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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Neutrinos in N -body simulations

In the next decade, cosmological surveys will have the statistical power to detect the absolute neutrino mass scale. N-body simulations of large-scale structure formation play a central role in interpreting data from such surveys. Yet these simulations are Newtonian in nature. We provide a quantitative study of the limitations to treating neutrinos, implemented as N-body particles, in N-body codes, focusing on the error introduced by neglecting special relativistic effects. Special relativistic effects are potentially important due to the large thermal velocities of neutrino particles in the simulation box. We derive a self-consistent theory of linear perturbations in Newtonian and nonrelativistic neutrinos and use this to demonstrate that N-body simulations overestimate the neutrino free-streaming scale, and cause errors in the matter power spectrum that depend on the initial redshift of the simulations. For z i ≲ 100, and neutrino masses within the currently allowed range, this error is ≲ 0.5%, though represents an up to ~10 % correction to the shape of the neutrino-induced suppression to the cold dark matter power spectrum. Here, we argue that the simulations accurately model nonlinear clustering of neutrinos so that the error is confined to linear scales.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians

A key property of many-body localized Hamiltonians is the area law entanglement of even highly excited eigenstates. Matrix product states (MPS) can be used to efficiently represent low entanglement (area law) wave functions in one dimension. An important application of MPS is the widely used density matrix renormalization group (DMRG) algorithm for finding ground states of one-dimensional Hamiltonians. Here, we develop two algorithms, the shift-and-invert MPS (SIMPS) and excited state DMRG which find highly excited eigenstates of many-body localized Hamiltonians. Excited state DMRG uses a modified sweeping procedure to identify eigenstates, whereas SIMPS applies the inverse of the shifted Hamiltonian to a MPS multiple times to project out the targeted eigenstate. To demonstrate the power of these methods, we verify the breakdown of the eigenstate thermalization hypothesis in the many-body localized phase of the random field Heisenberg model, show the saturation of entanglement in the many-body localized phase, and generate local excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

MICCO: An Enhanced Multi-GPU Scheduling Framework for Many-Body Correlation Functions

Calculation of many-body correlation functions is one of the critical kernels utilized in many scientific computing areas, especially in Lattice Quantum Chromodynamics (Lattice QCD). It is formalized as a sum of a large number of contraction terms each of which can be represented by a graph consisting of vertices describing quarks inside a hadron node and edges designating quark propagations at specific time intervals. Due to its computation- and memory-intensive nature, real-world physics systems (e.g., multi-meson or multi-baryon systems) explored by Lattice QCD prefer to leverage multi-GPUs. Different from general graph processing, many-body correlation function calculations show two specific features: a large number of computation-/data-intensive kernels and frequently repeated appearances of original and intermediate data. The former results in expensive memory operations such as tensor movements and evictions. The latter offers data reuse opportunities to mitigate the data-intensive nature of many-body correlation function calculations. However, existing graph-based multi-GPU schedulers cannot capture these data-centric features, thus resulting in a sub-optimal performance for many-body correlation function calculations. To address this issue, this paper presents a multi-GPU scheduling framework, MICCO, to accelerate contractions for correlation functions particularly by taking the data dimension (e.g., data reuse and data eviction) into account. This work first performs a comprehensive study on the interplay of data reuse and load balance, and designs two new concepts: local reuse pattern and reuse bound to study the opportunity of achieving the optimal trade-off between them. Based on this study, MICCO proposes a heuristic scheduling algorithm and a machine-learning-based regression model to generate the optimal setting of reuse bounds. Specifically, MICCO is integrated into a real-world Lattice QCD system, Redstar, for the first time running on multiple GPUs. The evaluation demonstrates MICCO outperforms other state-of-art works, achieving up to 2.25× speedup in synthesized datasets, and 1.49× speedup in real-world correlation functions.

