SEARCH · Engineering Papers

Results for “higher form”

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.

SourceResearch connectionFrom yearThrough year

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

At least 1,153 records · Page 64

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Hundreds of Low-mass Active Galaxies in the Galaxy And Mass Assembly (GAMA) Survey

We present an entirely new sample of 388 low-mass galaxies (M $\star$ ≤ 10 10 M ⊙ ) that have spectroscopic signatures indicating the presence of massive black holes (BHs) in the form of active galactic nuclei (AGNs) or tidal disruption events. Of these, 70 have stellar masses in the dwarf galaxy regime with 10 8 ≲ M $\star$ /M ⊙ ≲ 10 9.5 . We identify the active galaxies by analyzing optical spectra of a parent sample of ~23,000 low-mass emission-line galaxies in the Galaxy and Mass Assembly (GAMA) Survey Data Release 4, and employing four different diagnostics based on narrow emission-line ratios and the detection of high-ionization coronal lines. We find that 47 of the 388 low-mass active galaxies exhibit broad Hα in their spectra, corresponding to virial BH masses in the range M BH ~ 10 5.0–7.7 M ⊙ with a median BH mass of $\langle$M BH $\rangle$ ~ 10 6.2 M ⊙ . Our sample extends to higher redshifts (z ≤ 0.3; $\langle$z$\rangle$ = 0.13) than previous samples of AGNs in low-mass/dwarf galaxies based on Sloan Digital Sky Survey spectroscopy, which can be attributed to the spectroscopic limit of GAMA being ~2 mag deeper. Moreover, our multi-diagnostic approach has revealed low-mass active galaxies spanning a wide range of properties, from blue star-forming dwarfs to luminous "miniquasars" powered by low-mass BHs. As such, this work has implications for BH seeding and AGN feedback at low masses.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Dark energy, extra dimensions, and the Swampland

Perhaps the greatest challenge for fundamental theories based on compactification from extra dimensions is accommodating a period of accelerated cosmological expansion. Previous studies have identified constraints imposed by the existence of dark energy for two overlapping classes of compactified theories: (1) those in which the higher dimensional picture satisfies certain metric properties selected to reproduce known low energy phenomenology; or (2) those derived from string theory assuming they satisfy the Swampland conjectures. For either class, the analyses showed that dark energy is only possible if it takes the form of quintessence. In this paper, we explore the consequences for theories that belong to both classes and show that the joint constraints are highly restrictive, leaving few options.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Atomistic evidence of nucleation mechanism for the direct graphite-to-diamond transformation

The direct graphite-to-diamond transformation mechanism has been a subject of intense study and remains debated concerning the initial stages of the conversion, the intermediate phases, and their transformation pathways. Here, we successfully recover samples at the early conversion stage by tuning high-pressure/high-temperature conditions and reveal direct evidence supporting the nucleation-growth mechanism. Atomistic observations show that intermediate orthorhombic graphite phase mediates the growth of diamond nuclei. Furthermore, we observe that quenchable orthorhombic and rhombohedra graphite are stabilized in buckled graphite at lower temperatures. These intermediate phases are further converted into hexagonal and cubic diamond at higher temperatures following energetically favorable pathways in the order: graphite → orthorhombic graphite → hexagonal diamond, graphite → orthorhombic graphite → cubic diamond, graphite → rhombohedra graphite → cubic diamond. Furthermore, these results significantly improve our understanding of the transformation mechanism, enabling the synthesis of different high-quality forms of diamond from graphite.

