint on the location of non-thermal X-ray emission from pulsars. We plan to apply this procedure to several other promising candidates to confirm this new result.

Astronomy & Astrophysics

A Sensitivity-driven Wide Area Protection (SWAP) Coordination Tool for High Penetration of Inverter-based Resources (IBR)

Traditionally, power system generation sources have been composed of synchronous generators, of which the fault current behavior is understood with minimal differences between generation size and types due to the physics of their construction. Present protection schemes and modeling methods are based upon these understood characteristics. Most renewable generation is composed of inverter-based resources (IBR), in which fault current is determined by switching control software and hardware limitations, each of which can vary between manufacturers and even between models of the same manufacturer. The resulting fault current is low in magnitude, low in negative-sequence current, unpredictable phase angles, and is a challenge to model. These characteristics also result in a challenge to traditional protection schemes and fault simulation software. To address several of these concerns, the project has the following goals: 1. Improve IBR models: Improve IBR models used in short circuit (SC) programs to accurately capture the response of IBRs at the bulk power system (BPS) level for fault and protection studies. 2. Develop automation tool: Develop an automation tool that allows engineers to identify protection coordination and sensitivity issues by performing SC and protection coordination studies in a high IBR-penetrated grid by applying variations to the IBR models, faults, contingencies, etc. 3. Develop schemes: Develop new protection mitigation solution schemes that complement the existing protection systems to ensure safe operation of the BPS with higher IBR penetration levels. The project team did not achieve this final goal, as the Department of Energy (DOE) stopped the project early due to changes in DOE funding priorities. The termination notice came at the beginning of the final project phase, while the team was identifying and beginning to investigate protection issues. It should be noted that the team discussed a 100% penetration scenario. However, this scenario would require the use of grid-forming IBR models that are not presently available. Since developing these models requires additional effort, the 100% penetration scenario was not pursued during this project. In the future, developing the methodology and models for the 100% scenario could benefit the industry.

14 SOLAR ENERGY

Lanthanum-Promoted Electrocatalyst for the Oxygen Evolution Reaction: Unique Catalyst or Oxide Deconstruction?

A conventional performance metric for electrocatalysts that promote the oxygen evolution reaction (OER) is the current density at a given overpotential. However, the assumption that increased current density at lower overpotentials indicates superior catalyst design is precarious for OER catalysts in the working environment, as the crystalline lattice is prone to deconstruction and amorphization, thus greatly increasing the concentration of catalytic active sites. We show this to be the case for La 3+ incorporation into Co 3 O 4 . Powder X-ray diffraction (PXRD), Raman spectroscopy and extended X-ray absorption fine structure (EXAFS) reveal smaller domain sizes with decreased long-range order and increased amorphization for La-modified Co 3 O 4 . This lattice deconstruction is exacerbated under the conditions of OER as indicated by operando spectroscopies. The overpotential for OER decreases with increasing La 3+ concentration, with maximum activity achieved at 17% La incorporation. HRTEM images and electron diffraction patterns clearly show the formation of an amorphous overlayer during OER catalysis that is accelerated with La 3+ addition. O 1s XPS spectra after OER show the loss of lattice-oxide and an increase in peak intensities associated with hydroxylated or defective O-atom environments, consistent with Co(O) x (OH) y species in an amorphous overlayer. Furthermore, our results suggest that improved catalytic activity of oxides incorporated with La 3+ ions (and likely other metal ions) is due to an increase in the number of terminal octahedral Co(O) x (OH) y edge sites upon Co 3 O 4 lattice deconstruction, rather than enhanced intrinsic catalysis.

Catalysts

Green Era Anaerobic Digester

Green Era Educational NFP constructed and commissioned the Green Era Renewable Energy & Urban Farming Campus in Chicago’s Auburn Gresham neighborhood. The project transformed a long-vacant brownfield site into a commercial-scale anaerobic digestion facility that converts food waste into renewable natural gas and nutrient-rich material for agricultural use. The facility can process up to 80,000 wet tons of food waste annually and supports approximately 15 permanent jobs while advancing food waste diversion, renewable energy production, nutrient recovery and community revitalization.