Wang, Qihan↗
DOE OSTI2020

Estimation of Body Fat Percentage for Clinical Pharmacokinetic Studies in Children

Obesity is a prevalent childhood condition and the degree of adiposity appears likely to be an important covariate in the pharmacokinetics (PKs) of many drugs. We undertook these studies to facilitate the evaluation and, where appropriate, quantification of the covariate effect of body fat percentage (BF%) on PK parameters in children. We examined two large databases to determine the values and variabilities of BF% in children with healthy body weights and in those with obesity, comparing the accuracy and precision of BF% estimation by both clinical methods and demographically derived techniques. Additionally, we conducted simulation studies to evaluate the utility of the several methods for application in clinical trials. BF% was correlated with body mass index (BMI), but was highly variable among both children with healthy body weights and those with obesity. Bio‐impedance and several demographically derived techniques produced mean estimates of BF% that differed from dual x‐ray absorptiometry by < 1% (accuracy) and a SD of 5% or less (precision). Simulation studies confirmed that when the differences in precision among the several methods were small compared with unexplained between‐subject variability of a PK parameter, the techniques were of similar value in assessing the contribution of BF%, if any, as a covariate for that PK parameter. The combination of sex and obesity stage explained 68% of the variance of BF% with BMI. The estimation of BF% from sex and obesity stage can routinely be applied to PK clinical trials to evaluate the contribution of BF% as a potential covariate.

Green, Thomas P.↗
DOE OSTI2024

Body size and early marine conditions drive changes in Chinook salmon productivity across northern latitude ecosystems

Disentangling the influences of climate change from other stressors affecting the population dynamics of aquatic species is particularly pressing for northern latitude ecosystems, where climate‐driven warming is occurring faster than the global average. Chinook salmon (Oncorhynchus tshawytscha) in the Yukon‐Kuskokwim (YK) region occupy the northern extent of their species' range and are experiencing prolonged declines in abundance resulting in fisheries closures and impacts to the well‐being of Indigenous people and local communities. These declines have been associated with physical (e.g., temperature, streamflow) and biological (e.g., body size, competition) conditions, but uncertainty remains about the relative influence of these drivers on productivity across populations and how salmon–environment relationships vary across watersheds. To fill these knowledge gaps, we estimated the effects of marine and freshwater environmental indicators, body size, and indices of competition, on the productivity (adult returns‐per‐spawner) of 26 Chinook salmon populations in the YK region using a Bayesian hierarchical stock‐recruitment model. Across most populations, productivity declined with smaller spawner body size and sea surface temperatures that were colder in the winter and warmer in the summer during the first year at sea. Decreased productivity was also associated with above average fall maximum daily streamflow, increased sea ice cover prior to juvenile outmigration, and abundance of marine competitors, but the strength of these effects varied among populations. Maximum daily stream temperature during spawning migration had a nonlinear relationship with productivity, with reduced productivity in years when temperatures exceeded thresholds in main stem rivers. These results demonstrate for the first time that well‐documented declines in body size of YK Chinook salmon were associated with declining population productivity, while taking climate into account.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

SU-C-12A-01: Primary Vs. Scatter Contribution to Body CTDI: Experiment Results

Purpose: To quantify experimentally scatter contribution to CTDI in center and peripheral holes of the body (32-cm) phantom. Methods: All experiments were performed in Service Mode of 750CT-Discovery with both tube and table were in stationary position, and with large filter and 40- mm collimation. First, transmission through acrylic was measured using acrylic rods of various lengths (1-cm to 33-cm), at 80, 120, and 140 kVp. These data were utilized to obtain dose from primary beam at different depths of acrylic. Thus, scatter-to-primary ratio (SPR) was determined for center-hole by measuring exposure with a pencil chamber. For peripheral hole SPR, dose was measured at eight different tube angles from 0° to 180°. Change in primary dose with tube angle due to both shape of bowtie filter and distance from tube was measured in air; hence, dose from primary from each of the 8 phantom measurements was determined and SPR was calculated by integrating the fitted models for primary and scatter distributions as a function of distance from tube. Also, scatter contribution from different segments of phantom to center-hole dose was measured using a custom-built acrylic phantom, which had similar SPR at the center-hole to that of standard body phantom. Results: After correcting for stray radiation (off-focus, scatter from collimators, etc.) for primary measurements, preliminary results of SPRs in center-hole dose of the body phantom for 80, 120, and 140 kVp were 6.8, 6.2, and 6.0, respectively, and for peripheral hole were 1.45, 1.44, and 1.39. Forward-scatter and backscatter contributions to center dose, at any point during tube rotation, were respectively, 62% and 38% with 80 kVp, and 60% and 40% with 120 and 140 kVp. Conclusion: SPR in both center and peripheral holes of body CTDI phantom was determined experimentally. Also, distribution of contributing scatter to center hole was estimated.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-P-08: Establishment of Local Diagnostic Reference Levels of Routine Abdomen Exam in Computed Tomography According to Body Weight

