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DOE OSTI2025

BPS and near-BPS black holes in AdS 5 and their spectrum in $\mathcal{N}$ = 4 SYM

We study quantum corrections in the gravitational path integral around nearly 1/16-BPS black holes in asymptotically AdS 5 × S 5 space, dual to heavy states in 4D N = 4 super Yang-Mills. The analysis provides a gravitational explanation of why 1/16-BPS black holes exhibit an exact degeneracy at large N and why all such states have the same charges, confirming the belief that the superconformal index precisely counts the entropy of extremal black holes. We show the presence of a gap of order N −2 between the 1/16-BPS black holes and the lightest near-BPS black holes within the same charge sector. This is the first example of such a gap for black hole states within the context of AdS 5 holography. We also derive the spectrum of near-BPS states that lie above this gap. Our computation relies on finding the correct version of the N = 2 super-Schwarzian theory which captures the breaking of the SU(1, 1|1) symmetry when the black hole has finite temperature and non-zero chemical potential. Finally, we comment on possible stringy and non-perturbative corrections that can affect the black hole spectrum.

AdS-CFT Correspondence↗

DOE OSTI2025

Orientation reversal and the Chern-Simons natural boundary

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

Chern-Simons theories↗

DOE OSTI2024

Gravitational index of the heterotic string

The fundamental heterotic string has a tower of BPS states whose supersymmetric index has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of higher-derivative terms in four-dimensional N = 2 supergravity resolves the singularity. In doing so, we extend the recently-developed “new attractor mechanism” to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Nonperturbative quantum gravity in a closed Lorentzian universe

We study how meaningful physical predictions can arise in nonperturbative quantum gravity in a closed Lorentzian universe. In such settings, recent developments suggest that the quantum gravitational Hilbert space is one-dimensional and real for each α-sector, as induced by spacetime wormholes. This appears to obstruct the conventional quantum-mechanical prescription of assigning probabilities via projection onto a basis of states. While previous approaches have introduced external observers or augmented the theory to resolve this issue, we argue that quantum gravity itself contains all the necessary ingredients to make physical predictions. We demonstrate that the emergence of classical observables and probabilistic outcomes can be understood as a consequence of partial observability: physical observers access only a subsystem of the universe. Tracing out the inaccessible degrees of freedom yields reduced density matrices that encode classical information, with uncertainties exponentially suppressed by the environment’s entropy. We develop this perspective using both the Lorentzian path integral and operator formalisms and support it with a simple microscopic model. Our results show that quantum gravity in a closed universe naturally gives rise to meaningful, robust predictions without recourse to external constructs.

AdS-CFT Correspondence↗

DOE OSTI2024

Causal sets and an emerging continuum

Abstract Causal set theory offers a simple and elegant picture of discrete physics. But the vast majority of causal sets look nothing at all like continuum spacetimes, and must be excluded in some way to obtain a realistic theory. I describe recent results showing that almost all non-manifoldlike causal sets are, in fact, very strongly suppressed in the gravitational path integral. This does not quite demonstrate the emergence of a continuum—we do not yet understand the remaining unsuppressed causal sets well enough—but it is a significant step in that direction.

Astronomy & Astrophysics↗

DOE OSTI2024

Nuclear Quantum Effects on the Electronic Structure of Water and Ice

The electronic properties and optical response of ice and water are intricately shaped by their molecular structure, including the quantum mechanical nature of the hydrogen atoms. Despite numerous previous studies, a comprehensive understanding of the nuclear quantum effects (NQEs) on the electronic structure of water and ice at finite temperatures remains elusive. Here, we utilize molecular simulations that harness efficient machine-learning potentials and many-body perturbation theory to assess how NQEs impact the electronic bands of water and hexagonal ice. By comparing path-integral and classical simulations, we find that NQEs lead to a larger renormalization of the fundamental gap of ice, compared to that of water, ultimately yielding similar bandgaps in the two systems, consistent with experimental estimates. Our calculations suggest that the increased quantum mechanical delocalization of protons in ice, relative to water, is a key factor leading to the enhancement of NQEs on the electronic structure of ice.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

