Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix theories”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Random Tensor Networks with Non-trivial Links

Abstract Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that a better model consists of random tensor networks with link states that are not maximally entangled, i.e., have non-trivial spectra. In this work, we initiate a systematic study of the entanglement properties of these networks. We employ tools from free probability, random matrix theory, and one-shot quantum information theory to study random tensor networks with bounded and unbounded variation in link spectra, and in cases where a subsystem has one or multiple minimal cuts. If the link states have bounded spectral variation, the limiting entanglement spectrum of a subsystem with two minimal cuts can be expressed as a free product of the entanglement spectra of each cut, along with a Marchenko–Pastur distribution. For a class of states with unbounded spectral variation, analogous to semiclassical states in quantum gravity, we relate the limiting entanglement spectrum of a subsystem with two minimal cuts to the distribution of the minimal entanglement across the two cuts. In doing so, we draw connections to previous work on split transfer protocols, entanglement negativity in random tensor networks, and Euclidean path integrals in quantum gravity.

Physics↗
DOE OSTI2021

Polyampholyte physics: Liquid–liquid phase separation and biological condensates

Here we review the current understanding of molecular interactions that govern liquid-liquid phase separation (LLPS) of biological condensates. The connection between sequence, chain conformation, and phase separation of intrinsically disordered proteins (IDPs) and their model polyampholytes is discussed. In particular, we highlight how the charge pattern influences the conformation and phase behavior of natural IDPs. We then describe recent results from theoretical treatments of polyampholytes implementing random phase approximation, field-theoretic simulations, and transfer matrix theory that show an increase in charge segregation results in an increased tendency to phase separate.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Evidence of Skewness and Sub-Gaussian Character in Temperature-Dependent Distributions of One Million Electronic Excitation Energies in PbS Quantum Dots

Obtaining statistical distributions by sampling a large number of conformations is vital for an accurate description of temperature-dependent properties of chemical systems. However, constructing distributions with 105??106 samples is computationally challenging because of the prohibitively high computational cost of performing rst-principles quantum-mechanical calculations. In this work, we present a new technique called the Eective Stochastic Potential Conguration Interaction Singles (ESP-CIS) method to obtain excitation energies. The ESP-CIS method uses random matrix theory for the construction of an eective stochastic representation of the Fock operator and combines it with linear-response theory. Here, we perform excitation calculations on PbS quantum dots (0.75-1.75 nm) at temperatures of 200-400 K. Results from a total of 15 million excitation energy calculations (1 million samples for each of the three dots at ve dierent temperatures) revealed the distributions to be sub-Gaussian in nature with negative skewness. The distributions progressively became red-shifted with increasing temperature. The study shows that random distortions in structure from the minimum-energy geometry of these quantum dots are more likely to lower the excitation energies.

Scher, Jeremy A.↗
DOE OSTI2021

Partial dynamical symmetry versus quasi dynamical symmetry examination within a quantum chaos analyses of spectral data for even–even nuclei

Statistical analyses of the spectral distributions of rotational bands in 51 deformed prolate even–even nuclei in the 152 ≤ A ≤ 250 mass region $R_{{4_{1}^{ + } /2_{1}^{ + } }} \ge 3.00$ are examined in terms of nearest neighbor spacing distributions. Specifically, the focus is on data for 0 + , 2 + , and 4 + energy levels of the ground, gamma, and beta bands. The chaotic behavior of the gamma band, especially the position of the $2_{\gamma }^{ + }$ band-head compared to other levels and bands, is clear. The levels are analyzed within the framework of two models, namely, a SU(3)-partial dynamical symmetry Hamiltonian and a SU(3) two-coupled quasi-dynamical symmetry Hamiltonian, with results that are further analyzed using random matrix theory. The partial and quasi dynamics both yield outcomes that are in reasonable agreement with the known experimental results. However, due to the degeneracy of the beta and gamma bands within the simplest SU(3) picture, the theory cannot be used to describe the fluctuation properties of excited bands. By changing relative weights of the different terms in the partial and quasi dynamical Hamiltonians, results are obtained that show more GOE-like statistics in the partial dynamical formalism as the strength of the pairing term is increased. Also, in the quasi-dynamical symmetry limit, more correlations are found because of the stronger couplings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Microbunch rotation in an x-ray free-electron laser using a first-order achromatic bend

