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DOE OSTI2021

The Spiral Galaxies Flat Rotational Velocity Curve Explained by the Constant Group Velocity of a Nonlinear Density Wave

The rotation velocity curves of stars in galaxies, the motions of pairs of galaxies, and the behavior of galaxies in clusters and super-clusters all indicate that there is a lack of mass on different scales in the universe. In this paper, we derive the expression for rotational velocity using the nonlinear density wave theory considering only stellar components and we show that such theory can support the observed flat rotational velocity curve due to the main property of the soliton wave, which is a constant group velocity of the wave. The surface mass density (SMD) function, used to derive gravitational potential gradient and rotational velocity, is not assumed but rather derived as a solution of the nonlinear Srödinger equation, on the contrary to the widely used, in the literature, exponential disk approximation. Three parameters relevant to the curve shape are the intensities of equilibrium SMD, the amplitude of the wave, and total angular velocity or differential rotation, equivalently. Since the shape of the rotational velocity is highly sensitive to the mentioned parameters, this theory eventually provides a method for a very accurate estimation of galaxy mass and angular velocity as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

On the Cauchy problem for Boltzmann equation modeling a polyatomic gas

In the present article, we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the space homogeneous setting for the full non-linear case, under an extended Grad-type assumption on transition probability rates, which comprises hard potentials for both the relative speed and internal energy with the rate in the interval 0,2, multiplied by an integrable angular part and integrable partition functions. The Cauchy problem is resolved by means of an abstract ordinary differential equation (ODE) theory in Banach spaces for the initial data with finite and strictly positive gas mass and energy, finite momentum, and additionally finite K* polynomial moment, with K* depending on the rate of the transition probability and the structure of a polyatomic molecule or its internal degrees of freedom. Moreover, we prove that polynomially and exponentially weighted Banach space norms associated with the solution are both generated and propagated uniformly in time.

Physics↗

DOE OSTI2026

Magnus method for electronic structure calculations at extreme conditions

We present the application of Magnus based methods to the solution of first order coupled ordinary differential equations in High Energy Density (HED) physics applications. Our focus is on the application to quantum mechanical methods, specifically on the solution of the radial Dirac equation for real and complex energies. HED applications require accurate solutions across a wide range of spatial and energy domains, including regimes where the solutions exhibit pronounced oscillatory behavior. Such cases pose significant computational challenges. We demonstrate that Magnus-based integrators can efficiently and accurately address these challenges. We discuss the implementation of the Magnus method for the solution of the radial Dirac equation, including practical considerations such as the evaluation of matrix exponentials, numerical integration, error estimation, and adaptive step size control. We also discuss the application of these methods to complex energy Green’s function techniques and the efficient approximation of integrals of the solutions relevant to HED electronic structure calculations. Here, we demonstrate the accuracy and robustness of the resulting method in applications to the free-particle case, for which analytic solutions are available for comparison, as well as the challenging case of gold at HED conditions.

general physics↗

DOE OSTI2024

Analytic solutions of the DGLAP evolution and theoretical uncertainties

The energy dependence for the singlet sector of Parton Distributions Functions (PDFs) is described by an entangled pair of ordinary linear differential equations. Although there are no exact analytic solutions, it is possible to provide approximated results depending on the assumptions and the methodology adopted. These results differ in their sub-leading, neglected terms and ultimately they are associated with different treatments of the theoretical uncertainties. In this work, a novel analytic approach in Mellin space is presented and a new methodology for obtaining closed and exponentiated analytic solutions is devised. Different results for the DGLAP evolution at Next-Leading-Order are compared, discussing advantages and disadvantages for each solution. The generalizations to higher orders are addressed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Differentially Private Map Matching (DPMM) v1.0