03 NATURAL GAS

Adsorption, charge transfer and a coverage-driven transition of alkali metals on rutile TiO 2 (110)

The interaction of alkali metals with metal oxide surfaces is central to tuning surface reactivity in heterogeneous catalysis and photocatalysis. Here we present a comprehensive DFT+U study of the adsorption of alkali metals (Li, Na, K, Rb, Cs) on the (110) surface of rutile TiO 2 . At low coverage (θ = 1/8), all alkali metals bind preferentially to bridging oxygen sites with adsorption energies in the range −4.06 to −3.33 eV, transferring nearly one full electron (0.92–0.99 |e|) to the substrate and inducing Ti 4+ → Ti 3+ reduction. The excess charge localizes preferentially at subsurface Ti sites in the form of small polarons. Diffusion barriers indicate facile motion along bridging-oxygen rows, whereas inter-row hopping is strongly hindered. Coverage effects were examined systematically for potassium: adsorption energy and charge transfer per K atom decrease monotonically with increasing θ. Strikingly, a sharp energy discontinuity occurs between θ = 4/8 and θ = 5/8 (ΔE ≈ 1 eV per atom), which we identify as a coverage-driven structural transition arising from steric packing constraints and enhanced K–K electrostatic repulsion once every (1×1) surface cell is occupied. This structural transition perfectly correlates with a dramatic drop in the work function down to an ultra-low minimum of 0.84 eV at θ=5/8, followed by a metallization- driven recovery at higher coverages. Ab initio molecular dynamics simulations confirm zigzag K arrangements at moderate coverage (θ = 1/3), while at high coverage (θ = 2/3) short-range K–K correlations emerge without long-range order. These results provide atomistic insight into the structure–activity relationships underlying alkali promotion effects on oxide-supported catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Distributed Mafic Rock Resources for Carbon Mineralization in Arizona

Ex-situ carbon mineralization is a process by which CO2 is reacted with alkaline silicate minerals and rocks to produce stable carbonate materials, which can be used for other industrial processes. Arizona, U.S.A., hosts abundant surficial mafic rocks in three young volcanic fields, Geronimo-San Bernardino, San Francisco, and Springerville, and other distributed locations throughout the state. We created a Mafic Rock Resource Inventory (MRRI) that categorizes geochemical, physical, and textural characteristics of a diverse suite of surficial mafic rock samples and provide a benchmark reaction dataset parameterizing the temperature, pressure, and pH conditions best suited ex-situ mineralization in different rock types. MRRI data is publicly available online via a map-viewer. We establish two reaction condition sets, varied in temperature, pressure, and pH, where crystal-rich and glassy rocks reach maximum reaction extent and different carbonate phases are formed. Systematic ex-situ mineralization experiments on 21 diverse rock types show trends in geochemical, mineralogical, and reactivity behavior and establish maximum effective capture capacity. From this, scoria cones in three Arizona volcanic fields have a ~62 Gt effective CO₂ storage capacity with one of the fields having a ~42 Gt storage capacity in lava flows. Reactivity results have applications to alkaline mafic rock resources exposed globally, including producing additional effective storage capacity estimates and scaled commercialization of mafic rock ex-situ mineralization, should reaction extents be improved through advances in mineralization techniques. MRRI data were used to create a Direct Air Capture to Mineralization (DACM) systems model, technoeconomic analysis, and life-cycle assessment. These documents are presented as three appendices.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

Systems Engineering and Analysis in Support of a US Federal Staging Facility for UNF