Graphite-diamond phase transformation↗

DOE OSTI2021

A hybrid CoOOH-rGO/Fe 2 O 3 photoanode with spatial charge separation and charge transfer for efficient photoelectrochemical water oxidation

As a promising photoanode for photoelectrochemical (PEC) water oxidation, hematite (Fe 2 O 3 ) still suffers from poor charge mobility and serious charges recombination and sluggish surface oxygen evolution kinetics. Herein, a hybrid photoanode of cobalt (oxy)hydroxide coupled with reduced graphene oxide modified Fe 2 O 3 (CoOOH-rGO/Fe 2 O 3 ) is well crafted by a facile hydrothermal synthesis with a chelation-mediated in-situ growth method. Morphology characterizations indicate rGO forms the internal network among isolated Fe 2 O 3 and CoOOH nanosheets distribute on the terminal of Fe 2 O 3 , forming a spatial separated nanostructure. The resultant CoOOH-rGO/Fe 2 O 3 exhibits an obviously reduced onset potential of ca. 150 mV and a significantly enhanced photocurrent density of 2.56 mA cm -2 at 1.23 V, which is ca. 3.3 times higher than that of bare Fe 2 O 3 . Especially, the functions of rGO and CoOOH are studied by using electrochemical impedance spectroscopy, open circuit potentials and intensity modulated photocurrent spectroscopy. It is found rGO act as conductive network which facilitates the electron transfer from Fe 2 O 3 to the substrate, while CoOOH evidently passivate the surface states of Fe 2 O 3 , improve charge separation and provide catalytic active sites for water oxidation. Additionally, the spatial charge separation and charge transfer caused by CoOOH and rGO are responsible for the enhanced PEC performance of water oxidation. The rational design and the facile fabrication strategy exhibit great potential to be used for other PEC system with great efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Interdiffusion and Formation of Intermetallic Compounds in High-Temperature Power Electronics Substrate Joints Fabricated by Transient Liquid Phase Bonding

Power electronics packages typically comprise a dielectric substrate bonded to a metal layer and attached to heat sinks using a low-thermal-conductivity solder. These multiple layers increase the effective thermal resistance of the package and are responsible for package failures under cyclic thermal loads. Bonding the aluminum nitride dielectric layer (AlN) directly to a low coefficient of thermal expansion (CTE) aluminum silicon carbide (AlSiC) cold plate using copper-aluminum (Cu-Al) transient liquid phase (TLP) bonding has been shown to improve the mechanical reliability of the power electronic packages while making the package more compact by bringing the cooling solutions closer to the devices. This study aims to characterize the Cu-Al bonds formed during the TLP bonding of AlSiC with three different power electronics substrates: pure aluminum nitride (AlN), aluminum (DBA), and copper (DBC). The material compositions and microstructures of the bonds were analyzed using scanning electron microscopy (SEM), x-ray spectroscopy (EDS), confocal scanning acoustic microscopy (C-SAM), and x-ray diffraction (XRD). ..alpha..-Al solid compound was identified as the dominant phase in AlN-AlSiC and Al-AlSiC, with a notable presence of SiC particles. In contrast, three intermetallic phases - ..theta..-CuAl2, ..eta..-CuAl, and ..gamma..'- Cu9Al4 - were observed in the Cu-AlSiC bond. A computational solid-state diffusion model was developed to predict the intermetallic compounds (IMCs) formed during Cu-Al TLP bonding in each system, which supported the observation that an initial Cu volume fraction of 20 % in the material layers produced a final bond composition of >95 % Al with minimal IMC growth. However, increased Cu concentrations produced higher concentration gradients, leading to increased growth of IMCs, Kirkendall voids, and interstitial cracks.

DIRECT ENERGY CONVERSION↗

DOE OSTI2025

Molecular Level Understanding of Polyethylene Terephthalate (PET) Depolymerization in Base/Alcohol Hybrid Systems