Human mobility trajectories provide valuable information for developing mobility applications, as they contain diverse and rich information about the users. User mobility data is valuable for various applications such as intelligent transportation systems (ITS), commercial business models, and disease-spread models. However, such spatio-temporal traces may pose a threat to user privacy. GPS trajectories in their raw form are not suitable for transportation studies, as they require matching locations with nearest road links — a process called map-matching. This software implements a differential privacy (DP)-based map-matching algorithm, called DPMM, that generates link-level location trajectories in a privacy-preserving manner to protect users' origin destinations (OD) and travel paths. OD privacy is achieved by injecting Planar Laplace noise to the user OD GPS points. Travel-path privacy is provided with randomized travel path construction using exponential DP mechanism. The injected noise level is selected adaptively, by considering the link density of the location and the functional category of the localized links. For path privacy, our mechanism samples waypoints and selects candidate paths between waypoints. DPMM provides privacy effectively with respect to link density instead of other trajectory samples in the database compared to other privacy mechanisms. Compared to the different baseline models our DP-based privacy model offers closer query responses to the raw data in terms of individual and aggregate trajectory-level statistics with an average at absolute deviation from the baseline for individual statistics on ϵ = 1.0. Beyond individual trajectory statistics, the DPMM outperforms the other benchmark DP-based mechanisms on different aggregate statistics with up to 8x improvement in utility.

Peisert, Sean [Lawrence Berkeley National Laborato↗

DOE OSTI2026

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗

DOE OSTI2022

Quantum-inspired method for solving the Vlasov-Poisson equations

Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high-resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently, it has been proposed that matrix product state (MPS) methods, a quantum-inspired but classical algorithm, can be used to solve partial differential equations with exponential speed-up, provided that the solution can be compressed and efficiently represented as a MPS within some tolerable error threshold. Here, in this work, we explore the practicality of MPS methods for solving the Vlasov-Poisson equations for systems with one coordinate in space and one coordinate in velocity, and find that important features of linear and nonlinear dynamics, such as damping or growth rates and saturation amplitudes, can be captured while compressing the solution significantly. Furthermore, by comparing the performance of different mappings of the distribution functions onto the MPS, we develop an intuition of the MPS representation and its behavior in the context of solving the Vlasov-Poisson equations, which will be useful for extending these methods to higher-dimensional problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗

DOE OSTI2021

Strong coupling expansion of free energy and BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal models with fundamental hypermultiplets

As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625 ) of strong-coupling expansion of non-planar corrections in $ \mathcal{N} $ = 2 4d superconformal models we consider two special theories with gauge groups SU( N ) and Sp(2 N ). They contain N -independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding $ \mathcal{N} $ = 4 SYM theories. These $ \mathcal{N} $ = 2 theories can be realised on a system of N D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of AdS 5 × S 5 superstring. Starting with the localization matrix model representation for the $ \mathcal{N} $ = 2 partition function on S 4 we find exact differential relations between the 1 /N terms in the corresponding free energy F and the $ \frac{1}{2} $ -BPS Wilson loop expectation value $ \left\langle \mathcal{W}\right\rangle $ and also compute their large ’t Hooft coupling ( λ » 1) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable Sp(2 N ) case we find an exact resummed expression for the leading strong coupling terms at each order in the 1 /N expansion. We also determine the exponentially suppressed at large λ contributions to the non-planar corrections to F and $ \left\langle \mathcal{W}\right\rangle $ and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.

1/N expansion↗

DOE OSTI2023

Challenging the Curse of Dimensionality in Multidimensional Numerical Integration by Using a Low-Rank Tensor-Train Format

Numerical integration is a basic step in the implementation of more complex numerical algorithms suitable, for example, to solve ordinary and partial differential equations. The straightforward extension of a one-dimensional integration rule to a multidimensional grid by the tensor product of the spatial directions is deemed to be practically infeasible beyond a relatively small number of dimensions, e.g., three or four. In fact, the computational burden in terms of storage and floating point operations scales exponentially with the number of dimensions. This phenomenon is known as the curse of dimensionality and motivated the development of alternative methods such as the Monte Carlo method. The tensor product approach can be very effective for high-dimensional numerical integration if we can resort to an accurate low-rank tensor-train representation of the integrand function. In this work, we discuss this approach and present numerical evidence showing that it is very competitive with the Monte Carlo method in terms of accuracy and computational costs up to several hundredths of dimensions if the integrand function is regular enough and a sufficiently accurate low-rank approximation is available.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection–reaction equation

In this article, we present a general methodology to combine the Discontinuous Petrov–Galerkin (DPG) method in space and time in the context of methods of lines for transient advection–reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). Further, we also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection–reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

42 ENGINEERING↗

DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation

In this article, we present a general methodology to combine the Discontinuous PetrovGalerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). We also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection-reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Linear-depth quantum circuits for loading Fourier approximations of arbitrary functions

