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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 55 records · Page 3

Gamma Irradiation of NaCl-UCl 3 Salt for the Molten Chloride Fast Reactor

This report documents the results of the gamma ray irradiation of NaCl-UCl 3 eutectic salt in the Advanced Test Reactor (ATR) spent fuel pool gamma tube and subsequent analysis of capsules utilizing the Gas Assay Sample and Recharge (GASR) system. NaCl-UCl 3 salt capsules at four different temperatures, 75C, 150C, 300C and 600C, were irradiated shortly after the core internal changeout (CIC) of the ATR, beginning April 28 th of 2021, and ending on August 18 th of 2021. Re-positioning of the fuel elements in the spent fuel pool to move more fresh fuel elements around the gamma tube occurred on May 11 th of 2021, resulting in an approximate 20% increase in the dose rate and consequently the total absorbed dose. In total, the salt-filled capsules underwent 2638 hours of gamma irradiation from the adjacent freshly discharged ATR spent fuel. Capsule internal pressure measurements were taken via the Gas Assay Sample and Recharge (GASR) system in the INL Hot Fuels Examination Facility (HFEF) following completion of the irradiation. Based on the GASR analysis results, the primary conclusion from this experiment to-date is that radiolytic generation of chlorine gas is insignificant for the dose rates and total absorbed dose that these samples experienced. To elucidate more detailed effects of radiolysis on NaCl-UCl 3 eutectic salts and reach a more definitive conclusion, further advanced analyses such as electron microscopy, simultaneous thermal analysis, and electron paramagnetic resonance are recommended to analyze the capsule wall and salt samples.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Design of the unmanned Multiple Exploratory Probe System (MEPS) for Mars observations

The unmanned Multiple Exploratory Probe System (MEPS) is designed for Mars observations in preparation for manned missions to the planet early in the 21st century. MEPS will test vehicle systems, provide important data about the Martian surface and atmosphere, and assist the planning of manned missions. This mission will be a precursor to the manned missions. MEPS will consist of six primary systems. A Command Information Center (CIC) will be employed as an onboard mission control, communications link, and observation post. The Space Transportation Main Engine (STME) will be used to provide the thrust for Earth-Mars transit following vehicle construction near the Space Station. A polar lander/Orbital Transfer Vehicle (OTV) will be deployed during transit to achieve a polar orbit about Mars. A secondary propulsion will be used to place MEPS into orbit about Mars; this system and the aerobrake will circularize the orbit. Following orbit circulation, a satellite will be deployed to observe the Martian surface and atmosphere and to study the space environment. Polar and equatorial lander systems will land on Mars with rovers to collect surface and atmospheric samples while on-board laboratories will provide initial sample study. Two solid rocket booster/payload vehicles will launch samples into a low Mars orbit. The OTV will rendezvous with each payload capsule and then transfer the samples to Earth for hands-on observation.

Source record↗

X-31 flight test update

The goals of the tactical utility flight test are to verify the basic tactical lessons learned in simulation and determine the situational awareness implications of post-stall maneuvering. Tactics and lessons learned from post-stall engagements will supplement current fighter tactics and complement future fighter tactics development. Although the present envelope of the X-31 for carefree post stall (PST) use is limited to 225 KIAS versus 325 KIAS in simulations, the same initial conditions used in 'Pinball II' are being utilized in flight test. Starting conditions up to 325 KIAS are being flown during the build-up phase leading to the full close in air combat (CIC) evaluations. The flight control program has been modified to limit PST entry to below 225 KIAS. Full aft stick application above 225 KIAS cannot command angle of attack (AOA) in excess of 30 deg.