On the Interplay of Electronic and Lattice Screening on Exciton Binding in Two-Dimensional Lead Halide Perovskites

We use path integral Monte Carlo to study the energetics of excitons in layered, hybrid organic–inorganic perovskites in order to elucidate the relative contributions of dielectric confinement and electron–phonon coupling. While the dielectric mismatch between polar perovskite layers and nonpolar ligand layers significantly increases the exciton binding energy relative to their three-dimensional bulk crystal counterparts, formation of exciton polarons attenuates this effect. The contribution from polaron formation is found to be a nonmonotonic function of the lead halide layer thickness, which is clarified by a general variational theory. Accounting for both of these effects provides a description of exciton binding energies in good agreement with experimental measurements. By studying isolated layers and stacked layered crystals of various thicknesses, with ligands of varying polarity, we provide a systematic understanding of the excitonic behavior of this class of materials and how to engineer their photophysics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Neutron scattering and neural-network quantum molecular dynamics investigation of the vibrations of ammonia along the solid-to-liquid transition

Abstract Vibrational spectroscopy allows us to understand complex physical and chemical interactions of molecular crystals and liquids such as ammonia, which has recently emerged as a strong hydrogen fuel candidate to support a sustainable society. We report inelastic neutron scattering measurement of vibrational properties of ammonia along the solid-to-liquid phase transition with high enough resolution for direct comparisons to ab-initio simulations. Theoretical analysis reveals the essential role of nuclear quantum effects (NQEs) for correctly describing the intermolecular spectrum as well as high energy intramolecular N-H stretching modes. This is achieved by training neural network models using ab-initio path-integral molecular dynamics (PIMD) simulations, thereby encompassing large spatiotemporal trajectories required to resolve low energy dynamics while retaining NQEs. Our results not only establish the role of NQEs in ammonia but also provide general computational frameworks to study complex molecular systems with NQEs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Unraveling electronic correlations in warm dense quantum plasmas

The study of matter at extreme densities and temperatures has emerged as a highly active frontier at the interface of plasma physics, material science and quantum chemistry with relevance for planetary modeling and inertial confinement fusion. A particular feature of such warm dense matter is the complex interplay of Coulomb interactions, quantum effects, and thermal excitations, making its rigorous theoretical description challenging. Here, we demonstrate how ab initio path integral Monte Carlo simulations allow us to unravel this intricate interplay for the example of strongly compressed beryllium, focusing on two X-ray Thomson scattering data sets obtained at the National Ignition Facility. We find excellent agreement between simulation and experiment with a very high level of consistency between independent observations without the need for any empirical input parameters. Our results call into question previously used chemical models, with important implications for the interpretation of scattering experiments and radiation hydrodynamics simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Nuclear quantum effects in molecular liquids across chemical space

Abstract Nuclear quantum effects (NQEs) influence many physical and chemical phenomena, particularly those involving light atoms or occurring at low temperatures. However, their impact has been carefully quantified in few systems-like water-and is rarely considered more broadly. Here we use path-integral molecular dynamics to systematically investigate NQEs on thermophysical properties of 92 organic liquids at ambient conditions. Depending on chemical constitution, we find substantial impact across thermal expansivity, compressibility, dielectric constant, enthalpy of vaporization, and notably molar volume, which shows consistent, positive quantum-classical differences up to 5%; similar, less pronounced trends manifest as isotope effects from deuteration. Using data-driven analysis, we identify three features-molar mass, classical hydrogen density, and classical thermal expansivity-that accurately predict NQEs and facilitate understanding of how characteristics like branching and heteroatom content influence behavior. This work highlights the broad relevance of NQEs in molecular liquids, while also providing a conceptual and practical framework to anticipate their impact.