Purpose: The national diagnostic reference levels (NDRLs) is an efficient, concise and powerful standard for optimizing radiation protection of a patient. However, for each hospital the dose-reducing potential of focusing on establishment of local DRLs (LDRLs). A lot of study reported that Computed tomography exam contributed majority radiation dose in different medical modalities, therefore, routine abdomen CT exam was choose in initial pilot study in our study. Besides the mAs of routine abdomen CT exam was decided automatic exposure control by linear attenuation is relate to body shape of patient. In this study we would like to establish the local diagnostic reference levels of routine abdomen exam in computed tomography according to body weight of patient. Methods and Materials: There are two clinical CT scanners (a Toshiba Aquilion and a Siemens Sensation) were performed in this study. For CT examinations the basic recommended dosimetric quantity is the Computed Tomography Dose Index (CTDI). The patient sample involved 82 adult patients of both sexes and divided into three groups by their body weight (50–60 kg, 60–70 kg, 70–80 kg).Carried out the routine abdomen examinations, and all exposure parameters have been collected and the corresponding CTDIv and DLP values have been determined. The average values were compared with the European DRLs. Results: The majority of patients (75%) were between 50–70 Kg of body weight, the numbers of patient in each group of weight were 40–50:7; 50–60:29; 60–70:33; 70–80:13. The LDRLs in each group were 10.81mGy, 14.46mGy, 20.27mGy and 21.04mGy, respectively. The DLP were 477mGy, 630mGy, 887mGy and 959mGy, respectively. No matter which group the LDRLs were lower than European DRLs. Conclusions: We would like to state that this was a pioneer work in local hospital in Chiayi. We hope that this may lead the way to further developments in Taiwan.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Practical dose point-based methods to characterize dose distribution in a stationary elliptical body phantom for a cone-beam C-arm CT system

Purpose: To propose new dose point measurement-based metrics to characterize the dose distributions and the mean dose from a single partial rotation of an automatic exposure control-enabled, C-arm-based, wide cone angle computed tomography system over a stationary, large, body-shaped phantom. Methods: A small 0.6 cm{sup 3} ion chamber (IC) was used to measure the radiation dose in an elliptical body-shaped phantom made of tissue-equivalent material. The IC was placed at 23 well-distributed holes in the central and peripheral regions of the phantom and dose was recorded for six acquisition protocols with different combinations of minimum kVp (109 and 125 kVp) and z-collimator aperture (full: 22.2 cm; medium: 14.0 cm; small: 8.4 cm). Monte Carlo (MC) simulations were carried out to generate complete 2D dose distributions in the central plane (z = 0). The MC model was validated at the 23 dose points against IC experimental data. The planar dose distributions were then estimated using subsets of the point dose measurements using two proposed methods: (1) the proximity-based weighting method (method 1) and (2) the dose point surface fitting method (method 2). Twenty-eight different dose point distributions with six different point number cases (4, 5, 6, 7, 14, and 23 dose points) were evaluated to determine the optimal number of dose points and their placement in the phantom. The performances of the methods were determined by comparing their results with those of the validated MC simulations. The performances of the methods in the presence of measurement uncertainties were evaluated. Results: The 5-, 6-, and 7-point cases had differences below 2%, ranging from 1.0% to 1.7% for both methods, which is a performance comparable to that of the methods with a relatively large number of points, i.e., the 14- and 23-point cases. However, with the 4-point case, the performances of the two methods decreased sharply. Among the 4-, 5-, 6-, and 7-point cases, the 7-point case (1.0% [±0.6%] difference) and the 6-point case (0.7% [±0.6%] difference) performed best for method 1 and method 2, respectively. Moreover, method 2 demonstrated high-fidelity surface reconstruction with as few as 5 points, showing pixelwise absolute differences of 3.80 mGy (±0.32 mGy). Although the performance was shown to be sensitive to the phantom displacement from the isocenter, the performance changed by less than 2% for shifts up to 2 cm in the x- and y-axes in the central phantom plane. Conclusions: With as few as five points, method 1 and method 2 were able to compute the mean dose with reasonable accuracy, demonstrating differences of 1.7% (±1.2%) and 1.3% (±1.0%), respectively. A larger number of points do not necessarily guarantee better performance of the methods; optimal choice of point placement is necessary. The performance of the methods is sensitive to the alignment of the center of the body phantom relative to the isocenter. In body applications where dose distributions are important, method 2 is a better choice than method 1, as it reconstructs the dose surface with high fidelity, using as few as five points.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Thermomechanics of Deformations in an Anharmonic Solid Body