Groves, AL↗

The Impact of Radiation Damage on Photon Counting with an EMCCD for the WFIRST-AFTA Coronagraph

WFIRST-AFTA is a 2.4m class NASA observatory designed to address a wide range of science objectives using two complementary scientific payloads. The Wide Field Instrument (WFI) offers Hubble quality imaging over a 0.28 square degree field of view, and will gather NIR statistical data on exoplanets through gravitational microlensing. The second instrument is a high contrast coronagraph that will carry out the direct imaging and spectroscopic analysis of exoplanets, providing a means to probe the structure and composition of planetary systems. The coronagraph instrument is expected to operate in low photon flux for long integration times, meaning all noise sources must be kept to a minimum. In order to satisfy the low noise requirements, the Electron Multiplication (EM)-CCD has been baselined for both the imaging and spectrograph cameras. The EMCCD was selected in comparison with other candidates because of its low effective electronic read noise at sub-electron values with appropriate multiplication gain setting. The presence of other noise sources, however, such as thermal dark signal and Clock Induced Charge (CIC), need to be characterised and mitigated. In addition, operation within a space environment will subject the device to radiation damage that will degrade the Charge Transfer Efficiency (CTE) of the device throughout the mission lifetime. Here we present our latest results from pre- and post-irradiation testing of the e2v CCD201-20 BI EMCCD sensor, baselined for the WFIRST-AFTA coronagraph instrument. A description of the detector technology is presented, alongside considerations for operation within a space environment. The results from a room temperature irradiation are discussed in context with the nominal operating requirements of AFTA-C and future work which entails a cryogenic irradiation of the CCD201-20 is presented.

Peddada, Pavani↗

Interoffice Memorandum RE-04-21 "Advanced Test Reactor Power History Through Cycle 169A-1"

Table 1 lists the Advanced Test Reactor (ATR) N-16 constrained power history data since the Beryllium VI Core Internals Changeout (CIC) Cycle 134A-1 through Cycle 169A-1. The powers tabulated for Cycles 159A-1, 163A-1, and 167A-1 are higher than powers observed during operation, because powers are computed from cycle exposure, which for these cycles includes operation during the low-power “soak” portion of each cycle; whereas cycle length in Effective Full Power Days (EFPD) includes only the high-power “casualty” portion occurring after NF is established. Table 2 lists the accumulated N-16 lobe and total core exposure, as obtained from the ATR Data Acquisition System (RDAS) for Cycles 134A-1 through 169A-1. Table 3 lists the startup and shutdown dates and times, as obtained from logbooks or RDAS, depending on availability. The ATR power history prior to Cycle 134A 1 is presented in references (a) through (d).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Verification of the 3-Region Advanced Test Reactor MCNP Model

The verification of the 3-region homogenized fuel Advanced Test Reactor MCNP model. The 3-region model was compared to the 19-plate model found in the 94-CIC report. Flux tallies, energy deposition tallies, and quarter core mesh tallies were used to compare the two models. The 3-region model needed updating in order to make good comparisons between the models. The percent error from the flux and energy deposition tallies data shows that experiment positions inside the flux trap have higher errors than positions outside the fuel ring. The standard deviation data obtained from the mesh tallies shows that the two models agree within two standard deviations throughout the reactor. It is concluded that the model works adequately for what it is used for.

99 GENERAL AND MISCELLANEOUS↗

Verification of the 3-Region Advanced Test Reactor MCNP Model

The verification of the 3-region homogenized fuel Advanced Test Reactor MCNP model. The 3-region model was compared to the 19-plate model found in the 94-CIC report. Flux tallies, energy deposition tallies, and quarter core mesh tallies were used to compare the two models. The 3-region model needed updating in order to make good comparisons between the models. The percent error from the flux and energy deposition tallies data shows that experiment positions inside the flux trap have higher errors than positions outside the fuel ring. The standard deviation data obtained from the mesh tallies shows that the two models agree within two standard deviations throughout the reactor. It is concluded that the model works adequately for what it is used for.

