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Determination of the phase boundary of the omega to beta transition in Zr using in situ high-pressure and high-temperature X-ray diffraction

The high-pressure behavior of zirconium has been examined using the synchrotron X-ray diffraction technique to a pressure of 38 GPa and a temperature of 800 K employing a hydrothermal diamond anvil cell technique. The structural transition from the ω to the β phase was observed. This transition has a negative dP/dT gradient, which is in general agreement with those reported in previous studies. The transition boundary was determined to be, P (GPa)=41.2–0.025×T (K). The negative slope of the transition, dP/dT, determined in our study using the diamond anvil cell technique was less than half that estimated by the previous study using a large press apparatus. - Graphical abstract: Experimental results and phase boundary of the ω–β transition in Zr. - Highlights: • X-ray diffraction patterns of zirconium were measured by the synchrotron experiments. • High-pressure experiments were performed by an external-heated diamond anvil cell. • Phase diagram of zirconium was determined at high pressures and high temperatures. • Phase boundary between omega and beta transition has a negative dP/dT slope.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Determination of dislocation density by electron backscatter diffraction and X-ray line profile analysis in ferrous lath martensite

The microstructure and the dislocation density in as-quenched ferrous lath martensite were studied by different methods. The blocks, packets and variants formed due to martensitic transformation were identified and their sizes were determined by electron backscatter diffraction (EBSD). Concomitant transmission electron microscopy (TEM) investigation revealed that the laths contain subgrains with the size between 50 and 100 nm. A novel evaluation procedure of EBSD images was elaborated for the determination of the density and the space distribution of geometrically necessary dislocations from the misorientation distribution. The total dislocation density obtained by X-ray diffraction line profile analysis was in good agreement with the value determined by EBSD, indicating that the majority of dislocations formed due to martensitic transformation during quenching are geometrically necessary dislocations.

36 MATERIALS SCIENCE↗

Determination of thermal and electronic carrier transport properties of SnS thinfilms using photothermal beam deflection technique

Graphical abstract: Display Omitted Highlights: ► Determination of carrier transport properties of SnS thin films non-destructively. ► SnS thin films were deposited by chemical spray pyrolysis technique. ► Photothermal beam deflection technique is used for film analysis. ► Optimization of film deposition parameters. ► Photothermal imaging of SnS films. -- Abstract: Photothermal beam deflection technique is an efficient tool for non-destructive evaluation of thin films. Thin films of tin mono sulphide, which find application as absorber layer in photovoltaic cells, were deposited by chemical spray pyrolysis technique and their carrier transport properties were determined using photothermal beam deflection technique. Thermal diffusivity, minority carrier lifetime, mobility and surface recombination velocity of these films fabricated under different spray conditions like varying spray rate, Sn/S ratio and substrate temperature were determined. Photothermal beam deflection technique was also employed for constructing the thermal images of these films to evaluate the film uniformity.

36 MATERIALS SCIENCE↗

Preparation of gold nanoparticles and determination of their particles size via different methods

Graphical abstract: Preparation of gold nanoparticles via NaBH{sub 4} reduction method, and determination of their particle size, size distribution and morphology by using different techniques. - Highlights: • Gold nanoparticles were synthesized by NaBH{sub 4} reduction method. • Excess of reducing agent leads to tendency of aggregation. • The particle size, size distribution and morphology were investigated. • Particle size was determined both experimentally as well as theoretically. - Abstract: Gold nanoparticles have been used in various applications covering both electronics, biosensors, in vivo biomedical imaging and in vitro biomedical diagnosis. As a general requirement, gold nanoparticles should be prepared in large scale, easy to be functionalized by chemical compound of by specific ligands or biomolecules. In this study, gold nanoparticles were prepared by using different concentrations of reducing agent (NaBH{sub 4}) in various formulations and their effect on the particle size, size distribution and morphology was investigated. Moreover, special attention has been dedicated to comparison of particles size measured by various techniques, such as, light scattering, transmission electron microscopy, UV spectrum using standard curve and particles size calculated by using Mie theory and UV spectrum of gold nanoparticles dispersion. Particle size determined by various techniques can be correlated for monodispersed particles and excess of reducing agent leads to increase in the particle size.