Polyethylene terephthalate (PET) depolymerization in base/alcohol hybrid systems represents a promising low-energy approach for chemically recycling PET waste into valuable monomers. This study investigates the mechanistic pathways of PET depolymerization in NaOH/alcohol solutions, emphasizing the competing roles of hydroxide and alkoxide species. Utilizing a combination of experimental techniques, density functional theory (DFT) calculations, and molecular dynamics (MD) simulations, we explore how factors such as base concentration, alcohol chain length, and pKa values of alcohols influence PET depolymerization efficiency and pathways. Our findings indicate that alkoxide ions (RO⁻) exhibit notably higher reactivity than hydroxide ions (HO⁻), favoring an alcoholysis pathway in the base/alcohol hybrid system. Experimental results across a series of C1 to C5 alcohols show that longer-chain alcohols, particularly 1-butanol, achieve higher PET conversion, although this does not align solely with simple nucleophilicity trends of alkoxides. While DFT calculations reveal comparable activation energies for various alkoxides in PET depolymerization, MD simulations underscore the significant role of alcohol chain length, with longer-chain alcohols forming more stable or frequent interactions with PET. Additionally, the alkoxide concentration, influenced by the alcohol’s pK a , directly impacts PET conversion. These suggest that PET depolymerization is governed by a balance between alkoxide concentration and alkoxide-PET interactions, rather than activation energies or nucleophilicity alone. From a practical perspective, incorporating long-chain alcohols as cosolvents may enhance process efficiency but increases raw material costs by approximately 30%. However, long-chain alcohols present a safer and more sustainable alternative to hazardous cosolvents such as dichloromethane. This work offers a molecular-level understanding of PET depolymerization in base/alcohol systems and provides insights into optimizing these systems for more efficient and sustainable PET recycling processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Atomic-Scale Imaging Reveals Polar-π Interactions in Two-Dimensional Molecular Superlattices

Controlling coassembly of synthetic oligomers into binary superlattices at the atomic level is challenging. Here, we report a strategy for programming polar-π interactions in oligomeric peptoids, a class of sequence-defined peptidomimetics, facilitating the formation of homogeneous two-dimensional (2D) superlattices. N-2-phenylethyl and N-(2-perfluorophenyl)ethyl side chains, similar in size, but with contrasting electrostatic characteristics, were introduced at defined sequence positions to generate favorable dipolar aromatic interactions. The resulting nanosheets exhibit different crystal motifs depending on the side chain interactions: systems containing only one type of aromatic side chain form a parallel V-shaped motif driven by π-π interactions, whereas a combination of both types of aromatic side chains, either within one backbone or through the coassembly of two distinct peptoids, adopt an antiparallel V-shaped superlattice with higher thermal stability, driven by polar-π interactions. Cryogenic transmission electron microscopy directly resolved the packing arrangement of perfluorophenyl and phenyl rings in individual nanosheet superlattices, confirming that intermolecular polar-π interaction dominates the superlattice motifs and increases lattice stability. Molecular dynamics simulations and density functional theory calculations further substantiate the energetic favorability of polar-π interactions over π-π interactions, rationalizing the formation of homogeneous superlattices with enhanced thermal stability. Our discoveries establish a design principle for binary coassembly using sequence-defined oligomers, which enables control over unit cell geometry, lattice stability, and molecular registration through aromatic side chain polarization and sequence control. This ability to program atomic-scale binary superlattices opens new avenues for designing functional 2D soft materials.

Lee, Yen Jea [Lawrence Berkeley National Laborator↗

DOE OSTI2020

Entropy-stabilized single-atom Pd catalysts via high-entropy fluorite oxide supports

Single-atom catalysts (SACs) have attracted considerable attention in the catalysis community. However, fabricating intrinsically stable SACs on traditional supports (N-doped carbon, metal oxides, etc.) remains a formidable challenge, especially under high-temperature conditions. Here, we report a novel entropy-driven strategy to stabilize Pd single-atom on the high-entropy fluorite oxides (CeZrHfTiLa)O x (HEFO) as the support by a combination of mechanical milling with calcination at 900 °C. Characterization results reveal that single Pd atoms are incorporated into HEFO (Pd1@HEFO) sublattice by forming stable Pd–O–M bonds (M = Ce/Zr/La). Compared to the traditional support stabilized catalysts such as Pd@CeO 2 , Pd 1 @HEFO affords the improved reducibility of lattice oxygen and the existence of stable Pd–O–M species, thus exhibiting not only higher low-temperature CO oxidation activity but also outstanding resistance to thermal and hydrothermal degradation. This work therefore exemplifies the superiority of high-entropy materials for the preparation of SACs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Microstructure evolution during near- T g annealing and its effect on shear banding in model alloys