99 GENERAL AND MISCELLANEOUS↗

Development of Remote Cutting Tools for use at ATR - 20438

As a result of years of operations of the Advanced Test Reactor (ATR) at the Idaho National Lab (INL), the ATR canal has become congested due to the storage of materials including waste consisting of highly irradiated remote handled (RH) metals. In order to support its continuing nuclear mission the ATR requires canal space to support fuel storage and future core internal change out (CIC) components. INL staff determined that the canal must be cleaned out and waste removed to efficiently utilize the valuable canal floor space. It was determined that a methodology for processing, packaging, characterizing, and removing current and future irradiated hardware from the ATR canal is needed. Orano Federal Services (OFS) and its subcontractor Babcock Services Inc. (BSI) were selected to provide remote tooling in order to safely and efficiently size reduce the material currently stored in the ATR canal. INL developed detailed requirements that established the design and performance requirements for the tooling. Orano TN and BSI had recently successfully completed similar tasks in clearing highly activated materials from spent fuel pools and canals at commercial nuclear plants. That experience directly translated into a proven approach that could be used at the ATR thereby saving time and money and lowering risks. Based on BSI's demonstrated proficiency in the design and deployment of remote size reduction specialty tooling at comparable commercial facilities, Orano Federal Services was confident that a solution to INL's requirements could be delivered. The tooling had to be designed to be compatible with the operational requirements of the ATR canal as well as the functionality needed by the facility operators that will use the equipment. Some of the major design requirements and functions of the equipment included remote operations, capability to shear highly irradiated sections of aluminum and steel tubing, pipe, and components ranging in size from 0.6 cm to 16.5 cm diameter into 1.5 m -1.8 m lengths, utilizing buoyancy compensation to assist with underwater operations, and use commercially available existing technology and components as much as practical. The design team evaluated and selected commercially available equipment that could be modified to meet the design and performance specifications. In addition, a waste sizing table (WST) was designed and fabricated to further ensure the size reduction equipment would perform as expected and give the facility operators a stable and usable remote, underwater work platform. After successful development of the tooling, a mock up test and operator training was conducted to ensure the tooling performed as expected and met the requirements of INL. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Reactor Walkway Design for Gear Box Support Beam Removal

The walkway over the reactor is intended to be used in the core internal changeout (CIC) outage to replace the gear box suport beams. (GBSB) The current configuration of the in-tank platform prevents easily discharging the GBSB to the canal through the drop chute. The walkway's purpose is to increase operators access to the south irration deck, where the GBSB will be put into discharge cans, as well as the drop chute.

42 ENGINEERING↗

ATR Fuel Management

The sixth Core Internals Changeout (CIC) of ATR was completed on March 21, 2022, and Nuclear Testing (NT) commenced shortly thereafter. In support of NT, 235U flux wires were attached to flux wands using electrical tape and installed in water channels 2, 6, 11, 15 and 19 in each of the 40 ATR Mark VII fuel elements that comprise an ATR core to perform low power flux measurements during ATR Cycle 170CIC NT-3. The flux wands were fabricated from Poly (Methyl Methacrylate), or PMMA. Irradiated cobalt capsules were loaded in the ATR Northeast Irradiation Housing Assembly (NEIHA), the East Flux Trap (EFT), South Flux Trap (SFT), inboard A-positions and various H-positions as a 170CIC NT-3 core reactivity hold-down mechanism. The PMMA flux wands received significant gamma dose from the irradiated cobalt during NT-3 which caused discoloration, embrittlement and swelling of the flux wands. The removal of the degraded flux wands from the 0.078 in. wide by 50 in. long fuel element coolant channels has been a unique challenge. This presentation summarizes the cleaning techniques used to remove the flux wand debris from the elements, an aggressive PMMA irradiation experiment performed concomitantly with initial cleaning efforts, and planned inspection and qualification techniques that will be applied in the future to potentially requalify the impacted elements for re-use.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

