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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Qubit-efficient entanglement spectroscopy using qubit resets

One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable before noise dominates. Here, we develop qubit-efficient quantum algorithms for entanglement spectroscopy which avoid this tradeoff. In particular, we develop algorithms for computing the trace of the n -th power of the density operator of a quantum system, T r ( ρ n ) , (related to the Rényi entropy of order n ) that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices. Our algorithms, which require a number of qubits independent of n , are variants of previous algorithms with width proportional to n , an asymptotic difference. The crucial ingredient in these new algorithms is the ability to measure and reinitialize subsets of qubits in the course of the computation, allowing us to reuse qubits and increase the circuit depth without suffering the usual noisy consequences. We also introduce the notion of effective circuit depth as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. We perform numerical simulations to compare our algorithms to the original variants and show they perform similarly when subjected to noise. Additionally, we experimentally implement one of our qubit-efficient algorithms on the Honeywell System Model H0, estimating T r ( ρ n ) for larger n than possible with previous algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2011

Effects of Nose Bluntness on Hypersonic Boundary-Layer Receptivity and Stability Over Cones

The receptivity to freestream acoustic disturbances and the stability properties of hypersonic boundary layers are numerically investigated for boundary-layer flows over a 5 straight cone at a freestream Mach number of 6.0. To compute the shock and the interaction of the shock with the instability waves, the Navier-Stokes equations in axisymmetric coordinates were solved. In the governing equations, inviscid and viscous flux vectors are discretized using a fifth-order accurate weighted-essentially-non-oscillatory scheme. A third-order accurate total-variation-diminishing Runge-Kutta scheme is employed for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. The appearance of instability waves near the nose region and the receptivity of the boundary layer with respect to slow mode acoustic waves are investigated. Computations confirm the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary-layer transition. The current solutions, compared with experimental observations and other computational results, exhibit good agreement.

Kara, Kursat↗
DOE OSTI2023

Fluid dynamic and thermal performance of a slotted cylinder at low Reynolds number

The fluid dynamic and thermal performance of a circular cylinder with a slot parallel to the flow is numerically investigated. The study utilized the semi-implicit finite volume multi-material algorithm MPM-ICE, a component of the Uintah framework. The normalized slot width s/D ranges from 0.1 - 0.3, introducing an additional heat transfer surface area between ~ 10 and ~ 50%, and a mass reduction between ~ 13 and ~ 38% in the cylinder. We assumed two-dimensional incompressible flow and simulated a Reynolds number Re D between 100 and 1000. The slotted cylinders are found to have a total drag force reduction up to ~ 45%, compared to a solid cylinder despite the additional viscous drag force in the slot. Convection heat transfer is enhanced up to ~ 70%. Further, the slotted cylinder performance index, defined as the ratio of the heat rate to the drag force, increases up to maximum of ~ 3, indicating better overall thermal fluid performance. An entropy analysis showed the best performance index occurs at the highest Re D . Correlations for drag coefficient and Nusselt number are proposed along with an entropy optimization method.

42 ENGINEERING↗
NASA NTRS2003

Turbulence in Supercritical O2/H2 and C7H16/N2 Mixing Layers

This report presents a study of numerical simulations of mixing layers developing between opposing flows of paired fluids under supercritical conditions, the purpose of the study being to elucidate chemical-species-specific aspects of turbulence. The simulations were performed for two different fluid pairs O2/H2 and C7H16/N2 at similar reduced initial pressures (reduced pressure is defined as pressure divided by critical pressure). Thermodynamically, O2/H2 behaves more nearly like an ideal mixture and has greater solubility, relative to C7H16/N2, which departs strongly from ideality. Because of a specified smaller initial density stratification, the C7H16/N2 layers exhibited greater levels of growth, global molecular mixing, and turbulence. However, smaller density gradients at the transitional state for the O2/H2 system were interpreted as indicating that locally, this system exhibits enhanced mixing as a consequence of its greater solubility and closer approach to ideality. These thermodynamic features were shown to affect entropy dissipation, which was found to be larger for O2/H2 and concentrated in high-density-gradient-magnitude regions that are distortions of the initial density-stratification boundary. In C7H16/N2, the regions of largest dissipation were found to lie in high-density-gradient-magnitude regions that result from mixing of the two fluids.