By performing extensive molecular dynamics simulations, we investigate herein the deformation behavior in A l 90 S m 10 and C u 64.5 Z r 35.5 alloys after elongated isothermal annealing in the vicinity of the glass-transition temperature ( T g ). Different microstructural response to the annealing process was observed: A l 90 S m 10 maintains the glassy structure with improved energetic stability, enhanced short-range order (SRO), and a more pronounced spatial network that extends beyond the first atomic shell, while C u 64.5 Z r 35.5 forms nanocrystalline Laves C u 2 Zr phases. Shear banding occurs in both annealed systems under shear loading. For A l 90 S m 10 , the spatial network formed by the local clusters characterizing the SRO of the system is significantly weakened but remains appreciable in the shear band. In contrast, the crystalline ordering in the C u 64.5 Z r 35.5 is completely destroyed during shear banding. Consequently, while displaying higher yield strength, the annealed C u 64.5 Z r 35.5 sample appears to be less ductile. By carefully examining the effect of microstructures on the structural ordering in the shear band and the consequent mechanical response, our work contributes to a better understanding of the deformation mechanism of amorphous alloys as compared with that in crystalline materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Low Threshold, Long Wavelength Interband Cascade Lasers With High Voltage Efficiencies

Here, we report on the substantial advancement of long wavelength InAs-based interband cascade lasers (ICLs) utilizing advanced waveguides formed from hybrid cladding layers and targeting the 10-12 µm wavelength region. Modifications in the hole injector have improved carrier transport in these ICLs, resulting in significantly reduced threshold voltages (V th ) as low as 3.62 V at 80 K. Consequently, much higher voltage efficiencies were observed, peaking at about 73% at 10.3 µm and allowing for large output powers of more than 100 mW/facet. Also, low threshold current densities (J th ) of 8.8 A/cm 2 in cw mode and 7.6 A/cm 2 in pulsed mode near 10 µm were observed; a result of adjustments in the GaInSb hole well composition intended to reduce the overall strain accumulation in the ICL. Furthermore, an ICL from the second wafer operating at a longer wavelength achieved a peak voltage efficiency of 57% at 11.7 µm, with a peak output power of more than 27 mW/facet. This ICL went on to lase beyond 12 µm in both cw and pulsed modes, representing a new milestone in long wavelength coverage for ICLs with the standard W-QW active region.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Rapid Oxidation of Uranium Steel Alloys: Combustion Synthesis

This project explored the use of combustion synthesis as a rapid, high-temperature method for oxidizing uranium-bearing steel alloys. Traditional laboratory-scale synthesis methods often fail to replicate the thermal and kinetic conditions experienced by real-world particulates, particularly those formed under rapid quenching or high-temperature scenarios. Combustion synthesis offers a promising alternative by enabling fast, localized heating and flexible precursor selection. A series of targeted experiments were conducted using a U 2 NiCrFe 4 alloy as the precursor. The alloy was oxidized using combustion synthesis reactions fueled by uranyl nitrate and glycine, achieving peak temperatures exceeding 1,200 °C. Postreaction analysis using scanning electron microscopy (SEM), elemental mapping, and Raman spectroscopy revealed the formation of iron-based oxides, with limited but detectable evidence of uranium oxide phases such as UO 2 . The results indicate that under the rapid reaction and cooling conditions of combustion synthesis, iron oxides form preferentially, but uranium oxide formation is kinetically limited. These findings validate combustion synthesis as a viable method for simulating the oxidation behavior of uranium steels in extreme environments and lay the groundwork for future studies aimed at enhancing uranium oxide formation through higher temperatures or modified precursor compositions.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Thermal Characterization and Exhumation of Northwest San Juan Basin Area, NM