Abstract The ability to efficiently load functions on quantum computers with high fidelity is essential for many quantum algorithms, including those for solving partial differential equations and Monte Carlo estimation. In this work, we introduce the Fourier series loader (FSL) method for preparing quantum states that exactly encode multi-dimensional Fourier series using linear-depth quantum circuits. Specifically, the FSL method prepares a (Dn)-qubit state encoding the 2 Dn -point uniform discretization of aD-dimensional function specified by aD-dimensional Fourier series. A free parameter,m, which must be less thann, determines the number of Fourier coefficients, 2 D ( m + 1 ) , used to represent the function. The FSL method uses a quantum circuit of depth at most 2 ( n − 2 ) + ⌈ log 2 ( n − m ) ⌉ + 2 D ( m + 1 ) + 2 − 2 D ( m + 1 ) , which is linear in the number of Fourier coefficients, and linear in the number of qubits (Dn) despite the fact that the loaded function’s discretization is over exponentially many (2 Dn ) points. The FSL circuit consists of at most D n + 2 D ( m + 1 ) + 1 − 1 single-qubit and D n ( n + 1 ) / 2 + 2 D ( m + 1 ) + 1 − 3 D ( m + 1 ) − 2 two-qubit gates; we present a classical compilation algorithm with runtime O ( 2 3 D ( m + 1 ) ) to determine the FSL circuit for a given Fourier series. The FSL method allows for the highly accurate loading of complex-valued functions that are well-approximated by a Fourier series with finitely many terms. We report results from noiseless quantum circuit simulations, illustrating the capability of the FSL method to load various continuous 1D functions, and a discontinuous 1D function, on 20 qubits with infidelities of less than 10 −6 and 10 −3 , respectively. We also demonstrate the practicality of the FSL method for near-term quantum computers by presenting experiments performed on the Quantinuum H1-1 and H1-2 trapped-ion quantum computers: we loaded a complex-valued function on 3 qubits with a fidelity of over 95 % , as well as various 1D real-valued functions on up to 6 qubits with classical fidelities ≈99%, and a 2D function on 10 qubits with a classical fidelity ≈94%.

Physics↗

DOE OSTI2021

On the relation between active-region lifetimes and the autocorrelation function of light curves

ABSTRACT Rotational modulation of stellar light curves due to dark spots encloses information on spot properties and, thus, on magnetic activity. In particular, the decay of the autocorrelation function (ACF) of light curves is presumed to be linked to spot/active-region lifetimes, given that some coherence of the signal is expected throughout their lifetime. In the literature, an exponential decay has been adopted to describe the ACF. Here, we investigate the relation between the ACF and the active-region lifetimes. For this purpose, we produce artificial light curves of rotating spotted stars with different observation, stellar, and spot properties. We find that a linear decay and respective time-scale better represent the ACF than the exponential decay. We therefore adopt a linear decay. The spot/active-region time-scale inferred from the ACF is strongly restricted by the observation length of the light curves. For 1-yr light curves our results are consistent with no correlation between the inferred and the input time-scales. The ACF decay is also significantly affected by differential rotation and spot evolution: strong differential rotation and fast spot evolution contribute to a more severe underestimation of the active-region lifetimes. Nevertheless, in both circumstances the observed time-scale is still correlated with the input lifetimes. Therefore, our analysis suggests that the ACF decay can be used to obtain a lower limit of the active-region lifetimes for relatively long-term observations. However, strategies to avoid or flag targets with fast active-region evolution or displaying stable beating patterns associated with differential rotation should be employed.

Santos, A. R. G. (ORCID:0000000171956542)↗

DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Predictor-corrector models for lightweight massive machine-type communications in Industry 4.0

