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At least 397 records · Page 22

Three-point functions in $\mathrm{ABJM}$ and Bethe Ansatz

We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.

1/N Expansion↗

Lifting of two-mode states in the D1-D5 CFT

We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where one copy of the seed CFT has been excited by a pair of oscillators, each being either bosonic or fermionic. While such states are BPS at the orbifold point, they will in general ‘lift’ as the theory is deformed towards general values of the couplings. We compute the expectation value of this lift at second order in the deformation parameter for the above mentioned states. We write this lift in terms of a fixed number of nested contour integrals on a given integrand; this integrand depends on the mode numbers of the oscillators in the state. We evaluate these integrals to obtain the explicit value of the lift for various subfamilies of states. At large mode numbers one observes a smooth increase of the lift with the dimension of the state h; this increase appears to follow a ~ √h behavior similar to that found analytically in earlier computations for other classes of states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Manifestly causal in-in perturbation theory about the interacting vacuum

In-In perturbation theory is a vital tool for cosmology and nonequilibrium physics. Here, we reconcile an apparent conflict between two of its important aspects with particular relevance to De Sitter/inflationary contexts: (i) the need to slightly deform unitary time evolution with an iϵ prescription that projects the free (“Bunch-Davies”) vacuum onto the interacting vacuum and renders vertex integrals well-defined, and (ii) Weinberg’s “nested commutator” reformulation of in-in perturbation theory which makes manifest the constraints of causality within expectation values of local operators, assuming exact unitarity. We show that a modified iϵ prescription maintains the exact unitarity on which the derivation of (ii) rests, while nontrivially agreeing with (i) to all orders of perturbation theory.

79 ASTRONOMY AND ASTROPHYSICS↗

Dispersion formulas in QFTs, CFTs and holography

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n -points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Modular flow in JT gravity and entanglement wedge reconstruction

It has been shown in recent works that JT gravity with matter with two boundaries has a type II ∞ algebra on each side. As the bulk spacetime between the two boundaries fluctuates in quantum nature, we can only define the entanglement wedge for each side in a pure algebraic sense. As we take the semiclassical limit, we will have a fixed long wormhole spacetime for a generic partially entangled thermal state (PETS), which is prepared by inserting heavy operators on the Euclidean path integral. Under this limit, with appropriate assumptions of the matter theory, geometric notions of the causal wedge and entanglement wedge emerge in this background. In particular, the causal wedge is manifestly nested in the entanglement wedge. Different PETS are orthogonal to each other, and thus the Hilbert space has a direct sum structure over sub-Hilbert spaces labeled by different Euclidean geometries. The full algebra for both sides is decomposed accordingly. From the algebra viewpoint, the causal wedge is dual to an emergent type III 1 subalgebra, which is generated by boundary light operators. To reconstruct the entanglement wedge, we consider the modular flow in a generic PETS for each boundary. We show that the modular flow acts locally and is the boost transformation around the global RT surface in the semiclassical limit. It follows that we can extend the causal wedge algebra to a larger type III 1 algebra corresponding to the entanglement wedge. Within each sub-Hilbert space, the original type II ∞ reduces to type III 1 .

2D Gravity↗

Perturbation theory for the logarithm of a positive operator

In various contexts in mathematical physics, such as out-of-equilibrium physics and the asymptotic information theory of many-body quantum systems, one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the Tomita-Takesaki theory. Often, one encounters the situation where the operator under consideration, which we denote by ∆, can be related by a perturbative series to another operator ∆ 0 , whose logarithm is known. We set up a perturbation theory for the logarithm log ∆. It turns out that the terms in the series possess a remarkable algebraic structure, which enables us to write them in the form of nested commutators plus some “contact terms”.