The San Juan Basin (SJB), located in southwestern Colorado northwestern New Mexico, containing Paleozoic through middle Cenozoic strata, formed as a partitioned basin approximately 80 Ma in response to the Laramide orogeny. The SJB is a commercially mature, petroleum-producing basin, and currently being explored for CCUS and geothermal resources. Modern heat flow within the SJB is spatially variable with higher geothermal gradients in its northern and eastern portions. The temporal history of the basin thermal history is essential for understanding capacity for carbon storage and geothermal exploration. We present thermochronometric analyses of two surface and two subsurface samples to constrain spatial-temporal thermal evolution of the northwestern San Juan Basin. Apatite (U-Th)/He thermochronometric analyses were conducted on Cliff House and Kirtland Formation outcrops and subsurface samples of the Ojo Alamo and Pictured Cliffs Formations from a DOE funded, CCUS project pilot-well. In addition, vitrinite reflectance data and 1D basin modelling constrain possible time-temperature pathways of the samples in an area where no previous studies have constrained the uplift/exhumation of the Hogback Monocline using thermochronometry. Modeling suggests that elevated subsurface temperatures developed simultaneously with regional late Oligiocene volcanism in the San Juan Volcanic field and timing of maximum burial in the SJB. Late Miocene to Pliocene cooling/exhumation through the apatite (U-Th)/He partial retention zone support stratigraphic evidence of the Colorado Plateau uplift, possibly regional epeirogenic uplift driven by mantle processes.

02 PETROLEUM↗

DOE OSTI2024

Impedance Scan of Inverter-Based Resources and Diesel Generator for Stability Analysis: Preprint

Impedance-based methods are widely used for power system stability analysis with inverter-based resources (IBRs), e.g., assessing dynamic interactions between the power grid and an IBR, control interactions between multiple IBRs, and the sub-synchronous oscillation and damping phenomenon. Since it is difficult to get a numerical model 100% matching with the hardware IBR, using the hardware inverter directly to obtain its output impedance has become a prominent approach nowadays. Therefore, this article presents the impedance scan using hardware IBRs, and also a hardware diesel generator as it still stays with the grid before the grid completely goes to renewable. The devices under test (DuTs) for the impedance scan includes two 3-..phi.., 480 V, 60 Hz commercial grid-forming IBRs (one of 250 kVA and another of 125 kVA rating) in series with ..delta..-Y transformers, one 3-..phi.., 480 V, 60 Hz commercial grid-following IBR (of 125 kVA rating), and a 3-..phi.., 480 V, 60 Hz commercial diesel generator (of 187.5 kVA rating). Using voltage signals perturbed with sub-, inter-, and higher harmonic components, and measuring the current response, the positive-sequence impedances are computed via an offline- based post-analysis. Moreover, best-fit transfer functions are estimated that closely resemble the measured data points of the positive-sequence impedances. Based on the observations from various outcomes of the hardware experiments, this article also provides some fundamental insights on the equivalent positive- sequence impedance of a combination of multiple hardware components by comparing the estimated and the empirically computed impedances. A comparative insight on the damping capability of the DuTs using the positive-sequence impedances of the hardware is also discussed.

grid following inverter↗

DOE OSTI2020

Highly selective electrocatalytic CO 2 reduction to ethanol by metallic clusters dynamically formed from atomically dispersed copper

Direct electrochemical conversion of CO 2 to ethanol offers a promising strategy of lowering CO 2 emission while storing energy from renewable electricity. However, current electrocatalysts offer only limited selectivity toward ethanol. Here we report a copper catalyst synthesized by a unique Cu-Li amalgm method over a commercial carbon support that achieved Faradaic efficiency (FE) higher than 91% at -0.7 V (RHE) and the active potential as low as -0.4 V (RHE) during direct electrocatalytic CO 2 -to-ethanol conversion. The catalyst also demonstrated stability over an extended period of operation. A strong correlation between the catalytic selectivity and the initial Cu atoms dispersion was found and Operando X-ray absorption spectroscopy identified a dynamic and reversible transformation from atomically dispersed copper atoms to Cu n (n = 3 and 4) under the electrochemical reaction. Frist-principles calculations further elucidate the possible catalytic mechanism of CO 2 reduction over Cu n .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Auriga Streams – I: disrupting satellites surrounding Milky Way-mass haloes at multiple resolutions