The macroscopic laws determining the temperature and deformations of an anharmonic solid body in a given external temperature force field have been stated in the form of the first thermodynamics law supplemented by equations of state of the body. The internal and free energies necessary for it are found from the statistical sum in which some of degrees of freedom determining the body shape are discharged from statistical averaging. These functions of state have been calculated up to the first order of the perturbation theory in the anharmonicity for the microscopic dynamic model of the body with the interatomic interaction potential energy given as a series in powers of atom coordinates. The classical region of high temperatures is considered.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Towards the understanding of the genuine three-body interaction for p–p–p and p–p–Λ

Three-body nuclear forces play an important role in the structure of nuclei and hypernuclei and are also incorporated in models to describe the dynamics of dense baryonic matter, such as in neutron stars. So far, only indirect measurements anchored to the binding energies of nuclei can be used to constrain the three-nucleon force, and if hyperons are considered, the scarce data on hypernuclei impose only weak constraints on the three-body forces. In this work, we present the first direct measurement of the p–p–p and p–p–Λ systems in terms of three-particle correlation functions carried out for pp collisions at $\sqrt{s}$=13 TeV. Three-particle cumulants are extracted from the correlation functions by applying the Kubo formalism, where the three-particle interaction contribution to these correlations can be isolated after subtracting the known two-body interaction terms. A negative cumulant is found for the p–p–p system, hinting to the presence of a residual three-body effect while for p–p–Λ the cumulant is consistent with zero. This measurement demonstrates the accessibility of three-baryon correlations at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

MemHC: An Optimized GPU Memory Management Framework for Accelerating Many-body Correlation

The many-body correlation function is a fundamental computation kernel in modern physics computing applications, e.g., Hadron Contractions in Lattice quantum chromodynamics (QCD). This kernel is both computation and memory intensive, involving a series of tensor contractions, and thus usually runs on accelerators like GPUs. Existing optimizations on many-body correlation mainly focus on individual tensor contractions (e.g., cuBLAS libraries and others). In contrast, this work discovers a new optimization dimension for many-body correlation by exploring the optimization opportunities among tensor contractions. More specifically, it targets general GPU architectures (both NVIDIA and AMD) and optimizes many-body correlation’s memory management by exploiting a set of memory allocation and communication redundancy elimination opportunities: first, GPU memory allocation redundancy: the intermediate output frequently occurs as input in the subsequent calculations; second, CPU-GPU communication redundancy: although all tensors are allocated on both CPU and GPU, many of them are used (and reused) on the GPU side only, and thus, many CPU/GPU communications (like that in existing Unified Memory designs) are unnecessary; third, GPU oversubscription: limited GPU memory size causes oversubscription issues, and existing memory management usually results in near-reuse data eviction, thus incurring extra CPU/GPU memory communications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum Many-Body Scars: A Quasiparticle Perspective

Weakly interacting quasiparticles play a central role in the low-energy description of many phases of quantum matter. At higher energies, however, quasiparticles cease to be well defined in generic many-body systems owing to a proliferation of decay channels. In this review, we discuss the phenomenon of quantum many-body scars, which can give rise to certain species of stable quasiparticles throughout the energy spectrum. This goes along with a set of unusual nonequilibrium phenomena including many-body revivals and nonthermal stationary states. We provide a pedagogical exposition of this physics via a simple yet comprehensive example, that of a spin-1 XY model. We place our discussion in the broader context of symmetry-based constructions of many-body scar states, projector embeddings, and Hilbert space fragmentation. We conclude with a summary of experimental progress and theoretical puzzles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Biogeography of the ecosystems of the healthy human body