97 MATHEMATICS AND COMPUTING↗

Evaluation of precipitation indices in suites of dynamically and statistically downscaled regional climate models over Florida

Abstract The present work evaluates historical precipitation and its indices defined by the Expert Team on Climate Change Detection and Indices (ETCCDI) in suites of dynamically and statistically downscaled regional climate models (RCMs) against NOAA’s Global Historical Climatology Network Daily (GHCN-Daily) dataset over Florida. The models examined here are: (1) nested RCMs involved in the North American CORDEX (NA-CORDEX) program, (2) variable resolution Community Earth System Models (VR-CESM), (3) Coupled Model Intercomparison Project phase 5 (CMIP5) models statistically downscaled using localized constructed analogs (LOCA) technique. To quantify observational uncertainty, three in situ-based (PRISM, Livneh, CPC) and three reanalysis (ERA5, MERRA2, NARR) datasets are also evaluated against the station data. The reanalyses and dynamically downscaled RCMs generally underestimate the magnitude of the monthly precipitation and the frequency of the extreme rainfall in summer. The models forced with CanESM2 miss the phase of the seasonality of extreme precipitation. All models and reanalyses severely underestimate both the mean and interannual variability of mean wet-day precipitation (SDII), consecutive dry days (CDD), and overestimate consecutive wet days (CWD). Metric analysis suggests large uncertainty across NA-CORDEX models. Both the LOCA and VR-CESM models perform better than the majority of models. Overall, RegCM4 and WRF models perform poorer than the median model performance. The performance uncertainty across models is comparable to that in the reanalyses. Specifically, NARR performs poorer than the median model performance in simulating the mean indices and MERRA2 performs worse than the majority of models in capturing the interannual variability of the indices.

54 ENVIRONMENTAL SCIENCES↗

MFNets: data efficient all-at-once learning of multifidelity surrogates as directed networks of information sources

We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained via gradient-based minimization of a nonlinear least squares objective. While the vast majority of state-of-the-art assumes hierarchical connections between information sources, our approach works with flexibly structured information sources that may not admit a strict hierarchy. The formulation has two advantages: (1) increased data efficiency due to parsimonious multifidelity networks that can be tailored to the application; and (2) no constraints on the training data—we can combine noisy, non-nested evaluations of the information sources. Finally, numerical examples ranging from synthetic to physics-based computational mechanics simulations indicate the error in our approach can be orders-of-magnitude smaller, particularly in the low-data regime, than single-fidelity and hierarchical multifidelity approaches.

97 MATHEMATICS AND COMPUTING↗

Comparison of Observations and Predictions of Daytime Planetary-Boundary-Layer Heights and Surface Meteorological Variables in the Columbia River Gorge and Basin During the Second Wind Forecast Improvement Project

The second Wind Forecast Improvement Project (WFIP2) is an 18-month field campaign in the Pacific Northwest U.S.A., whose goal is to improve the accuracy of numerical-weather-prediction forecasts in complex terrain. The WFIP2 campaign involved the deployment of a large suite of in situ and remote sensing instrumentation, including eight 915-MHz wind-profiling radars, and surface meteorological stations. The evolution and annual variability of the daytime convective planetary-boundary-layer (PBL) height is investigated using the wind-profiling radars. Three models with different horizontal grid spacing are evaluated: the Rapid Refresh, the High-Resolution Rapid Refresh, and its nested version. The results are used to assess errors in the prediction of PBL height within the experimental and control versions of the models, with the experimental versions including changes and additions to the model parametrizations developed during the field campaign, and the control version using the parametrizations present in the National Oceanic and Atmospheric Administration/National Centers for Environmental Prediction operational version of the models at the start of the project. Results show that the high-resolution models outperform the low-resolution versions, the experimental versions perform better compared with the control versions, model PBL height estimations are more accurate on cloud-free days, and model estimates of the PBL height growth rate are more accurate than model estimates of the rate of decay. Finally, using surface sensors, we assess surface meteorological variables, finding improved surface irradiance and, to a lesser extent, improved 2-m temperature in the experimental version of the model.

54 ENVIRONMENTAL SCIENCES↗

Fundamental complement of a gravitating region

Any gravitating region a in any spacetime gives rise to a generalized entanglement wedge, the hologram e(a). Holograms exhibit properties expected of fundamental operator algebras, such as strong subadditivity, nesting, and no-cloning. But the entanglement wedge EW of an AdS boundary region B with commutant $\overline{B}$ satisfies an additional condition, complementarity: EW (B) is the spacelike complement of EW ($\overline{B}$) in the bulk. Here we identify an analogue of the boundary commutant $\overline{B}$ in general spacetimes: given a gravitating region a, its fundamental complement is the smallest wedge that contains all infinite world lines contained in the spacelike complement a' of a. We refine the definition of e(a) by requiring that it be spacelike to $\tilde{a}$. We prove that e(a) is the spacelike complement of e($\tilde{a}$) when the latter is computed in a'. We exhibit many examples of and of e(a) in de Sitter, flat, and cosmological spacetimes. Here, we find that a Big Bang cosmology (spatially closed or not) is trivially reconstructible: the whole universe is the entanglement wedge of any wedge inside it. But de Sitter space is not trivially reconstructible, despite being closed. We recover the AdS/CFT prescription by proving that EW (B) = e(causal wedge of B).