Bellan, Josette↗
NASA NTRS2002

Aspects of Supercritical Turbulence: Direct Numerical Simulation of O2/H2 and C7H16/N2 Temporal Mixing Layers

Results from Direct Numerical Simulations of temporal, supercritical mixing layers for two species systems are analyzed to elucidate species-specific turbulence aspects. The two species systems, O2/H2 and C7HG16/N2, have different thermodynamic characteristics; thus, although the simulations are performed at similar reduced pressure (ratio of the pressure to the critical pressure), the former system is dose to mixture ideality and has a relatively high solubility with respect to the latter, which exhibits strong departures from mixture ideality Due to the specified, smaller initial density stratification, the C7H16/N2 layers display higher growth and increased global molecular mixing as well as larger turbulence levels. However, smaller density gradients at the transitional state for the O2/H2 system indicate that on a local basis, the layer exhibits an enhanced mixing, this being attributed to the increased solubility and to mixture ideality. These thermodynamic features are shown to affect the irreversible entropy production (i.e. the dissipation), which is larger for the O2/H2 layer and is primarily concentrated in high density-gradient magnitude regions that are distortions of the initial density stratification boundary. In contrast, the regions of largest dissipation in the C7H16/N2 layer are located in high density-gradient magnitude regions resulting from the mixing of the two fluids.

Bellan, J.↗
NASA NTRS2004

Application of Simulated Annealing and Related Algorithms to TWTA Design

Simulated Annealing (SA) is a stochastic optimization algorithm used to search for global minima in complex design surfaces where exhaustive searches are not computationally feasible. The algorithm is derived by simulating the annealing process, whereby a solid is heated to a liquid state and then cooled slowly to reach thermodynamic equilibrium at each temperature. The idea is that atoms in the solid continually bond and re-bond at various quantum energy levels, and with sufficient cooling time they will rearrange at the minimum energy state to form a perfect crystal. The distribution of energy levels is given by the Boltzmann distribution: as temperature drops, the probability of the presence of high-energy bonds decreases. In searching for an optimal design, local minima and discontinuities are often present in a design surface. SA presents a distinct advantage over other optimization algorithms in its ability to escape from these local minima. Just as high-energy atomic configurations are visited in the actual annealing process in order to eventually reach the minimum energy state, in SA highly non-optimal configurations are visited in order to find otherwise inaccessible global minima. The SA algorithm produces a Markov chain of points in the design space at each temperature, with a monotonically decreasing temperature. A random point is started upon, and the objective function is evaluated at that point. A stochastic perturbation is then made to the parameters of the point to arrive at a proposed new point in the design space, at which the objection function is evaluated as well. If the change in objective function values (Delta)E is negative, the proposed new point is accepted. If (Delta)E is positive, the proposed new point is accepted according to the Metropolis criterion: rho((Delta)f) = exp((-Delta)E/T), where T is the temperature for the current Markov chain. The process then repeats for the remainder of the Markov chain, after which the temperature is decremented and the process repeats. Eventually (and hopefully), a near-globally optimal solution is attained as T approaches zero. Several exciting variants of SA have recently emerged, including Discrete-State Simulated Annealing (DSSA) and Simulated Tempering (ST). The DSSA algorithm takes the thermodynamic analogy one step further by categorizing objective function evaluations into discrete states. In doing so, many of the case-specific problems associated with fine-tuning the SA algorithm can be avoided; for example, theoretical approximations for the initial and final temperature can be derived independently of the case. In this manner, DSSA provides a scheme that is more robust with respect to widely differing design surfaces. ST differs from SA in that the temperature T becomes an additional random variable in the optimization. The system is also kept in equilibrium as the temperature changes, as opposed to the system being driven out of equilibrium as temperature changes in SA. ST is designed to overcome obstacles in design surfaces where numerous local minima are separated by high barriers. These algorithms are incorporated into the optimal design of the traveling-wave tube amplifier (TWTA). The area under scrutiny is the collector, in which it would be ideal to use negative potential to decelerate the spent electron beam to zero kinetic energy just as it reaches the collector surface. In reality this is not plausible due to a number of physical limitations, including repulsion and differing levels of kinetic energy among individual electrons. Instead, the collector is designed with multiple stages depressed below ground potential. The design of this multiple-stage collector is the optimization problem of interest. One remaining problem in SA and DSSA is the difficulty in determining when equilibrium has been reached so that the current Markov chain can be terminated. It has been suggested in recent literature that simulating the thermodynamic properties opecific heat, entropy, and internal energy from the Boltzmann distribution can provide good indicators of having reached equilibrium at a certain temperature. These properties are tested for their efficacy and implemented in SA and DSSA code with respect to TWTA collector optimization.