Electrons in an x-ray free electron laser (XFEL) develop periodic density fluctuations, known as microbunches, which enable the exponential gain of x-ray power in an XFEL. When an electron beam microbunched at a hard x-ray wavelength is kicked, microbunches are often washed out due to the dispersion and R 56 of the bend. An achromatic (dispersion-free) bend with a small R 56 , however, can preserve microbunches, which rotate to follow the new trajectory of the electron bunch. Rotated microbunches can subsequently interact in a repointed undulator to produce a new beam of off-axis x rays. In this work, we demonstrate hard x-ray multiplexing in the Linac Coherent Light Source hard x-ray undulator line using microbunch rotation through a 10 μ rad first-order-achromatic bend created by transversely offsetting quadrupole magnets in the FODO lattice. Quadrupole offsets are determined analytically from beam-matrix theory. We also discuss the application of microbunch rotation to out-coupling a cavity-based XFEL. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Extended nonergodic regime and spin subdiffusion in disordered SU(2)-symmetric Floquet systems

In this work, we explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-Abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entropy of the Floquet eigenstates is subthermal, although violating an area-law scaling with system sizes. We further compute the expectation value of local observables and find strong deviations from the eigenstate thermalization hypothesis. The infinite-temperature spin autocorrelation function decays at long times as $t^{–β}$ with $\textit{β}$ < 0.5, indicating subdiffusive transport at strong disorders.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Random insights into the complexity of two-dimensional tensor network calculations

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (“not too entangled”) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work, we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at a large bond dimension. Through this statistical-mechanics lens, we argue that (i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, and (ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. Furthermore, these results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Spectroscopic factors, overlaps, and isospin symmetry from an R -matrix point of view

Background: Spectroscopic factors, overlaps, and isospin symmetry are often used in conjunction with single-particle wave functions for the phenomenological analysis of nuclear structure and reactions. Many differing prescriptions for connecting these quantities to physically relevant asymptotic normalization constants or widths are available in the literature, but their relationship and degree of validity are not always clear. Purpose: This paper derives relationships among the above quantities of interest using well-defined methodology and starting assumptions. Method: R -matrix theory is used as the primary tool to interoperate among the quantities of interest to this work. Particular attention is paid to effects arising from beyond the nuclear surface, where isospin symmetry is strongly violated. Results: Relationships between the quantities of interest are derived. Example applications of these methods to mirror levels in nucleon + 12 C, nucleon + 16 O, and nucleon + 26 Al are presented. A new approach to multilevel mirror symmetry is derived and applied to the first three 2 + states of 18 O and 18 Ne. Conclusions: In this work, the relationship between the quantities of interest is clarified and certain procedures are recommended. It is found that the asymptotic normalization constant of the second 2 + state in 18 Ne deduced from the mirror state in 18 O is significantly larger than found in previous work. This finding has the effect of increasing the 17 F($\textit{p,γ}$) 18 Ne reaction rate in novae.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes

Studies of many-body non-Hermitian parity-time (PT)-symmetric quantum systems are attracting a lot of interest due to their relevance in research areas ranging from quantum optics and continuously monitored dynamics to Euclidean wormholes in quantum gravity and dissipative quantum chaos. While a symmetry classification of non-Hermitian systems leads to 38 universality classes, we show that, under certain conditions, PT-symmetric systems are grouped into 24 universality classes. We identify 14 of them in a coupled two-site Sachdev-Ye-Kitaev (SYK) model and confirm the classification by spectral analysis using exact diagonalization techniques. Intriguingly, in 4 of these 14 universality classes, AIII ν , BDI ν † , BDI + + ν , and CI − − ν , we identify a basis in which the SYK Hamiltonian has a block structure in which some blocks are rectangular, with ν ∈ N the difference between the number of rows and columns. We show analytically that this feature leads to the existence of ν robust purely eigenvalues, whose level statistics follow the predictions of Hermitian random matrix theory for classes A, AI, BDI, and CI, respectively. We have recently found that this ν is a topological invariant, so these classes are topological. By contrast, nontopological real eigenvalues display a crossover between Hermitian and non-Hermitian level statistics. Similarly to the case of Lindbladian dynamics, the reduction of universality classes leads to unexpected results, such as the absence of Kramers degeneracy in a given sector of the theory. Another novel feature of the classification scheme is that different sectors of the PT-symmetric Hamiltonian may have different symmetries. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Quantifying Quantum Chaos through Microcanonical Distributions of Entanglement