Bousso, Raphael [University of California, Berkele↗

Potential reductions in fine particulate matter and premature mortality following implementation of air pollution controls on coal-fired power plants in India

Coal-fired power plants (CFPPs) account for > 70% of electricity generation in India, but < 5% of facilities have installed technologies for sulfur dioxide (SO 2 ) and nitrogen oxide (NO X ) removal. Emissions of these pollutants lead to the formation of fine particulate matter (PM 2.5 ) and an increased risk of premature mortality for exposed populations. Here, we use a nested version of the GEOS-Chem global chemical transport model (0.5° × 0.625° resolution) for India to estimate reductions in PM 2.5 concentrations that could have been achieved by implementing existing emission control technologies like flue-gas desulfurization (FGD) and/or selective catalytic reduction (SCR). We quantify the associated burden of disease using the integrated exposure response (IER) and global exposure mortality model (GEMM) functions and compare the costs of premature mortality to those for FGD installation. Model simulations for 2010 suggest installation of FGD would have reduced mean annual PM 2.5 concentrations across India by 8%, compared to 3% with SCR installation, and 11% with both FGD and SCR. A 7–28% reduction in PM 2.5 was simulated for local communities closest to CFPPs (same model grid cell), leading to up to 17% reduction in annual premature mortality. Overall, more than 0.21–0.48 million premature deaths would have been avoided over a 10-year period if FGD had been implemented on all CFPPs, compared to 0.09–0.21 million with SCR and 0.22–0.72 million with both FGD and SCR. Benefits associated with such actions are approximately $\$18.1$–$\$604$ billion USD per year, which is equivalent to ~ 0.44 to 10% of India’s GDP. These results suggest that monetary benefits from avoided premature mortality far outweigh the capital and operational costs of FGD and/or SCR installation of $\$19.5$ billion and/or $\$32.8$ billion per year, respectively. This information is essential because the high costs of installation and operation are often given as reasons for delaying installation and commissioning. Finally, we conclude that policy actions to control air pollution from CFPPs are economically justifiable.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Graph-Based Modeling and Decomposition of Hierarchical Optimization Problems

We present a graph-theoretic modeling approach for hierarchical optimization that leverages the OptiGraph abstraction implemented in the Julia package Plasmo.jl. We show that the abstraction is flexible and can effectively capture complex hierarchical connectivity that arises from decision-making over multiple spatial and temporal scales (e.g., integration of planning, scheduling, and operations in manufacturing and infrastructures). We also show that the graph abstraction facilitates the conceptualization and implementation of decomposition and approximation schemes. Specifically, we propose a graph-based Benders decomposition (gBD) framework that enables the exploitation of hierarchical (nested) structures and that uses graph aggregation/partitioning procedures to discover such structures. In addition, we provide a Julia implementation of gBD, which we call PlasmoBenders.jl. We illustrate the capabilities using examples arising in the context of energy and power systems.

97 MATHEMATICS AND COMPUTING↗

Native bee Pollination Ecosystem Services in Agricultural Wetlands and Riparian Protected Lands

Abstract Many freshwater wetlands and riparian systems are protected within agricultural landscapes. Yet, pollinator ecosystem services are seldom considered key ecosystem services provided by these conservation easements. The purpose of this study is to explore the extent of protected aquatic lands to provide pollination ecosystem services by assessing pollinator abundances, crop yield changes, and value estimations of increased soybean yields from a subset of common native solitary bees. We created a novel geodatabase of United States Department of Agriculture (USDA) conservation easements and used this database in the InVEST crop pollination model to model wild solitary bee pollination. We then estimated the monetary value of yield increases provided by pollinators. We found that wetland uplands provided the greatest potential for pollination services for ground nesting bees, followed by herbaceous and forested riparian respectively. Stem nesters preferred forested riparian, then upland habitats. In soybeans fields, we found wild pollinators can provide up to 5.5% yield response from current private aquatic conservation lands. The current landscape is not optimized to use wetlands and riparian conservation lands as pollinator habitat, but these results suggest protected aquatic lands can sustainably increase wild pollination services to agricultural crops if landscapes are managed, protected, and optimized with pollinator services as co-benefit.