HDG-1 Experiment Irradiation Monitoring Data Qualification Final Report

SUMMARY The U.S. Department of Energy (DOE) Advanced Reactor Technologies (ART) Graphite Research and Development (GRD) Program is conducting a series of six experiments to quantify the effects of irradiation on nuclear-grade graphite. This report documents the qualification of irradiation monitoring data for the fifth experiment, High Dose Graphite-1 (HDG-1). Qualified monitoring data are required by the ART program to support the design and licensing of the first high-temperature reactor (HTR) nuclear plant. Data are classified as Qualified if they meet the usage requirements described in the experiment planning and quality assurance (QA) documents, Failed if they do not meet those requirements and provide no usable information, or Trend if they do not fully meet all requirements but still provide useful information subject to an assessment of how any deficiencies may affect a particular use of the data. HDG-1 irradiation began with Advanced Test Reactor (ATR) Cycle 168B on August 24, 2020, and concluded after Cycle 173C on January 27, 2025. The HDG-1 capsule was removed from the reactor core twice—during core internal change (CIC) Cycle 170A and powered axial locator mechanism (PALM) Cycle 172A—to prevent overheating of the graphite specimens during high-power PALM cycles. The capsule was therefore irradiated during a total of seven normal ATR cycles: 168B, 169A, 171A, 171B, 173A, 173B, and 173C. Irradiation monitoring data evaluated in this report include thermocouple (TC) temperature, gas flow rate, gas moisture, gas pressure, specimen load, and graphite stack displacement. Temperature. A total of 14,508,065 TC temperature records were captured. Of these, 13,901,785 (95.8%) are Qualified and 606,280 (4.2%) are Failed. The principal source of failed temperature data was the instrument failure of TC-9 (Zone 2) on June 24, 2024, and TC-10 (Zone 1) on July 5, 2024, near the end of Cycle 173A, which resulted in 595,554 Failed readings. An additional 379 missing values and 10,347 slightly negative values from TC-13 during ATR outages are also Failed. Neither TC-9 nor TC-10 was used as a temperature-control TC, and their failures did not compromise capsule condition monitoring. Correlation analysis of all 13 TCs found no evidence of virtual junction formation. Control chart analysis revealed clear downward drift of approximately 80°C for TC-6 (Zone 3) relative to other stable TCs, and possible downward drift of approximately 60°C for TC-13 relative to the Zone 5 control TC (TC-1), though TC-13 remained consistent with the Zone 2 control TC (TC-12). Gas flow. A total of 20,088,090 gas flow rate records were captured. Of these, 19,941,463 (99.3%) are Qualified and 146,627 (0.7%) are Failed due to missing values. All argon, helium, and total gas flow data were within expected ranges throughout the irradiation. Gas moisture. A total of 1,116,005 outlet gas moisture values were captured. Of these, 1,101,421 (98.7%) are Qualified and 14,584 (1.3%) are Failed, comprising 14,556 out-of-range values and 28 missing values. The out-of-range moisture values exceeded 22,000 ppmv for approximately 1 week at the beginning of Cycle 173A, when accumulated moisture evaporated after the capsule was retrieved from water storage during PALM Cycle 172A and reinserted into the east flux trap. Moisture levels returned to below 25 ppmv for the remaining three cycles, and the transient high-moisture event did not affect the integrity of specimen irradiation. Gas pressure. A total of 7,812,035 gas pressure values were captured. Of these, 6,642,048 (85.0%) are Qualified and 1,169,987 (15.0%) outlet pressure values are Failed, comprising 718,537 zero outlet pressure values due to sensor failure from Cycle 168B through Cycle 171B, 54,550 missing values, and 396,900 too-low outlet pressure values, ranging from 1.1 to 1.6 psia after sensor replacement during Cycle 173A. Load. A total of 6,696,030 load values were captured. Of these, 6,694,580 (99.98%) are Qualified and 1,450 (0.02%) are Failed due to missing values. Applied loads to the six specimen stacks were stable throughout the irradiation. Stack displacement. A total of 6,696,030 displacement values were captured. Of these, 5,713,297 (85.32%) are Qualified and 3,781 (0.06%) are Failed due to missing values. Stack displacement increased consistently throughout the irradiation, reaching approximately 3.08 in. for Channels 5 and 6 by the end of irradiation. 978,952 (14.62%) substantially elevated displacements observed for Channel 6 beginning in Cycle 171A and for Channel 5 beginning in Cycle 173A are assigned Trend status. Raising pressure. A total of 1,115,999 raising pressure values were captured. Of these, 1,115,430 (99.95%) are Qualified and 569 (0.05%) are Failed due to missing values. Ram pressure. A total of 6,696,030 ram pressure values were captured. Of these, 6,692,249 (99.95%) are Qualified and 3,484 (0.05%) are Failed due to missing values. Stack raising was perf

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Quantifying the Turbulent Entrainment‐Mixing Processes Based on Z ‐LWC Relationships of Cloud Droplets

Abstract Turbulent entrainment‐mixing processes profoundly influence the relationship between radar reflectivity factor and liquid water content ( Z ‐LWC) of cloud droplets. However, quantification of the entrainment‐mixing mechanisms based on the Z ‐LWC relationship is still lacking. To address this gap, 12,218 entrainment‐mixing cases are simulated using the Explicit Mixing Parcel Model. We examine the variations of the parameters in the power‐law relationship Z = a LWC b , and the relationship between parameter b and homogeneous mixing degree ( ψ ), a measure quantifying entrainment‐mixing processes. The results indicate that parameter b distributes within the range of 1–2, with a positive correlation between parameter b and ψ . The b ‐ ψ relationship is fitted, which connects the Z ‐LWC relationship for various entrainment‐mixing types. The results suggest the potential for employing a remote sensing approach to investigate the entrainment‐mixing mechanisms of non‐precipitating small cumulus/stratocumulus clouds, thereby overcoming the limitations of traditional observational studies that rely solely on aircraft observations.