Characterizing the biogeography of the microbiome of healthy humans is essential for understanding microbial associated diseases. Previous studies mainly focused on a single body habitat from a limited set of subjects. Here, we analyzed one of the largest microbiome datasets to date and generated a biogeographical map that annotates the biodiversity, spatial relationships, and temporal stability of 22 habitats from 279 healthy humans. We identified 929 genera from more than 24 million 16S rRNA gene sequences of 22 habitats, and we provide a baseline of inter-subject variation for healthy adults. The oral habitat has the most stable microbiota with the highest alpha diversity, while the skin and vaginal microbiota are less stable and show lower alpha diversity. The level of biodiversity in one habitat is independent of the biodiversity of other habitats in the same individual. The abundances of a given genus at a body site in which it dominates do not correlate with the abundances at body sites where it is not dominant. Additionally, we observed the human microbiota exhibit both cosmopolitan and endemic features. Finally, comparing datasets of different projects revealed a project-based clustering pattern, emphasizing the significance of standardization of metagenomic studies. The data presented here extend the definition of the human microbiome by providing a more complete and accurate picture of human microbiome biogeography, addressing questions best answered by a large dataset of subjects and body sites that are deeply sampled by sequencing.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

A correlation between seasonally changing photoperiod, whole body lipid, and condition factor in juvenile spring Chinook salmon (Oncorhynchus tshawytscha)

The regulation of lipid stores is a central process for the physiology and ecology of fishes. Seasonal variation in lipid stores has been directly linked to survival of fishes across periods of food deprivation. We assessed whether a seasonally changing photoperiod was correlated to seasonal changes in energetic status to help better understand these important processes. Groups of first feeding Chinook salmon fry were introduced to a seasonal photoperiod cycle, but the point of entrance into the seasonal cycle varied from near the winter solstice (December), to either side of the spring equinox (February & May). Temperature and feeding rate were similar for all treatments. Subsequently, condition factor and whole body lipid content were assessed through a seasonal progression. Throughout most of the experiment, length and weight did not differ between the different photoperiod treatments, however whole body lipid and Fulton’s condition factor did. Furthermore, changes in both whole body lipid and Fulton’s condition factor in all treatment groups followed a similar seasonal pattern that was inversely related to day length (highest K and lipid levels found during days with the least light). These results suggest that regardless of age or size, there is a correlation between seasonal changes in photoperiod and changes in body composition in juvenile Chinook salmonids.

Spangenberg, Dina K. (ORCID:000000018861395X)↗
DOE OSTI2016

Neurogenic Effects of Low-Dose Whole-Body HZE (Fe) Ion and Gamma Irradiation

Understanding the dose-toxicity profile of radiation is critical when evaluating potential health risks associated with natural and man-made sources in our environment. This study was done to evaluate the effects of low-dose whole-body high-energy charged (HZE) iron (Fe) ions and low-energy gamma exposure on proliferation and differentiation of adult-born neurons within the dentate gyrus of the hippocampus, cells deemed to play a critical role in memory regulation. To determine the dose-response characteristics of the brain to whole-body Fe-ion vs. gamma-radiation exposure, C57BL/6J mice were irradiated with 1 GeV/n Fe ions or a static 137 Cs source (0.662 MeV) at doses ranging from 0 to 300 cGy. The neurogenesis was analyzed at 48 h and one month postirradiation. These experiments revealed that whole-body exposure to either Fe ions or gamma radiation leads to: 1. An acute decrease in cell division within the dentate gyrus of the hippocampus, detected at doses as low as 30 and 100 cGy for Fe ions and gamma radiation, respectively; and 2. A reduction in newly differentiated neurons (DCX immunoreactivity) at one month postirradiation, with significant decreases detected at doses as low as 100 cGy for both Fe ions and gamma rays. The data presented here contribute to our understanding of brain responses to whole-body Fe ions and gamma rays and may help inform health-risk evaluations related to systemic exposure during a medical or radiologic/nuclear event or as a result of prolonged space travel.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2019