36 MATERIALS SCIENCE↗

Determination of total plutonium content in spent nuclear fuel assemblies with the differential die-away self-interrogation instrument

As a part of the Next Generation Safeguards Initiative Spent Fuel project, we simulate the response of the Differential Die-away Self-Interrogation (DDSI) instrument to determine total elemental plutonium content in an assayed spent nuclear fuel assembly (SFA). We apply recently developed concepts that relate total plutonium mass with SFA multiplication and passive neutron count rate. In this work, the multiplication of the SFA is determined from the die-away time in the early time domain of the Rossi-Alpha distributions measured directly by the DDSI instrument. Here, we utilize MCNP to test the method against 44 pressurized water reactor SFAs from a simulated spent fuel library with a wide dynamic range of characteristic parameters such as initial enrichment, burnup, and cooling time. Under ideal conditions, discounting possible errors of a real world measurement, a root mean square agreement between true and determined total Pu mass of 2.1% is achieved.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The quick and ultrasensitive determination of K in NaI using inductively coupled plasma mass spectrometry

A highly sensitive, novel and quick assay method utilizing inductively coupled plasma mass spectrometry was developed for the determination of K in NaI powders and NaI(Tl) scintillator crystals for use in ultralow background applications. The determination of K (viz. 40K), as well as Th and U and their daughters, is important in ultralow background detector materials to ensure incorporation of materials of sufficiently high radiopurity. Through the use of improved instrumentation, cool plasma operating conditions, and meticulously clean sample preparations, detection limits of 11 fg natK∙g-1 (or 341 pBq 40K∙kg-1) was attained for K in pure water. Detection limits in the sample matrix (i.e., NaI) were 0.529 ng natK∙g NaI-1 (or 16.4 Bq 40K∙kg NaI -1). A number of different precursor NaI powder samples and NaI(Tl) scintillator crystals were assayed for their K content. Determinations ranged from 0.757 – 31.4 ng natK∙g NaI-1. This method allows for the screening of materials to unprecedented levels in a fraction of the time compared to gamma counting techniques, providing a useful method for a more effective screening tool of K in ultralow background detector materials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Accurate determination of the electron spin polarization in magnetized iron and nickel foils for Møller polarimetry

The Møller polarimeter in Hall A at Jefferson Lab in Newport News, VA, has provided reliable measurements of electron beam polarization for the past two decades. Past experiments have typically required polarimetry at the 1% level of absolute uncertainty which the Møller polarimeter has delivered. However, the upcoming proposed experimental program including MOLLER and SoLID have stringent requirements on beam polarimetry precision at the level of 0.4% (The MOLLER Collaboration, 2014; The SoLID collaboration, 2019), requiring a systematic re-examination of all the contributing uncertainties. Møller polarimetry uses the double polarized scattering asymmetry of a polarized electron beam on a target with polarized atomic electrons. The target is a ferromagnetic material magnetized to align the spins in a given direction. In Hall A, the target is a pure iron foil aligned perpendicular to the beam and magnetized out of plane parallel or antiparallel to the beam direction. The acceptance of the detector is engineered to collect scattered electrons close to 90° in the center of mass frame where the analyzing power is a maximum (-7/9). One of the leading systematic errors comes from determination of the target foil polarization. Polarization of a magnetically saturated target foil requires knowledge of both the saturation magnetization and g', the electron g-factor which includes components from both spin and orbital angular momentum from which the spin fraction of magnetization is determined. Target foil polarization has been previously addressed in a 1997 publication “A precise target for Møller polarimetry” by de Bever et al. (1997) at a level of precision sufficient for experiments up to this point. Several shortcomings with the previous published value require revisiting the result prior to MOLLER. Here, we utilize the existing world data to provide a best estimate for target polarization for both nickel and iron foils including uncertainties in magnetization, high-field and temperature dependence, and fractional contribution to magnetization from orbital effects. We determine the foil electron spin polarization at 294 K to be 0.08020 ± 0.00018 (@4 T applied field) for iron and 0.018845+/-0.000053 (@2 T applied field) for nickel. Finally, we conclude with a brief discussion of additional systematic uncertainties to Møller polarimetry using this technique.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Scanning angle Raman spectroscopy: A nondestructive method for simultaneously determining mixed polymer fractional composition and film thickness