54 ENVIRONMENTAL SCIENCES↗

Competing conduction mechanisms in high performance carbon nanotube fibers

The performance of carbon nanotube (CNT) cables, a contender for copper-wire replacement, is tied to its metallic and semi-conducting-like conductivity responses with temperature; the origin of the semi-conducting-like response however is an underappreciated incongruity in literature. With controlled aspect-ratio and doping-degree, over 61 unique cryogenic experiments including anisotropy and Hall measurements, CNT cable performance is explored at extreme temperatures (65 mK) and magnetic-fields (60 T). A semi-conducting-like conductivity response with temperature becomes temperature-independent approaching absolute-zero, uniquely demonstrating for the first time the necessity of heterogeneous fluctuation induced tunneling; complete de-doping leads to localized hopping, contrasting graphite's pure metallic-like response. High-field magneto-resistance (including novel +22 % longitudinal magneto-resistance near room-temperature) is analyzed with hopping and classical two-band models, both yielding a similar parameter useful for conductor development. Varying field-orientation angle uncovers significant two- and four-fold symmetries that are shown to be from Aharonov-Bohm-like corrections to the curvature-induced bandgap, a first for macroscale CNT fibers. Tight-binding calculations using Green's Function formalism model the largest, coherent transport to-date in commensurate CNT bundles in magnetic-field, revealing non-uniform transmission across bundle cross-sections with doping restoring uniformity; independent of doping, transport in bundle-junction-bundle systems are predominantly from CNTs adjacent to the other bundle—demonstrating that smaller bundles are more efficient for electronic transport. The final impact is predicting the ultimate conductivity of heterogeneous CNT cables using temperature and field-dependent transport, surpassing conductivity of traditional metals.

36 MATERIALS SCIENCE↗

Visible-to-THz near-field nanoscopy

Optical microscopy has a key role in research, development and quality control across a wide range of scientific, technological and medical fields. However, diffraction limits the spatial resolution of conventional optical instruments to about half the illumination wavelength. A technique that surpasses the diffraction limit in the wide spectral range between visible and terahertz frequencies is scattering-type scanning near-field optical microscopy (s-SNOM). The basis of s-SNOM is an atomic force microscope in which the tip is illuminated with light from the visible to the terahertz spectral range. By recording the elastically tip-scattered light while scanning the sample below the tip, s-SNOM yields near-field optical images with a remarkable resolution of 10 nm, simultaneously with the standard atomic force microscopic topography image. This resolution is independent of the illumination wavelength, rendering s-SNOM a versatile nanoimaging and nanospectroscopy technique for fundamental and applied studies of materials, structures and phenomena. This Review presents an overview of the fundamental principles governing the measurement and interpretation of near-field contrasts and discusses key applications of s-SNOM. We also showcase emerging developments that enable s-SNOM to operate under various environmental conditions, including cryogenic temperatures, electric and magnetic fields, electrical currents, strain and liquid environments. Furthermore, all these recent developments broaden the applicability of s-SNOMs for exploring fundamental solid-state and quantum phenomena, biological matter, catalytic reactions and more.

