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Nuclear Safety [Vol. 36, No. 2, July-December 1995]

Nuclear Safety is a journal that covers significant issues in the field of nuclear safety. Its primary scope is safety in the design, construction, operation, and decommissioning of nuclear power reactors worldwide and the research and analysis activities that promote this goal, but it also encompasses the safety aspects of the entire nuclear fuel cycle, including fuel fabrication, spent-fuel processing and handling, and nuclear waste disposal, the handling of fissionable materials and radioisotopes, and the environmental effects of all these activities. Table of Contents for this issue follows. THE CHORNOBYL ACCIDENT: 195 The Chornobyl Accident Revisited, Part III: Chernobyl Source Term Release Dynamics and Reconstruction of Events During the Active Phase, A. R. Sich; GENERAL SAFETY CONSIDERATIONS: 218 Second ANS Workshop on the Safety of Soviet-Designed Nuclear Power Plants, R. A. Bari; 234 Elements of a Nuclear Criticality Safety Program, C. M. Hopper; 243 Rickover, Excellence, and Criticality Safety Programs, R. E. Wilson; ACCIDENT ANALYSIS: 249 Transient Analysis of the PIUS Advanced Reactor Design with the TRAC-PF1/MOD2 Code, B. E. Boyack, J. L Steiner, S. C. Harmony, H. J. Stumpf, and J. F. Lime; 278 The Hierarchy-By-Interval Approach to Identifying Important Models that Need Improvement in Severe-Accident Simulation Codes, T. J. Heames, M. Khatib-Rahbar, J. E. Kelly, R. P. Jenks-Johnson, and Y.-S. Chen; 290 RELAP5/MOD3 Code Coupling Model, R. P. Martin; 299 Missiles Caused by Severe Pressurized-Water Reactor Accidents, R. Krieg; DESIGN FEATURES: 310 Validation of COMMIX with Westinghouse AP-600 PCCS Test Data, J. G. Sun, T. H. Chien, J. Ding, and W T. Sha; ENVIRONMENTAL EFFECTS: 321 Spent Nuclear Fuel Characterization for a Bounding Reference Assembly for the Receiving Basin for Off-Site Fuel, S. D. Kahook, R. L. Garrett, L. R. Canas, and M J. Beckum; OPERATING EXPERIENCES: 332 Reactor Shutdown Experience, Compiled by J. W. Cletcher; U.S. NUCLEAR REGULATORY COMMISSION INFORMATION AND ANALYSES: 335 Reactor Coolant System Blowdown at Wolf Creek on September 17, 1994, J. V. Kauffman and S. L. Israel; RECENT DEVELOPMENTS: 344 Reports, Standards, and Safety Guides, D. S. Oueener; 349 Proposed Rule Changes as of June 30, 1995; ANNOUNCEMENTS: 320 Symposium on Acceptability of Risk From Radiation—Application to Manned Space Flight; 320 24th DOE/NRC Nuclear Air Cleaning and Treatment Conference; 361 Radiation Biology and Radiation Protection— Modern Developments and Tendencies in Radiation Biology; 362 1997 IEEE Sixth Conference on Human Factors and Power Plants; 354 The Authors; 360 Reviewers of Nuclear Safety, Vol. 36.

05 NUCLEAR FUELS

Process control-enabled mitigation of microstructural and plastic heterogeneities in additively manufactured Grade 91 steel