A scanning angle (SA) Raman spectroscopy method was developed to simultaneously measure the chemical composition and thickness of waveguide mixed polymer films with varying fractional compositions. In order to test the method, six films of polystyrene-block-poly(methyl methacrylate), some mixed with poly(methyl methacrylate) homopolymer (PS-b-PMMA:PMMA), and two films of poly(2-vinylnapthalene)-block-poly(methyl methacrylate) (P2VN-b-PMMA) were prepared. The film thickness ranged from 495 to 971 nm. The chemical composition and thickness of PS-b-PMMA:PMMA films was varied by the addition of the PMMA homopolymer and annealing the films in toluene. SA Raman peak amplitude ratios (1001 cm -1 for PS, 812 cm -1 for PMMA, and 1388 cm -1 for P2VN) were used to calculate the refractive index of the polymer film, an input parameter in calculations of the sum square electric field (SSEF). The film thickness was determined by SSEF models of the experimental Raman amplitudes versus the incident angle of light. The average film thickness determined by the developed SA Raman spectroscopy method was within 5% of the value determined by optical profilometry. In conclusion, SA Raman spectroscopy will be useful for in situ label-free analyses of mixed polymer waveguide films.

36 MATERIALS SCIENCE↗

Isotopic determination of uranium in soil by laser induced breakdown spectroscopy

Laser-induced breakdown spectroscopy (LIBS) operated under ambient pressure has been evaluated for isotopic analysis of uranium in real-world samples such as soil, with U concentrations in the single digit percentage levels. The study addresses the requirements for spectral decomposition of 235 U and 238 U atomic emission peaks that are only partially resolved. Although non-linear least-square fitting algorithms are typically able to locate the optimal combination of fitting parameters that best describes the experimental spectrum even when all fitting parameters are treated as free independent variables, the analytical results of such an unconstrained free-parameter approach are ambiguous. In this work, five spectral decomposition algorithms were examined, with different known physical properties (e.g., isotopic splitting, hyperfine structure) of the spectral lines sequentially incorporated into the candidate algorithms as constraints. It was found that incorporation of such spectral-line constraints into the decomposition algorithm is essential for the best isotopic analysis. The isotopic abundance of 235 U was determined from a simple two-component Lorentzian fit on the U II 424.437 nm spectral profile. For six replicate measurements, each with only fifteen laser shots, on a soil sample with U concentration at 1.1% w/w, the determined 235 U isotopic abundance was (64.6 ± 4.8)%, and agreed well with the certified value of 64.4%. Another studied U line - U I 682.691 nm possesses hyperfine structure that is comparatively broad and at a significant fraction as the isotopic shift. Thus, 235 U isotopic analysis with this U I line was performed with spectral decomposition involving individual hyperfine components. For the soil sample with 1.1% w/w U, the determined 235 U isotopic abundance was (60.9 ± 2.0)%, which exhibited a relative bias about 6% from the certified value. The bias was attributed to the spectral resolution of our measurement system - the measured line width for this U I line was larger than its isotopic splitting. In conclusion, although not the best emission line for isotopic analysis, this U I emission line is sensitive for element analysis with a detection limit of 500 ppm U in the soil matrix; the detection limit for the U II 424.437 nm line was 2000 ppm.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Correlating laser-induced breakdown spectroscopy with neutron activation analysis to determine the elemental concentration in the ionome of the Populus trichocarpa leaf