Many-body effects in transport and energy transfer

Many-body physics is common in defining responses of nanoscale to external perturbations such as bias, optical driving, temperature gradient. When applied to open systems these perturbations lead to matter and energy transfer between the system and its surroundings (baths) and/or cause intra-system dynamics. While many different theoretical techniques have been developed to describe system responses, not all of them are convenient (or even appropriate) when applied at nanoscale. Traditional theoretical techniques are either based on kinetic schemes (e.g., Redfield-Lindblad quantum master equation) or utilize quasiparticle description (e.g., single-particle scattering theory, input-output formalism, standard nonequilibrium Green’s functions technique). The former fails to account for quantum mechanics of the system-bath interface and may fail qualitatively when used in open interacting systems. The latter is inconvenient when many-body states description of the system is preferable, which is usual, e.g., in molecular optical spectroscopy. This project was devoted to development of new nonequilibrium Green’s function (NEGF) techniques and application of standard and many-body flavors of the NEGF to description of charge and energy transport, optical response, nonadiabatic molecular dynamics, and thermodynamics of nanoscale devices in general, and, in particular, of single-molecule junctions. In particular, Hubbard NEGF (new many-body flavor of the NEGF) was introduced as a new technique especially convenient in treatment of optoelectronic experiments in single-molecule junctions and useful in discussion of bias induced nuclear dynamics in junctions. The research also led to further technique developments and applications beyond the timing of this Award.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Unitary Bethe-Salpeter Methods in Two- and Three-Body Systems

The study of resonances, unstable particles formed in particle scattering, is motivated by the questions about the strong interaction and the composition of hadrons. In order to advance this study in the intermediate energy region, a variety of techniques are used. In this thesis, we present work done on two different analyses that use the principle of unitarity and the Bethe-Salpeter equation to study the resonances Lambda(1405), Sigma(1385), and a1(1260). Firstly, we perform a simultaneous analysis of Sand P-waves of the Strangeness = -1 two-body meson-baryon scattering amplitude using all low-energy data. For the first time, differential cross section data are included for chiral unitary coupled-channel models. From this model, S- and P-wave amplitudes are extracted and we observe both well-known I(JP)=0(1/2^-) S-wave states as well as a new I(JP)=1(1/2^+) state absent in quark models and lattice QCD results. Multiple statistical and phenomenological tests suggest that, while the data clearly require an I =1 P-wave resonance, the new state just accounts for the absence of the decuplet Sigma(1385)3/2+ in the model which is subsequently included in the parameterization. Secondly, we formulate the final state interaction of the a1(1260) resonance decay in a manifestly three-body-unitary parameterization and fit it to the a1(1260) lineshape measured by the ALEPH experiment. Dalitz plots calculated from this fit are presented. The work demonstrates the feasibility to numerically solve a previously derived amplitude and its generalization to isobars with spin and coupled channels. The model is a good test case because it can also be applied to other meson decays including exotic states and modified for the finite-volume problem as it arises in lattice QCD due to its manifest unitarity. The understanding of the resonances being analyzed in both the two-body work and the three-body work gives a better understanding of intermediate energy QCD.

Sadasivan, Daniel↗
DOE OSTI2025

Explicit block encodings of boundary value problems for many-body elliptic operators

Simulation of physical systems is one of the most promising use cases of future digital quantum computers. In this work we systematically analyze the quantum circuit complexities of block encoding the discretized elliptic operators that arise extensively in numerical simulations for partial differential equations, including high-dimensional instances for many-body simulations. When restricted to rectangular domains with separable boundary conditions, we provide explicit circuits to block encode the many-body Laplacian with separable periodic, Dirichlet, Neumann, and Robin boundary conditions, using standard discretization techniques from low-order finite difference methods. To obtain high-precision, we introduce a scheme based on periodic extensions to solve Dirichlet and Neumann boundary value problems using a high-order finite difference method, with only a constant increase in total circuit depth and subnormalization factor. We then present a scheme to implement block encodings of differential operators acting on more arbitrary domains, inspired by Cartesian immersed boundary methods. We then block encode the many-body convective operator, which describes interacting particles experiencing a force generated by a pair-wise potential given as an inverse power law of the interparticle distance. This work provides concrete recipes that are readily translated into quantum circuits, with depth logarithmic in the total Hilbert space dimension, that block encode operators arising broadly in applications involving the quantum simulation of quantum and classical many-body mechanics.

Kharazi, Tyler [University of California, Berkeley↗