Future Industry 4.0 scenarios are characterized by seamless integration between computational and physical processes. To achieve this objective, dense platforms made of small sensing nodes and other resource constraint devices are ubiquitously deployed. All these devices have a limited number of computational resources, just enough to perform the simple operation they are in charge of. The remaining operations are delegated to powerful gateways that manage sensing nodes, but resources are never unlimited, and as more and more devices are deployed on Industry 4.0 platforms, gateways present more problems to handle massive machine-type communications. Although the problems are diverse, those related to security are especially critical. To enable sensing nodes to establish secure communications, several semiconductor companies are currently promoting a new generation of devices based on Physical Unclonable Functions, whose usage grows every year in many real industrial scenarios. Those hardware devices do not consume any computational resource but force the gateway to keep large key-value catalogues for each individual node. In this context, memory usage is not scalable and processing delays increase exponentially with each new node on the platform. In this paper, we address this challenge through predictor-corrector models, representing the key-value catalogues. Models are mathematically complex, but we argue that they consume less computational resources than current approaches. The lightweight models are based on complex functions managed as Laurent series, cubic spline interpolations, and Boolean functions also developed as series. Unknown parameters in these models are predicted, and eventually corrected to calculate the output value for each given key. The initial parameters are based on the Kane Yee formula. An experimental analysis and a performance evaluation are provided in the experimental section, showing that the proposed approach causes a significant reduction in the resource consumption.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

RNAseq analysis of Cellvibrio japonicus during starch utilization differentiates between genes encoding carbohydrate active enzymes controlled by substrate detection or growth rate

ABSTRACT Bacterial utilization of starch is increasingly of interest as the importance and contributions of animal gut microbiomes become more defined. Consequently, identifying and characterizing the bacterial enzymes responsible for the degradation, transport, and metabolism of starch will enable developments in pharmaceutical, biotechnological, and culinary industries searching for novel prebiotics, carrier molecules, and low glycemic index sweeteners. The current challenge is that bacteria proficient at starch utilization often have hundreds of carbohydrate active enzymes, and it is unclear which are essential for starch utilization using only homology-based bioinformatics or computational methods. Complementary experimental data are also needed, especially to understand the regulation of bacterial starch utilization. We have completed an RNAseq analysis of the Gram-negative bacterium Cellvibrio japonicus and found that it has sophisticated regulation that includes substrate sensing and growth rate components for genes that encode starch-degrading enzymes. Among the 22 genes predicted to encode starch-active enzymes, C. japonicus has 10 alpha-amylases, 4 alpha-glucosidases, 2 pullulnases, and 2 cyclomaltodextrin glucanotransferases, 15 of which were up-regulated during exponential growth on starch and 8 up-regulated in stationary phase. Growth analyses with an enzyme secretion deficient mutant of C. japonicus suggested that secreted amylases are essential for this bacterium to degrade starch. Our approach of coupling a physiological growth assay with transcriptomic data provides a platform to identify targets for further genetic or biochemical analysis that can be broadly applied to other starch-utilizing bacteria. IMPORTANCE Understanding the bacterial metabolism of starch is important as this polysaccharide is a ubiquitous ingredient in foods, supplements, and medicines, all of which influence gut microbiome composition and health. Our RNAseq and growth data set provides a valuable resource to those who want to better understand the regulation of starch utilization in Gram-negative bacteria. These data are also useful as they provide an example of how to approach studying a starch-utilizing bacterium that has many putative amylases by coupling transcriptomic data with growth assays to overcome the potential challenges of functional redundancy. The RNAseq data can also be used as a part of larger meta-analyses to compare how C. japonicus regulates carbohydrate active enzymes, or how this bacterium compares to gut microbiome constituents in terms of starch utilization potential.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Twice upon a time: timelike-separated quantum extremal surfaces

The Python’s Lunch conjecture for the complexity of bulk reconstruction involves two types of nonminimal quantum extremal surfaces (QESs): bulges and throats, which differ by their local properties. The conjecture relies on the connection between bulk spatial geometry and quantum codes: a constricting geometry from bulge to throat encodes the bulk state nonisometrically, and so requires an exponentially complex Grover search to decode. However, thus far, the Python’s Lunch conjecture is only defined for spacetimes where all QESs are spacelike-separated from one another. Here we explicitly construct (time-reflection symmetric) spacetimes featuring both timelike-separated bulges and timelike-separated throats. Interestingly, all our examples also feature a third type of QES, locally resembling a de Sitter bifurcation surface, which we name a bounce. By analyzing the Hessian of generalized entropy at a QES, we argue that this classification into throats, bulges and bounces is exhaustive. We then propose an updated Python’s Lunch conjecture that can accommodate general timelike-separated QESs and bounces. Notably, our proposal suggests that the gravitational analogue of a tensor network is not necessarily the time-reflection symmetric slice, even when one exists.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