The US Department of Energy Office of Nuclear Energy (DOE-NE) Office of Spent Fuel and High-Level Waste Disposition is examining a set of system options and conducting supporting analyses to inform the development of an integrated waste management system, which may include one or more federal staging facilities (FSFs) for used nuclear fuel (UNF ) sited using a collaborative siting process. This paper focuses on the ongoing activities in two systems engineering and analysis work areas: (1) data and tools development, validation, and maintenance and (2) systems engineering execution. Within the first work area, the STANDARDS 5.0 UNF data and analysis tool, formerly known as UNF-ST&DARDS, is being developed as a foundational resource to assist in the management of UNF data. It has the key capability to model UNF throughout the entire back end of the fuel cycle. STANDARDS also includes several compatible analysis tools for the time-dependent characterization of UNF and related systems by interfacing with the SCALE code system for nuclear analysis and COBRA-SFS for thermal analysis. Also, within the data and tools area is the Next Generation System Analysis Model (NGSAM), which is an agent-based simulation software tool expressly designed to be capable of modeling the waste management system, including the transportation of UNF to and from a FSF. NGSAM has been developed to enable informed decision-making by providing the capability to analyze various potential system options for the management of UNF and high-level radioactive waste. Finally, in the systems engineering execution area, the team has begun to apply a disciplined systems engineering approach at the system level along with supporting analysis to guide the development of the FSF project requirements (including associated transportation infrastructure). Systems engineering principles and practices and their adaptation/application to design and development activities will ensure that the waste management system is effectively implemented as work proceeds. Other activities include investigating the implications of changes in various assumptions and parameters related to waste management systems, such as UNF acceptance rates, receipt logic, facility capacities and capabilities, use of standardized canisters, and different assumed facility operation start dates. Keywords: federal staging facility (FSF), used nuclear fuel (UNF), integrated waste management (IWM) system, Next Generation System Analysis Model (NGSAM), STANDARDS, systems engineering

Joseph, Robert

Advancing Building Performance: Field Results of Thin-Glass Triple-Pane Window Demonstrations

To meet California and the nation's ambitious energy targets, energy use in the building sector must drop dramatically. Windows continue to be the lowest thermally performing envelope system in the nation's buildings, resulting in poor overall envelope performance and potential impacts to human health and comfort. Current best practice new window performance is typically met by double-pane low-solar-gain glazing. Thin-glass triple-pane windows are a highly promising next step forward in performance and have been deployed in two California multi-family sites to quantify field performance and building energy savings. The technology assessed offers the performance benefits of traditional triple-pane but with little increase in weight or cost, enabling incremental costs competitive with alternative energy reduction solutions for the building envelope. This paper covers a detailed investigation into the demonstration project and measured performance benefits of the windows after a full year of data collection.

Hart, Robert

Spinel high-entropy oxides (FeNiCrMnZnX) 3 O 4 (X = Al, mg) as anode materials for high-performance lithium-ion batteries

To address the high cost, cobalt dependency, and resource constraints typical of conventional high-entropy oxide (HEO) anodes, this study reports the successful synthesis of two Co-free, six-component spinel-type HEOs(FeNiCrMnZnAl) 3 O 4 (HEO-Al) and (FeNiCrMnZnMg) 3 O 4 (HEO-Mg), via a sol-gel method. The distinct effects of Al 3+ and Mg 2+ incorporation on the electrochemical performance and lithium storage kinetics were systematically investigated. XRD, Raman, and TEM characterizations confirm that both materials possess a pure spinel phase, uniform particle size, and homogeneous elemental distribution. Notably, electrochemical evaluations reveal that HEO-Al delivers a superior reversible capacity of 480.7 mAh g −1 after 100 cycles at 0.1 A g −1 , and maintains 354.5 mAh g −1 after 1000 long-term cycles at 1 A g −1 , significantly outperforming HEO-Mg. Kinetic analysis indicates that HEO-Al exhibits lower charge transfer resistance, a higher Li + diffusion coefficient, and a pseudocapacitive contribution of up to 82%. Furthermore, these findings demonstrate that Al substitution effectively optimizes the structural stability and lithium storage kinetics of Co-free HEOs, providing a viable strategy for designing low-cost, highly stable HEO anode systems.

Anode materials

Role of Matter Interactions in Superradiant Phenomena

The superradiant phenomenon, usually described by the Dicke model, is a hallmark of strong light-matter interaction. Here, we explore how matter-matter interactions influence this phenomenon by performing ground-state simulations of Dicke-like models with both isotropic and anisotropic interactions. We find that Ising-type interactions produce two qualitatively distinct phase boundaries, one of which gives rise to an antiferromagnetic-normal phase connected to the superradiant regime via a first-order phase transition. Under anisotropic couplings, we uncover a strongly correlated phase where in-plane spin order coexists with superradiance, exhibiting sublinear scaling of the photon occupation per site and power-law decay of spin correlations. Furthermore, superradiance is strengthened by tuning either isotropic or anisotropic interactions, highlighting the role of intrinsic many-body correlations in shaping light-matter quantum phases.

Dicke model