Hillenbrand, Rainer [CIC nanoGUNE BRTA and Departm↗

Roadmap on advanced and / real-time characterisation of solid state materials and devices for energy applications

A strong societal and political drive is motivating the development and optimization of novel energy conversion and storage systems for decarbonization. The successful implementation of solid state devices such as fuel cells and secondary batteries depends, however, on achieving ambitious targets in terms of performance, reliability and cost competitiveness. Research and technology are addressing these needs through a holistic approach including exploration of new materials and nanoarchitectures, as well as system engineering. These significant efforts require the support of appropriate characterization tools capable of assessing nanometer-scale phenomena such as concentration profiles of ionic and electronic charges, local chemical compositions and their evolution over time across interfaces. This roadmap provides an overview of selected advanced characterization techniques for energy materials and devices. Specific focus is put on in situ/operando methods for probing electrochemical phenomena in real-time under realistic working conditions. Experts in the field provide an extensive review of the current state of the art in 2025 and the current and future challenges for the characterization of local chemistry and kinetics in the bulk of the material, in nanoarchitectures (e.g. thin films) and at the interfaces (e.g. grain boundaries, phase contacts, solid/liquid and solid/gas interfaces) . The aim is to provide a detailed guide to the techniques, describing opportunities and bottlenecks for their practical deployment and examples of successful applications.

25 ENERGY STORAGE↗

Anomalies in the Electronic Stopping of Slow Antiprotons in LiF

We present first-principles theoretical calculations for the electronic stopping power (SP) of both protons and antiprotons in LiF. Our results show the presence of the Barkas effect: a higher stopping for positively charged particles than their negatively charged antiparticles. In contrast, a previous study has predicted an anti-Barkas effect (higher stopping for negative charges) at low velocity [Qi, Bruneval and Maliyov, Phys. Rev. Lett. 128, 043401 (2022)]. Here, we explain this discrepancy by showing that this anti-Barkas effect appears for highly symmetric trajectories and disappears when considering trajectories that better reproduce the experimental setup. Our low-velocity results show that the SP of both protons and antiproton vanish for velocities under 0.1 a.u.

3-dimensional systems↗

Controlling magnetism and transport at perovskite cobaltite interfaces via strain-tuned oxygen vacancy ordering

Complex oxides such as perovskite cobaltites exhibit rich phenomena at interfaces due to the complex interplay between their structural, defect, electronic, and magnetic degrees of freedom. Here, we study this interplay here in the ferromagnetic metallic cobaltite La 1−𝑥 ⁢Sr 𝑥⁢ CoO 3−𝛿 , using specific substrates to vary both the heteroepitaxial strain (compressive vs tensile) and growth orientation ((001) vs (110)). Transmission electron microscopy, electron energy-loss spectroscopy, high-resolution X-ray diffraction, magnetometry, polarized neutron reflectometry, and electronic magnetotransport measurements are applied. Lattice mismatch and growth orientation are found to enable the precise control of interfacial oxygen vacancy ordering in La 1−𝑥⁢ Sr 𝑥 ⁢CoO 3−𝛿 , thus dictating strain relaxation and oxygen vacancy depth profiles, in turn controlling thickness-dependent magnetic and electronic properties. In particular, compressive strain and (110) orientations minimize deleterious magnetic/electronic dead layer effects, leading to the optimization of interfacial magnetism and transport. Strain and orientation tuning of oxygen vacancy ordering are thus established as powerful means to control physical properties at cobaltite-based interfaces, relevant to several fields.

36 MATERIALS SCIENCE↗

Parallel-in-time quantum simulation via Page and Wootters quantum time

In the past few decades, researchers have created a veritable zoo of quantum algorithms by drawing inspiration from classical computing, information theory, and even from physical phenomena. Here, we present quantum algorithms for parallel-in-time simulations that are inspired by the Page and Wootters formalism. In this framework, and thus in our algorithms, the classical time variable of quantum mechanics is promoted to the quantum realm by introducing a Hilbert space of “clock” qubits that are then entangled with the “system” qubits. We show that our algorithms can compute temporal properties over 𝑁 different times of many-body systems by only using log⁡(𝑁) clock qubits. As such, we achieve an exponential trade-off between time and spatial complexities. In addition, we rigorously prove that the entanglement created between the system qubits and the clock qubits has operational meaning, as it encodes valuable information about the system’s dynamics. We also provide a circuit depth estimation of all the protocols, showing a running time advantage in computation times over traditional sequential-in-time algorithms. In particular, for the case when the dynamics are determined by the Aubry-Andre model, we present a hybrid method for which our algorithms have a depth that only scales as 𝒪⁡(log⁡(𝑁)⁢𝑛). As a by-product, we can relate the previous schemes to the problem of equilibration of an isolated quantum system, thus indicating that our framework enables a new dimension for studying dynamical properties of many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