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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
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DOE OSTI2021

Random Matrix Theory in Cd isotopes

Random matrix theory (RMT) is used to provide a measure of the chaoticity (q) of calculated results for the spectra for various Cd isotopes. Here, the goal is to gain a better understanding of the internal dynamics in play; namely, whether it tracks with regular or irregular (chaotic) behavior as determined through an RMT analyses of calculated spectra. The basis-state configurations used to determine the spectra includes all positive, negative, natural (J π = 1 – , 2 + , ...), and unnatural parity configurations (J π = 0 – , 1 + , 2 – , ...), unless suppressed for comparative purposes. The results show that when intruder-state configurations are in play, regular behavior emerges, but when not in play, chaotic behavior seems to dominate the dynamics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Scattering matrix pole expansions for complex wave numbers in R -matrix theory

In this followup article to Ducru et al., we establish new results on scattering matrix pole expansions for complex wave numbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wave numbers. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift S and penetration P functions: the legacy Lane and Thomas's “force closure” approach versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF. Here, in this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and discover new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii a c . We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix—canceling spurious poles and guaranteeing generalized unitarity—while still being able to close channels below thresholds.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Modular-Invariant Random Matrix Theory and AdS 3 Wormholes

We develop a nonperturbative definition of RMT 2 : a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its 𝑛-point spectral correlations admit a prescribed modular-invariant lift to RMT 2 , which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the SL⁡(2,ℤ) spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT 2 lift of two-point correlations of the GUE Airy model. We propose that in AdS 3 pure gravity, semiclassical amplitudes for off-shell 𝑛-boundary torus wormholes with topology Σ 0,𝑛 × 𝑆 1 are given by the RMT 2 lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT 2 result.

conformal field theory↗
DOE OSTI2021

Shadow poles in the alternative parametrization of R-matrix theory

In this work, we discover new, hitherto unknown, shadow poles in Brune’s alternative parametrization of R-matrix theory [C. R. Brune, Phys. Rev. C 66, 044611 (2002)]. Where these poles are, and how many, depends on how one continues R-matrix operators to complex wavenumbers (specially the shift S and penetration P functions). This has little consequence for the exact R-matrix formalism (past the last energy threshold), as we show one can still always fully reconstruct the scattering matrix with only the previously known alternative parameters (poles and corresponding resonance widths), for which there were as many poles as the number of levels Nλ. However, we generalize the alternative parametrization to the Reich-Moore formalism, and show that the choice of continuation is now critical as it changes the alternative parameters values (poles and residue widths are now complex). In order to establish nuclear libraries with alternative parameters, the nuclear community will thus have to decide what convention to adopt. We argue in favor of analytical continuation (against the legacy Lane and Thomas approach) in a follow-up article [P. Ducru, Phys. Rev. C, submitted (2020)]. We observe the first evidence of shadow poles in the alternative parametrization of R-matrix theory in isotope xenon 134 Xe spin-parity group J π = 1=2 (–) , and show how they indeed depend on the choice of continuation to complex wavenumbers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

R-matrix School 2025: Introduction to R-matrix Theory

This technical memo serves as a lecture material for the R-matrix school 2025 and distributed among the participants. The manuscript discusses in details the introduction to the R-matrix theory including its algorithm to calculate reaction cross sections and derivation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Random matrix theory of the isospectral twirling

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref. [1]. The relevant ensembles of Hamiltonians are those defined by salient spectral probability distributions. The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems: Frame potentials, Loschmidt Echos, OTOCs, Entanglement, Tripartite mutual information, coherence, distance to equilibrium states, work in quantum batteries and extension to CP-maps. Moreover, we perform averages in these ensembles by random matrix theory and show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Soft theorems in matrix theory

We show that the Banks-Fischler-Shenker-Susskind matrix model for M-theory obeys the leading and subleading soft theorems expected from eleven-dimensional supergravity. The subleading soft theorem implies the amplitude is Lorentz symmetric. This is argued for general four point amplitudes, but only for restricted kinematics for five and higher point amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Three point amplitudes in matrix theory

We compute the three graviton amplitude in the Banks-Fischler-Shenker-Susskind matrix model for M-theory. Even though the three point amplitude is determined by super Poincare invariance in eleven dimensional M-theory, it requires a non-trivial computation in the matrix model. We consider a configuration where all three gravitons carry non-zero longitudinal momentum. To simplify the problem, we compactify one additional dimension and relate the amplitude to a supersymmetric index computation. Here, we find agreement with the expected answer even at finite values of N.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Data-Driven Refinement of Electronic Energies from Two-Electron Reduced-Density-Matrix Theory

The exponential computational cost of describing strongly correlated electrons can be mitigated by adopting a reduced-density-matrix (RDM)-based description of the electronic structure. While variational two-electron RDM (v2RDM) methods can enable large-scale calculations on such systems, the quality of the solution is limited by the fact that only a subset of known necessary N-representability constraints can be applied to the 2RDM in practical calculations. Here, we demonstrate that violations of partial three-particle (T1 and T2) N-representability conditions, which can be evaluated with knowledge of only the 2RDM, can serve as physics-based features in a machine-learning (ML) protocol for improving energies from v2RDM calculations that consider only two-particle (PQG) conditions. Proof-of-principle calculations demonstrate that the model yields substantially improved energies, relative to reference values from configuration-interaction-based calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Indirect reactions and connection with R-matrix theory