Synergizing wire arc-directed energy deposition (WA-DED) additive manufacturing (AM) with particle-strengthened creep strength-enhanced ferritic (CSEF) steels enables fabrication and repair of critical power-plant components. Investigations focused on fusion-welded particle-strengthened CSEF steels, such as Grade 91 steel, have linked microstructurally heterogeneous regions—forming due to heat affected zones (HAZ)—with premature failure during elevated temperature service. Fusion-based AM, including WA-DED, likewise generates microstructurally and plastically heterogeneous regions due to spatiotemporally varying thermokinetics during deposition. However, works investigating such microstructural heterogeneities, their implications for mechanical behavior, and strategies to mitigate their formation remain scarce. This work identifies microstructurally and plastically heterogeneous regions within the WA-DED-processed Grade 91 steel. Spatial microhardness variations in the as-fabricated specimen correlate with the variation in the attributes of grain, martensitic microstructure, and precipitates across the fusion zone and HAZ. Digital image correlation-enabled tensile tests performed at 500 °C revealed pronounced deformation localization and a wave-like strain distribution, with wavelength close to the melt pool depth, indicating susceptibility of the as-fabricated components to premature creep failure. Such heterogeneity in microstructural and mechanical behavior was attributed to recurring solid-state phase transformations. Subsequently, an interlayer temperature control strategy was implemented, wherein maintaining interlayer temperature above the martensitic start temperature mitigated the heterogeneous microstructural and plastic response in the as-fabricated condition. Findings open pathways to achieving deformation-localization- and creep-resistant microstructures in WA-DED fabricated particle-strengthened CSEF steel components, reducing reliance on post-welding heat treatments—conventionally required to enhance creep resistance—and enabling on-demand, short lead-time fabrication of next-generation power-plant components.

Heat affected zones

Nuclear Safety [Vol. 37, No. 2, April-June 1996]

Nuclear Safety is a journal that covers significant issues in the field of nuclear safety. Its primary scope is safety in the design, construction, operation, and decommissioning of nuclear power reactors worldwide and the research and analysis activities that promote this goal, but it also encompasses the safety aspects of the entire nuclear fuel cycle, including fuel fabrication, spent-fuel processing and handling, and nuclear waste disposal, the handling of fissionable materials and radioisotopes, and the environmental effects of all these activities. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 97 The Nuclear Community and the Public: Cognitive and Cultural Influences on Thinking About Nuclear Risk, M. A. Meyer; 109 Twenty-Third Water Reactor Safety Information Meeting, D. A. Copinger; ACCIDENT ANALYSIS: 126 Analysis of a PWR LBLOCA Without SCRAM, Trevor N. Tyler, Rafael Macian-Juan and John H. Mahaffy; DESIGN FEATURES: 139 Vulnerability of Multiple-Barrier Systems, N. C. Lind; ENVIRONMENTAL EFFECTS: 149 A Study of Wet Catalytic Oxidation of Radioactive Spent Ion Exchange Resin by Hydrogen Peroxide, Xingchao Jian, Tianbao Wu, and Guichun Yun; 157 A Comparison Study and Resolution of Differences Between Emergency Response and Safety Analysis Codes Used at the Savannah River Site, A. A. Simpkins; OPERATING EXPERIENCES: 164 Reactor Shutdown Experience, Compiled by J. W. Cletcher; RECENT DEVELOPMENTS: 167 Reports, Standards, and Safety Guides, D. S. Queener; 172 Proposed Rule Changes as of Dec. 31,1995; ANNOUNCEMENTS: 178 American Nuclear Society 1997 Annual Meeting; 178 American Nuclear Society Nuclear Criticality and Safety Division Topical Meeting; 176 The Authors.

05 NUCLEAR FUELS

A Review of the Influence of Processing Parameters on ODS Steels Produced via Additive Manufacturing Techniques

Abstract This paper reviews current observations regarding processing conditions for oxide dispersion-strengthened steels consolidated through additive manufacturing techniques. Variations in ODS steels observed across process parameters include changes in grain size, grain texture, oxide size, density of oxides, porosity, melt pool characteristics, and mechanical properties. These properties were then compared across techniques to understand which techniques and processing conditions lead to the highest strength, ductility, and oxide density. Current literature suggests that a mix of grain types, in the form of either morphology or phase, can significantly increase the strength of printed ODS steels. Meanwhile, the most ductile samples, regardless of consolidation technique or matrix material, were made from feedstock with oxide additions located on the powder surface. Reported grain and oxide sizes were plotted against the ratio of laser power to scan speed, volumetric energy density, and normalized enthalpy. No strong correlation between these values and microstructural features was observed. The plots that were made suggest that a larger data set, more in-depth representative equations, and more defined material properties as a function of specific feedstock used are necessary to determine a value that can be correlated to the printed ODS steel microstructure.

deJong, Matthew

Generation of 3.3-mJ, 2.45-µm, sub-2-cycle laser pulses via hollow-core fiber pulse compression

We demonstrate nonlinear compression of mid-infrared pulses from a Cr:ZnSe chirped-pulse amplifier using a gas-filled stretched hollow-core fiber followed by bulk-material compression. Starting from 90 fs, 2.45 µm pulses with 5.3 mJ energy, spectral broadening in the gas-filled capillary combined with optimized dispersion management enables compression to 15 fs, less than two optical cycles at 2.45 µm, with 3.3 mJ pulse energy, corresponding to a peak power of approximately 0.12 TW. The simplicity of the approach, based on a single hollow-core fiber stage and bulk dispersion compensation, makes it scalable to higher energies and establishes a robust route to mid-infrared drivers for high harmonic generation and attosecond applications.