Radke, Eric M.↗
NASA NTRS1994

Equilibrium, stability, and orbital evolution of close binary systems

We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We consider both synchronized and nonsynchronized systems, constructing the compressible generalizations of the classical Darwin and Darwin-Riemann configurations. Our method can be applied to a wide variety of binary models where the stellar masses, radii, spins, entropies, and polytropic indices are all allowed to vary over wide ranges and independently for each component. We find that both secular and dynamical instabilities can develop before a Roche limit or contact is reached along a sequence of models with decreasing binary separation. High incompressibility always makes a given binary system more susceptible to these instabilities, but the dependence on the mass ratio is more complicated. As simple applications, we construct models of double degenerate systems and of low-mass main-sequence star binaries. We also discuss the orbital evoltuion of close binary systems under the combined influence of fluid viscosity and secular angular momentum losses from processes like gravitational radiation. We show that the existence of global fluid instabilities can have a profound effect on the terminal evolution of coalescing binaries. The validity of our analytic solutions is examined by means of detailed comparisons with the results of recent numerical fluid calculations in three dimensions.

Lai, Dong↗
DOE OSTI2020

Unveiling the Finite Temperature Physics of Hydrogen Chains via Auxiliary Field Quantum Monte Carlo

The ability to accurately predict the finite temperature properties and phase diagrams of realistic quantum solids is central to uncovering new phases and engineering materials with novel properties ripe for device applications. Nonetheless, there remain comparatively few many-body techniques capable of elucidating the finite temperature physics of solids from first principles. Here, we take a significant step toward developing such a technique by generalizing our previous, exact fully ab initio finite temperature Auxiliary Field Quantum Monte Carlo (FT-AFQMC) method to model periodic solids and employing it to uncover the finite temperature physics of periodic hydrogen chains. Our chains’ unit cells consist of 10 hydrogen atoms modeled in a minimal basis, and we sample 5 k-points from the first Brillouin zone to arrive at a supercell consisting of 50 orbitals and 50 electrons. Based upon our calculations of these chains’ many-body energies, free energies, entropies, heat capacities, double and natural occupancies, and charge and spin correlation functions, we outline their metal–insulator and magnetic ordering as a function of both H–H bond distance and temperature. At low temperatures approaching the ground state, we observe both metal–insulator and ferromagnetic–antiferromagnetic crossovers at bond lengths between 0.5 and 0.75 Å. We then demonstrate how this low-temperature ordering evolves into a metallic phase with decreasing magnetic order at higher temperatures. In order to contextualize our results, we compare the features we observe to those previously seen in one-dimensional, half-filled Hubbard models at finite temperature and in ground state hydrogen chains. Interestingly, we identify signatures of the Pomeranchuk effect in hydrogen chains for the first time and show that spin and charge excitations that typically arise at distinct temperatures in the Hubbard model are indistinguishably coupled in these systems. Beyond qualitatively revealing the many-body phase behavior of hydrogen chains in a numerically exact manner without invoking the phaseless approximation, our efforts shed light on the further theoretical developments that will be required to construct the phase diagrams of the more complex transition metal, lanthanide, and actinide solids of longstanding interest to physicists.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Thermodynamics and magnetism in the two-dimensional to three-dimensional crossover of the Hubbard model

The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using the determinant quantum Monte Carlo method, a simple realization of anisotropy in the three-dimensional (3D) Hubbard model in which the tunneling between planes, $t_⊥$, is unequal to the intraplane tunneling $\textit{t}$. This model interpolates between the three-dimensional isotropic ($t_⊥ = t$) and two-dimensional (2D;$t_⊥$ = 0) systems. In this work, we show that at fixed interaction strength to tunneling ratio ($\textit{U/t}$), anisotropy can enhance the magnetic structure factor relative to both 2D and 3D results. However, this enhancement occurs at interaction strengths below those for which the Néel temperature $T_{\text{Néel}}$ is largest, in such a way that the structure factor cannot be made to exceed its value in isotropic 3D systems at the optimal $\textit{U/t}$. We characterize the 2D-3D crossover in terms of the magnetic structure factor, real space spin correlations, number of doubly occupied sites, and thermodynamic observables. An interesting implication of our results stems from the entropy's dependence on anisotropy. As the system evolves from 3D to 2D, the entropy at a fixed temperature increases. Correspondingly, at fixed entropy, the temperature will decrease going from 3D to 2D. This suggests a cooling protocol in which the dimensionality is adiabatically changed from 3D to 2D.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2005

Generalized Maximum Entropy

A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].