A characteristic feature of “quantum chaotic” systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this feature, we introduce a framework that allows us to compare the properties of eigenstates in local systems with those of pure random states. In particular, our framework defines a notion of distance between quantum state ensembles that utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints). This notion gives rise to a quantitative metric for quantum chaos that not only accounts for averages of the distributions but also higher moments. The differences in moments are compared on a highly resolved scale set by the standard deviation of the RMT distribution, which is exponentially small in system size. As a result, the metric can distinguish between chaotic and integrable behaviors and, in addition, quantify and compare the of chaos (in terms of proximity to RMT behavior) between two systems that are assumed to be chaotic. We implement our framework in local, minimally structured, Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed-field Ising model (MFIM). Importantly, for Hamiltonian systems, we find that the reference random distribution must be appropriately constrained to incorporate the effect of energy conservation in order to describe the ensemble properties of midspectrum eigenstates. The metric captures deviations from RMT across all models and parameters, including those that have been previously identified as strongly chaotic, and for which other diagnostics of chaos such as level spacing statistics look strongly thermal. In Floquet circuits, the dominant source of deviations is the second moment of the distribution, and this persists for all system sizes. For the MFIM, we find significant variation of the KL divergence in parameter space. Notably, we find a small region where deviations from RMT are minimized, suggesting that “maximally chaotic” Hamiltonians may exist in fine-tuned pockets of parameter space. Published by the American Physical Society 2024

Physics↗
DOE OSTI2025

Fluctuations in Hill’s equation parameters and application to cosmic reheating

Cosmic inflation provides a compelling framework for explaining several observed features of our Universe, but its viability depends on an efficient reheating phase that converts the inflaton’s energy into Standard Model particles. This conversion often proceeds through nonperturbative mechanisms such as parametric resonance, which is described by Hill’s equation. In this work, we investigate how stochastic fluctuations in the parameters of Hill’s equation can influence particle production during reheating. We show that such fluctuations can arise from couplings to light scalar fields and can significantly alter the stability bands in the resonance structure, thereby enhancing the growth of fluctuations and broadening the region of efficient energy transfer. Using random matrix theory and stochastic differential equations, we decompose the particle growth rate into deterministic and noise-induced components and demonstrate analytically and numerically that even modest noise leads to substantial particle production in otherwise stable regimes. Furthermore, these results suggest that stochastic effects can robustly enhance the efficacy of reheating across a wide swath of parameter space, with implications for early Universe cosmology, UV completions involving multiple scalar fields, and the resolution of the cosmological moduli problem.

Cosmology↗
DOE OSTI2021

Simulation of enhanced light extraction from periodic, disordered, and quasi-periodic OLED structures

Here we have developed a rigorous scattering matrix theory of light emission from periodically structured media using a Green’s function approach. We computationally simulate the spectral power inside the structure, incorporating Purcell factor enhancements, and find internal waveguiding modes and plasmonic losses. We simulate the light-outcoupling factor η out and describe how corrugations and structured media can enhance η out . We have extended our framework to describe non-periodic disordered arrays as well as aperiodic quasi-crystalline arrays. Flat organic light-emitting diodes (OLEDs) have low outcoupling with η out ~20% since most of the light is trapped in waveguided modes in higher index layers or lost to plasmonic excitations at the metal cathode. Periodically corrugated OLEDs can achieve highly enhanced η out ~65%-70% for pitch values between 1000 and 2000 nm, representing an enhancement factor >3 over planar structures. Periodic corrugations strongly diffract trapped waveguided and plasmonic modes to the emissive air cone. Disordered templates also can cause significant enhanced outcoupling with η out ~50%-55% for smaller nearest-neighbor separations of 300–400 nm. Quasi-crystalline tilings can also lead to enhancements of η out ~50%-55%. This framework can be utilized to design novel structured media that can generate high light extraction.

42 ENGINEERING↗
DOE OSTI2020

Machine learning applied to classifying neutron resonances

The performance of nuclear reactors and other nuclear systems depends on a precise understanding of the neutron interaction cross sections for materials used in these systems. These cross sections exhibit resonance structure whose shape is determined in part by the angular momentum quantum numbers of the resonances. The correct assignment of the quantum numbers of neutron resonances is therefore of paramount importance. In this project, we apply a machine learning technique, namely decision trees, to automate the quantum number assignments. The tree is trained from simulated data generated to mimic the errors found in real data. We explore the use of several physics-motivated features for training our trees, including the nearest neighbor spacing distribution, cumulative level distribution, and channel width distributions. Initial results using random matrix theory motivated fits which demonstrated that we can determine resonance spin groups somewhat reliably. If we use these fits as features in our trees, we can train them to spot outliers corresponding to misassigned resonances. We found that with the large number of features used in this project that the decision tree tended to over t training data resulting in poor performance with respect to the test data. By reducing the number of features, we can achieve nearly perfect assignment of quantum numbers with our training data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Statistical Hauser-Feshbach model calculation for (α, n) reaction cross section and discrete level population