Britton, Mathew [SLAC National Accelerator Laborat

Interface-induced fast Li+ transport in mixed ionic–electronic conductors

Interfacial instability between lithium metal and solid-state electrolytes limits the performance of all-solid-state lithium metal batteries (ASSLBs), leading to parasitic reactions, non-uniform Li+ flux, and dendrite growth. Here, we develop a composite interlayer composed of the anti-perovskite Li2OHCl0.75Br0.25 (AP) and carbon nanotubes (CNTs) to enhance both interfacial stability and ionic transport. The AP–CNT interlayer exhibits enhanced Li+ conductivity arising from interfacial electron transfer from AP to CNTs, which generates a built-in electric field that facilitates Li+ migration. Lithium symmetric cells incorporating this interlayer achieve a high critical current density of 2.4 mA cm−2 at 55 °C. This design integrates chemical robustness with coupled ion–electron transport, offering a generalizable strategy for safe, dendrite-free, and high-performance ASSLBs.

He, Chenche

Probing the fatigue enhancement in a thermally aged cast duplex stainless steel by in situ neutron diffraction

After long-term thermal aging at 400 °C for 3000 h and 10,000 h, a cast duplex stainless steel exhibits promoted fatigue performance, including enhanced three-stage cyclic hardening and prolonged fatigue life. Utilizing in situ neutron diffraction, the phase-specific stresses are resolved, and their evolutions over entire fatigue cycling reveal the underlying mechanisms of the fatigue enhancement. It is found that the ferrite phase bears a much higher stress than the austenite matrix under both as-received and aged conditions. The enhanced cyclic hardening in Stage I is attributed to the strengthening of both phases due to thermal aging, while the enhancement in Stage III results from the martensitic transformation induced strengthening. The fatigue life is prolonged thanks to the cyclic hardening and the delay of martensitic transformation in the austenite phase after thermal aging.

Yu, Dunji [ORNL] (ORCID:0000000189467851)

Heat metrics and thresholds reshape population exposure and inequality signals

Extreme heat is intensifying worldwide, yet estimates of heat hazard and exposure inequality depend on both the heat metric and how extreme days are defined. Using summer 2022 across the Mediterranean, we quantify population heat exposure with four metrics—land surface temperature (LST), air temperature (Ta), heat index (HI), and wet-bulb globe temperature (WBGT)—under absolute (fixed-value) and relative (anomaly-based) thresholds. Under absolute thresholds, total heat exposure differs by more than two orders of magnitude across metrics (31.3 billion person-days for Ta vs 0.3 billion for HI). Geographic hotspots also diverge: WBGT concentrates in humid coastal North Africa (e.g. the Nile Delta), whereas Ta and LST are more widespread. Under relative thresholds, exposure totals converge and cross-metric hotspot agreement increases (e.g. Ta–WBGT top-tercile overlap increases from 10.7% to 29.0%), shifting hotspots toward densely populated southern Europe. Crucially, the exposure–deprivation relationship also reverses across threshold frameworks: absolute thresholds concentrate exposure in more deprived North Africa and the Middle East, whereas relative thresholds shift the burden toward less-deprived European cities. This sensitivity is decision-relevant: city rankings based on WBGT exposure duration are almost completely reordered when switching threshold frameworks. Threshold choice therefore systematically reshapes hotspot patterns and inequality signals. Reporting both absolute and relative exposures can reveal hidden hotspots and support more targeted heat-risk monitoring and intervention planning.