Hinson, Audra L. (ORCID:0000000242314820)↗

Topographic Controls on the Distribution of Summer Monsoon Precipitation over South Asia

In this work, we use a high-resolution (9 km) one-way nested regional climate modeling framework to systematically evaluate individual and aggregate roles of various components of topography in the precipitation distribution during South Asian Summer Monsoon (SASM). While it is not the arrival but the north-northwestward extent of summer monsoon precipitation that is regulated by the presence of elevated surfaces in South Asia, both the thermal and mechanical topographic forcing play a role. Topography not only provides mechanical uplifting and prevents dry air entrainment, it also helps regulate the strength of upper level anticyclone and tropical easterly jet, all of which are necessary to sustain a conducive environment for monsoon precipitation in the South Asian summer. In turn, precipitation feedbacks positively by accelerating the tropospheric diabatic warming through atmospheric latent heating and by maintaining the moisture supply through local recycling. Modifications in the topography, particularly the removal of the Tibetan Plateau, substantially modulates the moist flow in the lower troposphere and the anticyclonic circulation in the upper troposphere to an extent that the northern branch of SASM becomes substantially weaker. These changes give way to negative precipitation anomalies and eventually to an environment where the cycle of feedbacks that runs the process of monsoon progression over land becomes inefficient. The design of topographic modification experiments can influence precipitation response; therefore, we advise caution in the interpretation of these and previously reported results.

54 ENVIRONMENTAL SCIENCES↗

The hierarchical energy landscape of screw dislocation motion in refractory high-entropy alloys

High-entropy alloys (HEAs) with concentrated solid solutions are conceived to possess a rugged atomic and energy landscape in which dislocation motion necessarily proceeds to accommodate mechanical deformation. Fundamental questions remain as to how rough the energy landscape is and to what extent it can be influenced by the local ordering of their constituent elements. Here, we construct and report the potential energy landscape (PEL) governing screw dislocation motion in refractory HEAs that reveals a hierarchical and multilevel structure with a collection of small basins nested in large metabasin. This striking feature pertaining to HEAs exerts a trapping force and back stress on saddle point activations, retarding dislocation movement. Further, by introducing chemical short-range order, the energy landscape is smoothed but skewed to different degrees that shifts the rate-liming process from kink-glide to kink-pair nucleation. The chemical disorder-roughened PEL in HEAs, analogous to structural disorder induced in metallic glasses, signifies the role of various barrier-hopping processes underlying the extraordinary mechanical behaviors of the two distinct groups of materials.

36 MATERIALS SCIENCE↗

Incorporating geological structure into sensitivity analysis of subsurface contaminant transport

Simulating subsurface contaminant transport at the kilometer-scale often entails modeling reactive flow and transport within and through complex geologic structures. These structures are typically meshed by hand and as a result geologic structure is usually represented by one or a few deterministically generated geological models for uncertainty studies of flow and transport in the subsurface. Uncertainty in geologic structure can have a significant impact on contaminant transport. In this study, the impact of geologic structure on contaminant tracer transport in a shale formation is investigated for a simplified generic deep geologic repository for permanent disposal of spent nuclear fuel. An open-source modeling framework is used to perform a sensitivity analysis study on transport of two tracers from a generic spent nuclear fuel repository with uncertain location of the interfaces between the stratum of the geologic structure. The automated workflow uses sampled realizations of the geological structural model in addition to uncertain flow parameters in a nested sensitivity analysis. Concentration of the tracers at observation points within, in line with, and downstream of the repository are used as the quantities of interest for determining model sensitivity to input parameters and geological realization. Finally, the results of the study indicate that the location of strata interfaces in the geological structure has a first-order impact on tracer transport in the example shale formation, and that this impact may be greater than that of the uncertain flow parameters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp ( t H ) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. Here, we provide optimized decompositions up to order t 6 . The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n = 2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