Cheeseman, Peter↗
NASA NTRS1993

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Godfrey, Andrew G.↗
DOE OSTI2025

An entropy-based debiasing approach to quantifying experimental coverage for novel applications of interest in the nuclear community

This manuscript proposes a novel information-theoretic approach to the quantification of experimental relevance, i.e., coverage, to achieve optimal data assimilation results for nuclear engineering applications. Specifically, this work posits the need for a new metric, called coverage (q C ) of an application’s quantity of interest, i.e., eigenvalue or power peaking for an advanced reactor concept, defined herein as the theoretically maximum achievable reduction in the quantity’s uncertainty given measurements from a pool of experiments in a manner that is independent of the data assimilation procedure employed. Currently, reduction in a quantity’s uncertainty is strongly biased by the underlying assumptions of the assimilation procedure to account for the under-determined nature of such problems and the similarity criterion employed to identify relevant experiments. To address this challenge, this work has developed a coverage metric, q C , based on mutual information, which establishes a new conceptual framework for assessing coverage, one that is independent of the model parameters and responses degree of variations in both the experimental and application domains, i.e., linear vs non-linear, and their prior uncertainty distributions, i.e., Gaussian vs. non-Gaussian. The q C is an entropic measure capable of addressing coverage for general nonlinear problems with non-Gaussian uncertainties and inclusive of the measurement uncertainties from multiple experiments. Numerical experiments from manufactured analytical problems as well as a set of benchmarks from the ICSBEP handbook are employed to demonstrate its theoretical and practical performance as compared to the c k -based experiment selection methodology, commonly employed in the neutronic community. The manuscript then employs other well-known adaptations to existing data assimilation methodologies for nonlinear and non-Gaussian problems capable of achieving the coverage posited by q C .

Bayesian data assimilation↗
NASA NTRS2007

A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.

Loh, Ching Y.↗
NASA NTRS1993

Effects of shock strength on shock turbulence interaction

Direct numerical simulation (DNS) and linear analysis (LIA) of isotropic turbulence interacting with a shock wave are performed for several upstream shock normal Mach numbers (M(sub 1)). Turbulence kinetic energy (TKE) is amplified across the shock wave, but this amplification tends to saturate beyond M(sub 1) = 3.0. TKE amplification and Reynolds stress anisotropy obtained in DNS are consistent with LIA predictions. Rapid evolution of TKE immediate downstream of the shock wave persists for all shock strengths and is attributed to the transfer between kinetic and potential modes of turbulence energy through acoustic fluctuations. Changes in energy spectra and various length scales across the shock wave are predicted by LIA, which is consistent with DNS results. Most turbulence length scales decrease across the shock. Dissipation length scale (rho-bar q(exp 3) / epsilon), however, increases slightly for shock waves with M(sub 1) less than 1.65. Fluctuations in thermodynamic variables behind the shock wave stay nearly isentropic for M(sub 1) less than 1.2 and deviate significantly from isentropy for the stronger shock waves due to large entropy fluctuation generated through the interaction.

Lee, Sangsan↗
NASA NTRS2004

Part 1 of a Computational Study of a Drop-Laden Mixing Layer

This first of three reports on a computational study of a drop-laden temporal mixing layer presents the results of direct numerical simulations (DNS) of well-resolved flow fields and the derivation of the large-eddy simulation (LES) equations that would govern the larger scales of a turbulent flow field. The mixing layer consisted of two counterflowing gas streams, one of which was initially laden with evaporating liquid drops. The gas phase was composed of two perfect gas species, the carrier gas and the vapor emanating from the drops, and was computed in an Eulerian reference frame, whereas each drop was tracked individually in a Lagrangian manner. The flow perturbations that were initially imposed on the layer caused mixing and eventual transition to turbulence. The DNS database obtained included transitional states for layers with various liquid mass loadings. For the DNS, the gas-phase equations were the compressible Navier-Stokes equations for conservation of momentum and additional conservation equations for total energy and species mass. These equations included source terms representing the effect of the drops on the mass, momentum, and energy of the gas phase. From the DNS equations, the expression for the irreversible entropy production (dissipation) was derived and used to determine the dissipation due to the source terms. The LES equations were derived by spatially filtering the DNS set and the magnitudes of the terms were computed at transitional states, leading to a hierarchy of terms to guide simplification of the LES equations. It was concluded that effort should be devoted to the accurate modeling of both the subgridscale fluxes and the filtered source terms, which were the dominant unclosed terms appearing in the LES equations.

Okong'o, Nora A.↗
DOE OSTI2020

Material coherence from trajectories via Burau eigenanalysis of braids

In this paper, we provide a numerical tool to study a material’s coherence from a set of 2D Lagrangian trajectories sampling a dynamical system, i.e., from the motion of passive tracers. We show that eigenvectors of the Burau representation of a topological braid derived from the trajectories have levelsets corresponding to components of the Nielsen–Thurston decomposition of the dynamical system. One can thus detect and identify clusters of space–time trajectories corresponding to coherent regions of the dynamical system by solving an eigenvalue problem. Unlike previous methods, the scalable computational complexity of our braid-based approach allows the analysis of large amounts of trajectories.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations

In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Large-d phase transitions in holographic mutual information

In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in G N in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large- d , we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large- d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, where analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above 5, our exact numerical results are well approximated analytically by working to next-to-leading order in the large- d expansion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