Mediterranean

End-To-End Decentralized Transmission Line Protection in IBR-Dominated Weak Grids Using Interpretable Data-Driven Methods

Traditional transmission line protection relies on predictable synchronous-based fault signatures, which frequently fail under the non-standard, current-limited fault characteristics of Inverter-Based Resources (IBRs). This study investigates how to achieve secure, communication-free fault isolation in IBR-dominated weak grids without relying on opaque, computationally heavy "black-box" machine learning algorithms. To address this, we propose a novel, standalone, and inherently interpretable data-driven protection framework. Unlike centralized methods requiring multi-terminal communication, this decentralized approach relies solely on local measurements using a hierarchical linear-kernel Support Vector Machine (SVM). The methodology decomposes the protection task into four sequential stages that mimic traditional protection elements: fault detection and fault direction identification, fault type classification, zone classification, and location estimation. This multi-stage architecture allows for specialized feature engineering at each stage, combining high computational efficiency with logic traceability. The framework's end-to-end performance was validated via C-code and PSCAD/EMTDC co-simulation, utilizing a real-world utility network and an OEM black-box IBR model. The proposed relay achieves 97.2% overall accuracy and provides a reliable trip decision within a 2.5-cycle window. The results confirm 100% accuracy in fundamental fault detection, reliable zone selectivity across low to moderate fault resistances, and robust security against non-fault transients, proving its immediate viability for integration into commercial numerical relays.

24 POWER TRANSMISSION AND DISTRIBUTION

Identifying Suitable Front Contacts for High‐Efficiency Cd(Se,Te) Solar Cells on Space‐Qualified Cover Glass

Deployment of photovoltaics in space requires devices that combine high-efficiency, low areal mass, and resilience to harsh environments. Historically, high-efficiency multijunction III–V materials have dominated space power systems; however, their high cost and limited manufacturing throughput motivate the exploration of scalable alternatives. While CdTe-based thin-film photovoltaics offer an attractive option, their performance on non-conventional substrates can suffer from front contact instability under higher-temperature processing. Here, the role of front contact chemistry in limiting cell performance is investigated using CdTe-based devices fabricated on 150 μm thick Ceria-doped space-qualified 0214 Corning glass. A matrix of four transparent conducting oxides (TCOs: CTO, AZO, ITO, IZO) combined with two n-type emitters (MZO, IGO) reveals chemical stability at the front interface—rather than absorber composition alone—governs recombination losses, voltage deficits, and device reproducibility. Chemically stable front contact combinations suppress elemental diffusion and interfacial degradation, resulting in significantly improved carrier lifetimes and junction quality. These insights are validated through record-certified Cd(Se,Te) cell efficiencies of 18.4% under AM1.5G and 16.2% under AM0 illumination on ultra-thin glass. Beyond CdTe, this work provides a general framework for the rational selection of TCO/emitter interfaces in superstrate thin-film photovoltaics, including emerging technologies like metal halide perovskites, while enabling high-efficiency, lightweight photovoltaics for space applications.

14 SOLAR ENERGY

PIP-II LLRF Master Oscillator and Precision Reference Line - Station Level Design and Testing

The PIP-II superconducting linac at Fermilab requires a highly stable RF Reference Line to maintain phase syn- chronization throughout the accelerator. Temperature- induced changes in the electrical length of long coaxial cables can introduce phase drift and measurement errors. The reference-line architecture mitigates these effects by phase averaging the forward and reflected RF signals, while a phase-locked loop anchors the system to the mas- ter oscillator. This work focuses on the characterization, validation, and mechanical integration of station-level RF assemblies using CAD modeling, vector network analyzer measurements, and spectrum analyzer testing. PID-controlled thermal plates will stabilize critical RF components and further reduce temperature-dependent phase and amplitude variations. These methods sup- port repeatable, standardized designs that can be reliably integrated across the different reference-line stations.