We calculate the α-particle induced reactions on 17,18 O, 19 F, and 23 Na, in the energy range 0 ≤ E α ≤ 10 MeV, with a particular attention to the branching ratios of populated discrete levels in the (α,n) channels. Since there are too many open channels to employ the R-matrix theory, we apply the statistical Hauser-Feshbach model to calculate these reaction cross sections and branching ratios. The branching ratio is defined as b n = $\frac{σ_n}{Σ_iσ_i + σ_c}$ , where σ n is the n-th level production cross section after the neutron emission, and σ c is the production of the continuum state. In the cases of our target nuclei and the energy range of interest, the residual nuclei of the neutron emission channel are always in their discrete states, so that σ c can be negligible.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

EDA R-Matrix Evaluations Report on n+ 9 Be, n+ 16 O [Slides]

This presentation discusses new developments in light-element R-matrix evaluation and recent light-element work. The presentation also reviewed R-matrix theory, EDAf90 code implementation, including interface EDAf90 with NJOY, ENDFtk, EXFOR/CSISRS, and a new evaluation for n+ 9 Be. The presentation concludes by stating that further development is needed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

R-matrix Resolved Resonance Region Evaluation of 140,142 Ce

Oak Ridge National Laboratory completed the resolved resonance region (RRR) evaluation of the two most abundant cerium isotopes, 140 Ce (88.45%) and 142 Ce (11.11%), as requested by the US Nuclear Criticality Safety Program. These evaluations are based on recent high-resolution transmission and capture measurements performed on nat Ce and highly enriched 142 Ce samples at the JRC-Geel Linear Accelerator facility, as well as measured thermal constants available from the EXFOR database. Starting from the resonance parameters of the ENDF/B-VIII.0 library followed by a preliminary R-matrix analysis, an updated set of resonance parameters and corresponding covariance information were derived by fitting these measured data using the Reich–Moore approximation of the R -matrix theory, as implemented in the SAMMY code system. The 140 Ce RRR upper energy limit was kept at 200 keV, whereas the 142 Ce resonance region was extended from 13 to 26 keV. Updated statistical properties were obtained for the new evaluations and compared to those derived from the ENDF/B-VIII.0 nuclear data library. The new evaluation work improved some of the discrepancies found in previous work, such as the capture resonance integral and stellar Maxwellian-averaged cross sections. These integral quantities were mainly derived from the fit of the latest measured data, especially the neutron capture yield data for 142 Ce isotope.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Potential absence of observed π2 linear-chain structures in 14O via 10C(α,α) resonances scattering

Background: The preference for light nuclear systems to coagulate into -particle clusters has been well-studied. The possibility of a linear chain configuration of -particles would allow for a new way to study this phenomenon. Purpose: A rotational band of states in C has been claimed showing a linear chain structure. The mirror system, O, has been studied here to examine how this linear chain structure is affected by replacing the valence neutrons with protons. Method: A beam of C was incident into a chamber filled with He:CO gas with the tracks recorded inside the TexAT Time Projection Chamber and the recoil -particles detected by a silicon detector array to measure the cross section. Results: The experimental cross section was compared with previous studies and fit using R-Matrix theory with the previously-observed O states being transformed to the C using mirror symmetry. The measured cross section does not replicate the claimed states, with the predicted cross section exceeding that observed at several energies and angles. Conclusion: A series of possibilities are highlighted with the most likely being that the originally-seen C states did not constitute a rotational band with a potentially incorrect spin assignment due to the limitations of the angular correlation method with non-zero spin particles. The work highlights the difficulties in measuring broad resonances corresponding to a linear chain state in a high level density.

Bishop, J.↗
DOE OSTI2026

Three-nucleon lepton-number-violating potentials in chiral effective field theory and their matrix elements in light nuclei

Here, we derive the three-nucleon neutrinoless double-𝛽 decay potential in a Δ-full chiral effective field theory through next-to-next-to-next-to leading order in Weinberg's power counting. The matrix elements of the resulting operators are computed in light nuclei using variational Monte Carlo with wave functions constructed from the Norfolk family of nuclear interactions. We find that three-nucleon corrections induce a modest quenching of the total nuclear matrix elements. We discuss model dependencies and the potential impact of these corrections on the sensitivity of experimental programs to probe lepton number violating parameters. These results provide a benchmark for many-body methods capable of reaching heavier nuclei of experimental interest.

Chambers-Wall, Graham [Washington University, St. ↗