Science & Technology - Other Topics↗

DOE OSTI2024

Deuteration removes quantum dipolar defects from KDP crystals

Abstract Dielectric properties of the hydrogen-bonded ferroelectric crystal KH 2 PO 4 (KDP) differ significantly from those of KD 2 PO 4 (DKDP). It is well established that deuteration affects the interplay of hydrogen-bond switches and heavy ion displacements that underlie the emergence of macroscopic polarization, but a detailed microscopic model is missing. We show that all-atom path integral molecular dynamics simulations can predict the isotope effects, revealing the microscopic mechanism that differentiates KDP and DKDP. Proton tunneling generates phosphate configurations that do not contribute to the polarization. At low temperatures, these quantum dipolar defects are substantial in KDP but negligible in DKDP. These intrinsic defects explain why KDP has lower spontaneous polarization and transition entropy than DKDP. The prominent role of quantum fluctuations in KDP is related to the unusual strength of the hydrogen bonds and should be equally important in other crystals of the KDP family, which exhibit similar isotope effects.

Yang, Bingjia (ORCID:0000000340749553)↗

DOE OSTI2026

Enhancing the efficiency of time-dependent density functional theory calculations of dynamic response properties

X-ray Thomson scattering (XRTS) constitutes an essential technique for diagnosing material properties under extreme conditions, such as high pressures and intense laser heating. Time-dependent density functional theory (TDDFT) is one of the most accurate available ab initio methods for modeling XRTS spectra, as well as a host of other dynamic material properties. However, strong thermal excitations, along with the need to account for variations in temperature and density as well as the finite size of the detector significantly increase the computational cost of TDDFT simulations compared to ambient conditions. In this work, we present a broadly applicable method for optimizing and enhancing the efficiency of TDDFT calculations. Our approach is based on a one-to-one mapping between the dynamic structure factor and the imaginary time density–density correlation function, which naturally emerges in Feynman’s path integral formulation of quantum many-body theory. Specifically, we combine rigorous convergence tests in the imaginary time domain with a constraints-based attenuation of narrow-band fluctuations to improve the efficiency of TDDFT modeling without the introduction of any significant bias. As a result, we can report a speed-up by up to an order of magnitude, thus substantially reducing the burden of computational cost required for XRTS analysis.

Moldabekov, Zhandos A. [Helmholtz-Zentrum Dresden-↗

DOE OSTI2024

Toward first principles-based simulations of dense hydrogen

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g., planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange–correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principles PIMC as well as in DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions that are based on first principles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Model-free Rayleigh weight from x-ray Thomson scattering measurements

X-ray Thomson scattering (XRTS) has emerged as a powerful tool for the diagnostics of matter under extreme conditions. In principle, it gives one access to important system parameters such as the temperature, density, and ionization state, but the interpretation of the measured XRTS intensity usually relies on theoretical models and approximations. In this context, a key property is given by the Rayleigh weight that describes the electronic localization around the ions. Here, we show that it is possible to extract the Rayleigh weight directly from the experimental data without the need for any model calculations or simulations. As a practical application, we consider an experimental measurement of strongly compressed Be at the National Ignition Facility [Döppner et al., Nature 618, 270–275 (2023)]. We demonstrate that experimental results for the Rayleigh weight open up new avenues for the interpretation of XRTS experiments by matching the measurement with ab initio simulations such as density functional theory or path integral Monte Carlo. Interestingly, this new procedure leads to significantly lower density compared to previously used chemical models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Accuracy of Kohn–Sham density functional theory for warm- and hot-dense matter equation of state

We study the accuracy of Kohn–Sham density functional theory (DFT) for warm- and hot-dense matter (WDM and HDM). Specifically, considering a wide range of systems, we perform accurate ab initio molecular dynamics simulations with temperature-independent local/semilocal density functionals to determine the equations of state at compression ratios of 3x–7x and temperatures near 1 MK. We find very good agreement with path integral Monte Carlo benchmarks, while having significantly smaller error bars and smoother data, demonstrating the accuracy of DFT for the study of WDM and HDM at such conditions. In addition, using a Δ-machine learned force field scheme, we confirm that the DFT results are insensitive to the choice of exchange-correlation functional, whether local, semilocal, or nonlocal.