Mosher, Alexander [U. Illinois, Chicago]

Integrated Simulation of Weld Residual Stress Evolution and Crack Propagation Using XFEM

Nuclear power plant components operate in environments that promote multiple degradation mecha- nisms, several of which involve crack initiation and growth. An ongoing effort in the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program is developing a general capability within the Multiphysics Object Oriented Simulation Environment (MOOSE) framework for simulating three-dimensional crack growth under a range of driving conditions, including fatigue, stress corrosion cracking (SCC), brittle fracture, and stress-relaxation cracking. This report demonstrates an end-to-end workflow that uses this capability to model weld-residual-stress-driven SCC in the J-groove weld of a pressurized-water reactor control rod drive mechanism penetration in the vessel head. The workflow consists of a thermomechanical welding simulation with temperature-dependent plasticity, followed by cooldown to ambient conditions, and a restart of the simulation using the MOOSE extended finite element method (XFEM) module to propagate a three-dimensional crack through the residual stress field. New welding capabilities were developed to properly initialize newly activated elements in the weld region, and robustness improvements were made to the mesh-based algorithm for defining cutting planes in the 3D XFEM algorithm, allowing it to handle complex crack fronts and stress fields. Together these advances allowed the simulated SCC crack to grow from an initial elliptical flaw in the weld, across the weld, through the tube wall, and almost to the triple point (where the weld, tube, and reactor pressure vessel head intersect) over roughly 36 years of simulated service. These results demonstrate a workflow that can be extended to fully three-dimensional welding simulations and more complex crack interaction problems.

42 - ENGINEERING

Erosion of high-Z refractory coatings for helicon plasma source window

Proto-MPEX (Materials Plasma Exposure eXperiment), a linear plasma device (LPD), using a high power radio frequency (RF) (⩾100 kW, 13.56 MHz) helicon plasma source, has suffered RF sheath-induced window erosion. The sputtered impurities from the window surface transport toward the downstream target affecting plasma-material interaction studies. The rectified sheath voltage formed was high enough to cause window erosion by light ions due to its low-Z components (e.g. Si 3 N 4 and AlN). Hence, we are proposing impurity mitigation strategies, which involve the application of a Faraday screen to lower the rectified sheath voltage and the application of high-Z refractory coatings on the existing window plasma-facing surface. In this work, we report the erosion of two different coatings, i.e., tantalum oxide (Ta 2 O 5 ) and hafnium oxide (HfO 2 ) on a silicon nitride (Si 3 N 4 ) window material under conditions of low-energy deuterium (D) ion impact, well below the Ta 2 O 5 sputtering energy threshold (i.e. 250 eV). The test samples were RF-biased and exposed to a high D-ion fluence (∼10 26 m −2 ) in Plasma Interaction with Surface Component Experimental Station (PISCES-A) LPD. The experimentally measured sputtering yields of the high-Z refractory coatings below the sputtering energy threshold of Ta 2 O 5 indicate an increased erosion due to the plasma impurities, especially due to oxygen. Improving the vacuum level could reduce the oxygen impurities and increase the lifespan of the coated helicon window for plasma operation. Post-surface analysis indicates no preferential erosion of oxygen or enrichment of the high-Z surface component. This is likely due to an effective energy transfer from the impurity ion for sputtering of the high-Z component in the coating. With the reduced rectified sheath voltage at the window surface and improved vacuum conditions, the proposed high-Z refractory coatings offer a promising solution for reducing window erosion in future MPEX plasma operations at ORNL.

RF bias

Nuclear Safety [Vol. 36, No. 1, January-June 1995]