The black cottonwood poplar (Populus trichocarpa) leaf ionome (inorganic trace elements and mineral nutrients) is an important aspect for determining the physiological and developmental processes contributing to biomass production. A number of techniques are used to measure the ionome, yet characterizing the leaf spatial heterogeneity remains a challenge, especially in solid samples. Laser-induced breakdown spectroscopy (LIBS) has been used to determine the elemental composition of leaves and is able to raster across solid matrixes at 10 μm resolution. Here, we evaluate the use of LIBS for solid sample leaf elemental characterization in relation to neutron activation. In fact, neutron activation analysis is a laboratory-based technique which is used by the National Institute of Standards and Technology (NIST) to certify trace elements in candidate reference materials including plant leaf matrices. Introduction to the techniques used in this research has been presented in this manuscript. Neutron activation analysis (NAA) data has been correlated to the LIBS spectra to achieve quantification of the elements or ions present within poplar leaves. The regression coefficients of calibration and validation using multivariate analysis (MVA) methodology for six out of seven elements have been determined and vary between 0.810 and 0.998. LIBS and NAA data has been presented for the elements such as, calcium, magnesium, manganese, aluminum, copper, and potassium. Chlorine was also detected but it did not show good correlation between the LIBS and NAA techniques. This research shows that LIBS can be used as a fast, high-spatial resolution technique to quantify elements as part of large-scale field phenotyping projects.

59 BASIC BIOLOGICAL SCIENCES↗

Experimental determination of critical resolved shear stress for strain-induced phase transformation

The current investigation reports the first attempt to measure the critical resolved shear stress to initiates strain-induced phase transformation in a three-dimensional polycrystalline aggregate using high-energy diffraction microscopy (HEDM). In situ tensile testing was performed on a Fe38.5Mn20Co20Cr15Si5Cu1.5 metastable alloy exhibiting transformation-induced plasticity (TRIP). Grains with a higher propensity for strain-induced phase transformation were tracked using HEDM. A sharp drop in grain specific stress, coinciding with the appearance of a new ε-hcp grain oriented relative to the parent γ-fcc phase, was taken as evidence of grain-specific stress required to trigger phase transformation. The highest resolved shear stress on the potential transformation systems was identified as the critical resolved shear stress (CRSS) for strain-induced phase transformation. For the studied metastable alloy, CRSS for transformation was determined to be 86±3 MPa which was very close to theoretical CRSS value determined using Schmid factor (89±12 MPa) compared to the value determined using Taylor factor (62±7 MPa).

Jain, Roopam↗

Application of spatial and non-spatial data analysis in determination of the factors that impact municipal solid waste generation rates in Turkey

Highlights: Black-Right-Pointing-Pointer Spatial autocorrelation exists in municipal solid waste generation rates for different provinces in Turkey. Black-Right-Pointing-Pointer Traditional non-spatial regression models may not provide sufficient information for better solid waste management. Black-Right-Pointing-Pointer Unemployment rate is a global variable that significantly impacts the waste generation rates in Turkey. Black-Right-Pointing-Pointer Significances of global parameters may diminish at local scale for some provinces. Black-Right-Pointing-Pointer GWR model can be used to create clusters of cities for solid waste management. - Abstract: In studies focusing on the factors that impact solid waste generation habits and rates, the potential spatial dependency in solid waste generation data is not considered in relating the waste generation rates to its determinants. In this study, spatial dependency is taken into account in determination of the significant socio-economic and climatic factors that may be of importance for the municipal solid waste (MSW) generation rates in different provinces of Turkey. Simultaneous spatial autoregression (SAR) and geographically weighted regression (GWR) models are used for the spatial data analyses. Similar to ordinary least squares regression (OLSR), regression coefficients are global in SAR model. In other words, the effect of a given independent variable on a dependent variable is valid for the whole country. Unlike OLSR or SAR, GWR reveals the local impact of a given factor (or independent variable) on the waste generation rates of different provinces. Results show that provinces within closer neighborhoods have similar MSW generation rates. On the other hand, this spatial autocorrelation is not very high for the exploratory variables considered in the study. OLSR and SAR models have similar regression coefficients. GWR is useful to indicate the local determinants of MSW generation rates. GWR model can be utilized to plan waste management activities at local scale including waste minimization, collection, treatment, and disposal. At global scale, the MSW generation rates in Turkey are significantly related to unemployment rate and asphalt-paved roads ratio. Yet, significances of these variables may diminish at local scale for some provinces. At local scale, different factors may be important in affecting MSW generation rates.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Determining heavy metals in spent compact fluorescent lamps (CFLs) and their waste management challenges: Some strategies for improving current conditions