Suryanarayana, Phanish (ORCID:0000000151720049)↗

DOE OSTI2026

Thermal exchange-correlation functionals: Capturing quantum electron behavior in warm, dense plasmas

We summarize and give perspective upon recent progress in developing non-empirical constraint-based thermal (i.e., free energy) exchange-correlation (XC) density functionals essential for accurate description of the quantum behavior of electrons in warm, dense plasmas. After delineating the critical role of ground-state functionals for zero-temperature, time-dependent DFT, we outline the underpinnings of local density approximation, generalized gradient approximation (GGA), and meta-GGA XC free-energy functionals. Two basic thermalization principles for upgrading ground-state XC functionals to successful thermal ones are emphasized. Then, we turn to a long-standing challenge, assessment of the accuracy of well-founded functionals. Unlike the ground state, there are a few exact results for large T and P. An exception is path integral Monte Carlo (PIMC) data for dense H/D and He plasmas. For those, we did ab initio molecular dynamics simulations under selected thermodynamic conditions employing five thermal XC functionals: two approximate thermal GGAs, fully thermal GGA, an approximate meta-GGA, and fully thermal meta-GGA. Comparisons with the PIMC data show that functionals thermalized by augmenting a non-thermal functional with a lower-level thermal contribution are inferior to functionals with thermal XC and spatial inhomogeneity effects taken into account at the same level of refinement. We believe this and similar evidence should be convincing to the high-energy density physics community of the necessity of use of proper thermal XC functionals in simulation studies of finite-temperature quantum effects in warm, dense plasmas.

Ab-initio molecular dynamics↗

DOE OSTI2026

Structured electrolytes facilitate Grotthuss-type transport for enhanced proton-coupled electron transfer reactions

Concentrated hydrogen-bonded electrolytes (CoHBEs) are structured, electrochemically stable, less-volatile alternatives to aqueous and dilute nonaqueous electrolytes, however, with high viscosities that limit molecular diffusion. This work provides an understanding of the proton conduction mechanism in CoHBEs based on mixtures of acids and azoles and establishes a link between the structurally dictated transport properties and the proton-coupled electron transfer (PCET) reaction rates that can be leveraged for enhancing electrochemical reactions. Diffusion and relaxation NMR studies suggest a breaking of the viscosity–conductivity tradeoff, where at high azole concentrations (>45 mol%), Grotthuss transport is more likely with lowered proton transfer energy barriers between the azole and the acid according to the machine learning (ML) accelerated ab initio path integral MD (AI-PIMD) simulations. Proton conduction pathways are found to be switchable between the hydrogen bonding networks of the acid and the azole, with imidazole chain forming structures better facilitating Grotthuss hopping. Supported by small-angle neutron scattering studies, the chains are found to have six member molecules on average with maximum of 3 to 4 imidazole/imidazoliums at 50 to 60 mol%. Despite their high viscosities, the measured PCET rates for quinones and phenazines measured in the protic CoHBEs present relatively high electron transfer rate constants (k 0 ~ 10 −4 cm/s), validated by rotating disc electrode and scanning electrochemical microscopy measurements. The results demonstrate that strategic tuning of hydrogen-bond donor–acceptor interactions enables the decoupling of proton transport and viscosity, thereby impacting PCET reactions.

electrokinetics↗

DOE OSTI2025

Criticality analysis of nuclear binding energy neural networks

Machine learning methods, in particular deep learning methods such as artificial neural networks (ANNs) with many layers, have become widespread and useful tools in nuclear physics. However, these ANNs are typically treated as ‘black boxes’, with their architecture (width, depth, and weight/bias initialization) and the training algorithm and parameters chosen empirically by optimizing learning based on limited exploration. We test a non-empirical approach to understanding and optimizing nuclear physics ANNs by adapting a criticality analysis based on renormalization group flows in terms of the hyperparameters for weight/bias initialization, training rates, and the ratio of depth to width. This treatment utilizes the statistical properties of neural network initialization to find a generating functional for network outputs at any layer, allowing for a path integral formulation of the ANN outputs as a Euclidean statistical field theory. We use a prototypical example to test the applicability of this approach: a simple ANN for nuclear binding energies. We find that with training using a stochastic gradient descent optimizer, the predicted criticality behavior is realized, and optimal performance is found with critical tuning. However, the use of an adaptive learning algorithm leads to somewhat superior results without concern for tuning and thus obscures the analysis. Nevertheless, the criticality analysis offers a way to look within the black box of ANNs, which is a first step towards potential improvements in network performance beyond using adaptive optimizers.

artificial neural network↗