Nuclear Safety is a journal that covers significant issues in the field of nuclear safety. Its primary scope is safety in the design, construction, operation, and decommissioning of nuclear power reactors worldwide and the research and analysis activities that promote this goal, but it also encompasses the safety aspects of the entire nuclear fuel cycle, including fuel fabrication, spent-fuel processing and handling, and nuclear waste disposal, the handling of fissionable materials and radioisotopes, and the environmental effects of all these activities. Table of Contents for this issue follows. THE CHORNOBYL ACCIDENT: 1 The Chornobyl Accident Revisited, Part II: The State of the Nuclear Fuel Located Within the Chornobyl Sarcophagus, A A. Borovoi and A. R. Sich; GENERAL SAFETY CONSIDERATIONS: 33 Nuclear Power Safety in Central and Eastern Europe, R. Wilson; 46 Safety of Nuclear Power Reactors in the Former Eastern European Countries, S. Chakraborty; 53 Technical Note: On the Definition of Common-Cause Failures, H. Paula; ACCIDENT ANALYSIS: 58 Modeling and Analysis of Core-Debris Recriticality During Hypothetical Severe Accidents in the Advanced Neutron Source Reactor, S.-H. Kim, V. Georgevich, D. B. Simpson, C. O. Slater, and R. P. Taleyarkhan; 68 Ignitability of Hydrogen/Oxygen/Diluent Mixtures in the Presence of Hot Surfaces, R. K. Kumar and G. W. Koroll; 94 Coupled RELAP5 and CONTAIN Accident Analysis Using PVM, K. A. Smith, A. J. Baratta, and G. E. Robinson; CONTROL AND INSTRUMENTATION: 109 Application of Fuzzy Logic in Nuclear Reactor Control Part I: An Assessment of State-of-the-Art, A. S. Heger, N. K. Alang-Rashid, and M. Jamshidi; DESIGN FEATURES: 122 Twenty-Third DOE/NRC Nuclear Air-Cleaning and Treatment Conference, R. R. Bellamy, J. J. Hayes, and M. W. First; ENVIRONMENTAL EFFECTS: 135 Atmospheric Dispersion and the Radiological Consequences of Normal Airborne Effluents from a Nuclear Power Plant, D. Fang, C. Z. Sun, and L. Yang; 142 Calculation of Distribution Coefficients for Radionuclides in Soils and Sediments, I. Puigdomenech and U. Bergstrom: OPERATING EXPERIENCES: 155 Reactor Shutdown Experience, Compiled by J. W. Cletcher; U.S. NUCLEAR REGULATORY COMMISSION INFORMATION AND ANALYSES: 158 Operating Experience Feedback Report—Reliability of Safety-Related Steam Turbine-Driven Standby Pumps Used in U.S. Commercial Nuclear Power Plants, J. R. Boardman; 166 Turbine Building Hazards, H. L Ornstein; RECENT DEVELOPMENTS: 169 Reports, Standards, and Safety Guides, D. S. Queener; 175 Proposed Rule Changes as of Dec. 31,1994; ANNOUNCEMENTS: 32 Harvard School of Public Health In-Place Filter Testing Workshop; 134 International Conference on Advances in the Operational Safety of Nuclear Power Plants; 193 30th Tennessee Industries Week; 193 DOE Technical Standards Program 1995 Workshop; 194 Multiphase Flow Experiments and Instrumentation; 180 The Authors; 185 Indexes to Nuclear Safety, Volumes 34 and 35.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Simulating hindered grain boundary diffusion using the smoothed boundary method

Abstract Grain boundaries can greatly affect the transport properties of polycrystalline materials, particularly when the grain size approaches the nanoscale. While grain boundaries often enhance diffusion by providing a fast pathway for chemical transport, some material systems, such as those of solid oxide fuel cells and battery cathode particles, exhibit the opposite behavior, where grain boundaries act to hinder diffusion. To facilitate the study of systems with hindered grain boundary diffusion, we propose a model that utilizes the smoothed boundary method to simulate the dynamic concentration evolution in polycrystalline systems. The model employs domain parameters with diffuse interfaces to describe the grains, thereby enabling solutions with explicit consideration of their complex geometries. The intrinsic error arising from the diffuse interface approach employed in our proposed model is explored by comparing the results against a sharp interface model for a variety of parameter sets. Finally, two case studies are considered to demonstrate potential applications of the model. First, a nanocrystalline yttria-stabilized zirconia solid oxide fuel cell system is investigated, and the effective diffusivities are extracted from the simulation results and are compared to the values obtained through mean-field approximations. Second, the concentration evolution during lithiation of a polycrystalline battery cathode particle is simulated to demonstrate the method’s capability.

Materials Science

Reverse Logistics Ev Battery Recycling Agent Base Model

This represents the initial regional tier of the electric vehicle (EV) battery recycling agent base model. Through this model, we can ascertain the number of EV purchases at both the state and regional levels. We employ census data to develop a diverse household profile to inform decisions regarding the acquisition of new or used EVs. The number of EV purchases at the state level will affect the future demand for recycling, reuse, and repurposing of end-of-life EV batteries. Additionally, tax credits, EV rebate programs, and the financial capacity of households will influence the number of EV purchases, thereby further impacting the demand for EV battery recycling.

Alam, Lamia [Idaho National Laboratory (INL), Idah

Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is #BQP-complete in the worst case. In this work, we introduce QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

97 MATHEMATICS AND COMPUTING