Highlights: • Heavy metals in spent compact fluorescent lamps (CFLs) determined. • Current waste management condition of CFLs in Iran assessed. • Currently, waste of CFLs is disposed by municipal waste stream in waste landfills. • We propose extended producer responsibility (EPR) for CFLs waste management. - Abstract: From environmental viewpoint, the most important advantage of compact fluorescent lamps (CFLs) is reduction of green house gas emissions. But their significant disadvantage is disposal of spent lamps because of containing a few milligrams of toxic metals, especially mercury and lead. For a successful implementation of any waste management plan, availability of sufficient and accurate information on quantities and compositions of the generated waste and current management conditions is a fundamental prerequisite. In this study, CFLs were selected among 20 different brands in Iran. Content of heavy metals including mercury, lead, nickel, arsenic and chromium was determined by inductive coupled plasma (ICP). Two cities, Tehran and Tabriz, were selected for assessing the current waste management condition of CFLs. The study found that waste generation amount of CFLs in the country was about 159.80, 183.82 and 153.75 million per year in 2010, 2011 and 2012, respectively. Waste generation rate of CFLs in Iran was determined to be 2.05 per person in 2012. The average amount of mercury, lead, nickel, arsenic and chromium was 0.417, 2.33, 0.064, 0.056 and 0.012 mg per lamp, respectively. Currently, waste of CFLs is disposed by municipal waste stream in waste landfills. For improving the current conditions, we propose by considering the successful experience of extended producer responsibility (EPR) in other electronic waste management. The EPR program with advanced recycling fee (ARF) is implemented for collecting and then recycling CFLs. For encouraging consumers to take the spent CFLs back at the end of the products’ useful life, a proportion of ARF (for example, 50%) can be refunded. On the other hand, the government and Environmental Protection Agency should support and encourage recycling companies of CFLs both technically and financially in the first place.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Alpha Shape Analysis (ASA) Framework for Post- Clustering Property Determination in Atom Probe Tomographic Data

While application of clustering algorithms to atom probe tomography data have enabled quantification of solute clusters in terms of number density, size, and subcomposition there exist other properties (e.g., volume, surface area, and composition) that are better determined by defining an interface between the cluster and the surrounding matrix. The limitation in composition results from an ion selection step where the expected matrix ion types are omitted from the cluster search algorithm to enhance the contrast between the matrix and cluster and to reduce the complexity of the search. Previously, composition determination within solute clusters has utilized a secondary envelopment and erosion step on top of conventional methods such as maximum separation. In this work, we present a novel stochastic method that combines the particle identification fidelity of a conventional clustering algorithm with the analytical flexibility of mesh-based approaches through the generation of alpha shapes for each identified cluster. Furthermore, the corresponding mesh accounts for concave components of the clusters and determines the volume and surface area of the clusters; additionally, the mesh boundary is utilized to update the total composition according to the internal ions.

42 ENGINEERING↗

Rapid Determination of Uranium Isotopic Abundance from Cotton Swipes: Direct Extraction via a Planar Surface Reader and Coupling to a Microplasma Ionization Source