In a hierarchically formed Universe, galaxies accrete smaller systems that tidally disrupt as they evolve in the host’s potential. We present a complete catalogue of disrupting galaxies accreted onto Milky Way-mass haloes from the Auriga suite of cosmological magnetohydrodynamic zoom-in simulations. We classify accretion events as intact satellites, stellar streams, or phase-mixed systems based on automated criteria calibrated to a visually classified sample, and match accretions to their counterparts in haloes re-simulated at higher resolution. Most satellites at the present day have lost substantial amounts of stellar mass – 67 per cent have $f_\text{bound} < 0.97$ (our threshold of lost stellar mass to no longer be considered intact), while 53 per cent satisfy a more stringent $f_\text{bound} < 0.8$. Streams typically outnumber intact systems, contribute a smaller fraction of overall accreted stars, and are substantial contributors at intermediate distances from the host centre ($\sim$0.1 to $\sim 0.7R_\text{200m}$, or $\sim$35 to $\sim$250 kpc for the Milky Way). We also identify accretion events that disrupt to form streams around massive intact satellites instead of the main host. Streams are more likely than intact or phase-mixed systems to have experienced pre-processing, suggesting this mechanism is important for setting disruption rates around Milky Way-mass haloes. All of these results are preserved across different simulation resolutions, though we do find some hints that satellites disrupt more readily at lower resolution. The Auriga haloes suggest that disrupting satellites surrounding Milky Way-mass galaxies are the norm and that a wealth of tidal features waits to be uncovered in upcoming surveys.

galaxies: haloes↗

DOE OSTI2023

The Role of Transition Metals on Chemo-Mechanical Instabilities in Prussian Blue Analogues For K-Ion Batteries: The Case Study on KNHCF Versus KMHCF

Prussian blue analogues (PBAs) cathodes can host diverse monovalent and multivalent metal ions due to their tunable structure. However, their electrochemical performance suffers from poor cycle life associated with chemo-mechanical instabilities. This study investigates the driving forces behind chemo-mechanical instabilities in Ni- and Mn-based PBAs cathodes for K-ion batteries by combining electrochemical analysis, digital image correlation, and spectroscopy techniques. Capacity retention in Ni-based PBA is 96% whereas it is 91.5% for Mn-based PBA after 100 cycles at C/5 rate. During charge, the potassium nickel hexacyanoferrate (KNHCF) electrode experiences a positive strain generation whereas the potassium manganese hexacyanoferrate (KMHCF) electrode undergoes initially positive strain generation followed by a reduction in strains at a higher state of charge. Overall, both cathodes undergo similar reversible electrochemical strains in each charge–discharge cycle. There is ~0.80% irreversible strain generation in both cathodes after 5 cycles. XPS studies indicated richer organic layer compounds in the cathode-electrolyte interface (CEI) layer formed on KMHCF cathodes compared to the KNHCF ones. Faster capacity fades in Mn-based PBA, compared to Ni-based ones, is attributed to the formation of richer organic compounds in CEI layers, rather than mechanical deformations. In conclusion, understanding the driving forces behind instabilities provides a guideline to develop material-based strategies for better electrochemical performance.

25 ENERGY STORAGE↗

DOE OSTI2026

Heavy long-lived dark vector via a gluonic portal

We study a dark gauge boson Z′ that exclusively couples to the QCD gluons through higher dimensional operators. These operators are generated from integrating out of heavy ultraviolet resonances carrying both QCD and dark gauge charges. With SU(3)C gauge invariance, charge and parity symmetries preserved, we find that the leading effective operators are restricted to have the form of Z′GGG and Z′Z′GG at dimension-eight, which can naturally render the Z′ particle long-lived, and serve as a viable dark matter candidate. We investigate the phenomenology of these operators with both collider experiments and cosmological observation, without and with the assumption that this dark gauge boson plays the role of the dominant dark matter component. For an unstable Z′, we show that depending on its lifetime, it can be probed by various observables up to ultraviolet physics scale around 10 9 GeV. For Z′ being dark matter, we find that $m_{Z'}$ ≳ 1 TeV is consistent with the thermal freeze-out scenario. In contrast, in the freeze-in scenario, the extremely small couplings leave the relevant parameter space largely unconstrained by current experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