It is often the case that nuclear reactions that are important for societal applications or basic science are difficult to measure directly in existing facilities for accelerated beams. The difficulty might be associated with an exceedingly small cross section, as the ones obtained at beam energies well below the Coulomb barrier, or with the impossibility of devising a short-lived target, as is the case for neutron-induced reactions on unstable isotopes. The fruitful line of experimental research addressing this issue with alternative (indirect) reactions has been developed in parallel to the theory needed to make the connection between the observed data and the desired cross sections of the (direct) reaction under study. Within this context, we present here an explicit connection between the indirect cross section and the R-matrix parameters which describe the energy-dependent cross section of the desired direct reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Towards excitations and dynamical quantities in correlated lattices with density matrix embedding theory

Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining excitations and dynamical spectral functions by using the techniques of DMET to approximate the matrix elements that arise in a single-mode inspired excitation ansatz. We demonstrate this approach in the one-dimensional Hubbard model, comparing the neutral excitations, single-particle density of states, charge, and spin dynamical structure factors to benchmarks from the Bethe ansatz and density matrix renormalization group. Finally, our work highlights the potential of these ideas in building computationally efficient approaches for dynamical quantities.

1-dimensional systems↗
DOE OSTI2026

Pressure-induced 𝐵⁢1 to 𝐵⁢2 phase transition in CeN studied by 𝑎⁢𝑏 𝑖⁢𝑛⁢𝑖⁢𝑡⁢𝑖⁢𝑜 correlation matrix renormalization theory calculations

We apply correlation matrix renormalization theory (CMRT) to cerium nitride (CeN) under pressure. For 𝐵⁢1 (NaCl-type) phase, CMRT gives an equation of state consistent with ambient pressure experiments. It produces electronic density-of-state (DOS) characterized by a sharp 4⁢𝑓 quasiparticle resonance peak pinned at the Fermi level and two subbands formed by strong hybridization between the localized Ce-4⁢𝑓 electrons and the itinerant Ce-5⁢𝑑 and N-2⁢𝑝 electrons below the Fermi level, consistent with x-ray photoemission spectroscopy experiments. Upon compression, CMRT predicts a first-order 𝐵⁢1 → 𝐵⁢2 (CsCl-type) transition with ∼11% volume collapse in agreement with experiments. Across the transition, the 4⁢𝑓 spectrum broadens, the 4⁢𝑓 orbital occupancy increases, and the hybridization with conduction states enhances, signaling a crossover from partially localized to more itinerant 4⁢𝑓 behavior. Furthermore, these features are in excellent agreement with experimental observations, demonstrating that CMRT provides a parameter-free description and prediction of correlation-driven structural and electronic transitions in rare-earth compounds.

Ab initio calculations↗
DOE OSTI2024

A principle of maximum ignorance for semiclassical gravity

The principle of maximum ignorance posits that the coarse-grained description of a system is maximally agnostic about its underlying microscopic structure. We briefly review this principle for random matrix theory and for the eigenstate thermalization hypothesis. We then apply this principle in holography to construct ensembles of random mixed states. This leads to an ensemble of microstates which models our microscopic ignorance, and which on average reproduces the effective semiclassical physics of a given bulk state. We call this ensemble the state-averaging ansatz. The output of our model is a prediction for semiclassical contributions to variances and higher statistical moments over the ensemble of microstates. The statistical moments provide coarse-grained — yet gravitationally non-perturbative — information about the microstructure of the individual states of the ensemble. We show that these contributions exactly match the on-shell action of known wormhole configurations of the gravitational path integral. These results strengthen the view that wormholes simply parametrize the ignorance of the microstructure of a fundamental state, given a fixed semiclassical bulk description.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Computational Protocol to Evaluate Electron–Phonon Interactions Within Density Matrix Perturbation Theory

We present a computational protocol, based on density matrix perturbation theory, to obtain non-adiabatic, frequency-dependent electron–phonon self-energies for molecules and solids. Our approach enables the evaluation of electron–phonon interaction using hybrid functionals, for spin-polarized systems, and the computational overhead to include dynamical and non-adiabatic terms in the evaluation of electron–phonon self-energies is negligible. We discuss results for molecules, as well as pristine and defective solids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Ab initio description of bcc iron with correlation matrix renormalization theory

We applied the ab initio spin-polarized correlation matrix renormalization theory to the ferromagnetic state of the bulk bcc iron. We showed that it was capable of reproducing the equilibrium physical properties and the pressure-volume curve in good comparison with experiments. We then focused on the analysis of its local electronic correlations. By exploiting different local fluctuation-related physical quantities as measures of electronic correlation within target orbits, we elucidated the different roles of t 2g and e g states in both spin channels and presented compelling evidence to showcase this distinction in their electronic correlation.

3-dimensional systems↗