The collection of solid particulates and liquids from surfaces by the use of cloth swipes is fairly ubiquitous. In such methods, there is a continuous concern regarding the ability to locate and quantitatively sample the analyte species from the material. In this effort, we demonstrate the initial coupling of an Advion Plate Express plate reader to a liquid sampling–atmospheric pressure glow discharge (LS-APGD) microplasma ionization source with an Orbitrap mass spectrometer to perform uranium isotopic analyses of solution residues on cotton swipes. The Plate Express employs a sampling probe head to engage and seal against the swipe surface. Subsequentially, the analyte residues are desorbed and transported within a 2% HNO 3 electrolyte flow to the ionization source. Quantitative recoveries were observed following a single 30 s extraction step, with the absolute mass sampled per extraction being ~100 ng. While the intrasample variability in the analytical responses for triplicate sampling of the same swipe yield ~30% RSD, this lack of precision is offset by the ability to determine isotope ratios for enriched uranium specimens with a precision of better than 10% RSD. Pooled, intersample precision ( n = 9) was found to be <5%RSD across the various sample compositions. Finally, 235 U/ 238 U determinations (ranging from 0.053 to 1.806) were accurate with errors of <10%, absolute. The 234 U- and 236 U-inclusive ratios were determined with similar accuracy in enriched samples. While the driving force for the effort is in the realm of nuclear nonproliferation efforts, the ubiquitous use of cloth swipes across many application areas could benefit from this convenient approach, including the use of versatile, reduced-format mass spectrometer systems.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Mass Spectrometric Determination of Uranium and Thorium in High Radiopurity Polymers Using Ultra Low Background Electroformed Copper Crucibles for Dry Ashing

A rapid new method for determining the U and Th mass concentrations in high radiopurity plastics is described, consisting of 1) dry ashing the plastic sample and tracers in low mass crucibles made of ultra low background electroformed copper (ULB EF-Cu) foil cut and folded into boats, 2) dissolving both the ash and the boat in acid, 3) performing a column separation to remove copper, and 4) determining the elements of interest by isotope dilution mass spectrometry. This method was demonstrated on both unfluorinated and fluorinated plastics, demonstrating high tracer recoveries and detection limits to pg/g (i.e., parts per trillion) levels or below, corresponding to μBq/kg of material. Samples of biomedical polyester (Max-Prene® 955) and a fluoropolymer (polyvinylidene fluoride, PVDF) were analyzed in powder raw material forms as well as solids in the form of pellets or injection molded parts. The polyester powder contained 6 pg/g and 2 pg/g for Th and U respectively. These levels correspond to 25 and 25 μBq/kg radioactivity, respectively. Determinations on samples of PVDF powder were typically below 1 pg/g for Th and 2 pg/g for U, corresponding to 4 and 25 μBq/kg radioactivity, respectively. The use of low mass ULB EF-Cu boats for dry ashing successfully overcame the problem of crucible-generated contaminants in the analysis; absolute detection limits, calculated as 3 × standard deviation of the process blanks, were typically 20-100 fg within a sample set. Complete dissolution of the ash and low mass boat provided high tracer recoveries, and provides a convincing method to recover both the tracer and sample isotopes when full equilibration of tracer isotopes with sample isotopes is not possible prior to beginning chemical sample processing on solids.

EFCu Electroformed copper↗

Determination of Carbonyl Groups in Pyrolysis Bio-oils Using Potentiometric Titration: Review and Comparison of Methods

Carbonyl compounds present in bio-oils are known to be responsible for bio-oil property changes upon storage and during upgrading. As such, carbonyl content has previously been used as a method of tracking bio-oil aging and condensation reactions with less variability than viscosity measurements. Given the importance of carbonyls in bio-oils, accurate analytical methods for their quantification are very important for the bio-oil community. Potentiometric titration methods based on carbonyl oximation have long been used for the determination of carbonyl content in pyrolysis bio-oils. Here in this study, we present a modification of the traditional carbonyl oximation procedures that results in less reaction time, smaller sample size, higher precision, and more accurate carbonyl determinations. Some compounds such as carbohydrates are not measured by the traditional method (modified Nicolaides method), resulting in low estimations of the carbonyl content. Furthermore, we have shown that reaction completion for the traditional method can take up to 300 hours. The new method presented here (the modified Faix method) reduces the reaction time to 2 hours, uses triethanolamine (TEA) in the place of pyridine, and requires a smaller sample size for the analysis. Carbonyl contents determined using this new method are consistently higher than when using the traditional titration methods.

09 BIOMASS FUELS↗

Determining the N -Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