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Results for “Generalization Bounds”

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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Signaling and scrambling with strongly long-range interactions

Strongly long-range interacting quantum systems—those with interactions decaying as a power law 1/$r^α$ in the distance $\textit{r}$ on a $\textit{D}$-dimensional lattice for $\textit{α ≤ D}$—have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum-information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. In a step towards rectifying this problem, we prove two Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. In this work, our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for $\textit{α ≤ D/2}$. Our second bound pertains to generic long-range interacting spin Hamiltonians and gives a tight lower bound for the signaling time to extensive subsets of the system for all $\textit{α < D}$. This many-site signaling time lower bounds the scrambling time in strongly long-range interacting systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Magnetoanisotropic thermal transport in a topological Josephson junction

Highlights: • Thermal conductance is sensitive to orientation and magnitude of the exchange field. • The NDTC is exhibited and tuned by the magnitude of the exchange field. • The interplay of zero-energy ABSs and thermal transport has been well inferred. • Our findings can apply to the energy control in hybridized mesoscopic systems. The thermal transport in Joesphson junctions, particularly, based on topological insulators (TIs), has not been extensively studied so far. Herein, we theoretically investigate the magnetoanisotropic thermal transport in a TI-based Josephson hybrid structure with a ferromagnetic insulator sandwiched between two superconductors (SCs). It is shown that the thermal conductance and current both are considerably sensitive to the orientation and magnitude of the exchange field. In particular, the negative differential thermal conductance is exhibited, which is modulated by the exchange field. More interestingly, zero-energy Andreev bound states are confirmed with the help of the thermal conductance, which in turn demonstrates itself to be of significance in the thermal transport. It is expected that these findings could have potential applications for the energy control in various hybridized mesoscopic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Comparing approaches for introducing polycyclic aromatic hydrocarbons to Ge(001) to seed graphene nanoribbon synthesis by CH 4 chemical vapor deposition

Here, we evaluate two approaches for introducing polycyclic aromatic hydrocarbons (PAHs) to a graphene catalyst substrate as part of a two-step chemical vapor deposition (CVD) process for growing graphene nanoribbons (GNRs). In this process, PAHs first form graphene-like seeds on Ge, and then GNRs are subsequently evolved from these PAH-derived seeds via substrate-mediated anisotropic growth kinetics during the CVD of CH4. The first seeding approach sublimes controlled doses of PAH thin films into the CVD chamber, while the second delivers PAHs directly from the vapor phase at set concentrations. Using these two approaches, we measure the dependence of GNR density on PAH dose and compare the experimental results with predictions from a rate model of PAH diffusion, desorption, and clustering. We find that PAHs that more strongly adsorb to the catalyst surface (generally larger PAHs) desirably remain more individualized prior to GNR evolution whereas smaller, more weakly bound PAHs aggregate into larger clusters with various sizes on Ge that are undesirable for synthesizing more monodisperse GNRs. As a result, this work is important because it offers a framework that enables the rational selection and design of seed molecules, advancing anisotropic GNR CVD synthesis.

CVD↗
DOE OSTI2023

Infinite neural network quantum states: entanglement and training dynamics

We study infinite limits of neural network quantum states (∞-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For ∞-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an ∞-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. ∞-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

quantum state supervised learning↗
DOE OSTI2021

Dark energy survey year 1 results: Constraining baryonic physics in the Universe

ABSTRACT Measurements of large-scale structure are interpreted using theoretical predictions for the matter distribution, including potential impacts of baryonic physics. We constrain the feedback strength of baryons jointly with cosmology using weak lensing and galaxy clustering observables (3 × 2pt) of Dark Energy Survey (DES) Year 1 data in combination with external information from baryon acoustic oscillations (BAO) and Planck cosmic microwave background polarization. Our baryon modelling is informed by a set of hydrodynamical simulations that span a variety of baryon scenarios; we span this space via a Principal Component (PC) analysis of the summary statistics extracted from these simulations. We show that at the level of DES Y1 constraining power, one PC is sufficient to describe the variation of baryonic effects in the observables, and the first PC amplitude (Q1) generally reflects the strength of baryon feedback. With the upper limit of Q1 prior being bound by the Illustris feedback scenarios, we reach $\sim 20{{\ \rm per\ cent}}$ improvement in the constraint of $S_8=\sigma _8(\Omega _{\rm m}/0.3)^{0.5}=0.788^{+0.018}_{-0.021}$ compared to the original DES 3 × 2pt analysis. This gain is driven by the inclusion of small-scale cosmic shear information down to 2.5 arcmin, which was excluded in previous DES analyses that did not model baryonic physics. We obtain $S_8=0.781^{+0.014}_{-0.015}$ for the combined DES Y1+Planck EE+BAO analysis with a non-informative Q1 prior. In terms of the baryon constraints, we measure $Q_1=1.14^{+2.20}_{-2.80}$ for DES Y1 only and $Q_1=1.42^{+1.63}_{-1.48}$ for DESY1+Planck EE+BAO, allowing us to exclude one of the most extreme AGN feedback hydrodynamical scenario at more than 2σ.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Production of meson molecules in ultraperipheral heavy ion collisons

In this work we present a calculation of exotic charmonium production in ultraperipheral collisions, in which the exotic state is explicitly treated as a meson molecule. Our formalism is general, but we focus on the lightest possible exotic charmonium state: a 𝐷 + ⁢𝐷 − molecular bound state. It was proposed some time ago, and it has been an object of experimental searches. Here we study the production of the open charm pair in the process 𝛾⁢𝛾 → 𝐷 + ⁢𝐷 − . Then we use a prescription to project the free pair |𝐷 + ⁢𝐷 − ⟩ onto a bound state at the amplitude level and compute the cross section of the process 𝛾⁢𝛾 → 𝐵 (where 𝐵 is the bound state). Finally, we convolute this last cross section with the equivalent photon distributions coming from the projectile and target in an ultraperipheral collision and find the 𝐴⁢𝐴 → 𝐴⁢𝐴⁢𝐵 cross section, which, for 𝑃⁢𝑏 −𝑃⁢𝑏 collisions at $\sqrt{s_{NN}}$ =5.02 TeV, is of the order of 3 μ⁢b.

Sobrinho, F. C.↗
DOE OSTI2025

Warm and fuzzy dark matter: Free streaming of wave dark matter

Wave or fuzzy dark matter that is produced with relativistic wave numbers exhibits free-streaming effects analogous to warm or hot particle dark matter with relativistic momenta. Axions produced after inflation provide such a warm or mildly relativistic candidate, where the enhanced suppression and observational bounds are only moderately stronger than that from wave propagation of initially cold axions. More generally, the free-streaming damping also impacts isocurvature fluctuations from generation in causally disconnected patches. As coherent spatial fluctuations free stream away they leave incoherent and transient superpositions in their wakes. These multiple wave momentum streams are the wave analog of particle phase space fluctuations or directional collisionless damping of massive neutrinos or hot dark matter. The observable impact on both adiabatic and isocurvature fluctuations of fuzzy dark matter can differ from their cold dark matter counterparts due to free streaming depending on how warm or hot is their momentum distribution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Non-Gaussian Generalized Two-Mode Squeezing: Applications to Two-Ensemble Spin Squeezing and Beyond

Bosonic two-mode squeezed states are paradigmatic entangled Gaussian states that have wide utility in quantum information and metrology. Here, in this study, we show that the basic structure of these states can be generalized to arbitrary bipartite quantum systems in a manner that allows simultaneous, Heisenberg-limited estimation of two independent parameters for finite-dimensional systems. Further, we show that these general states can always be stabilized by a relatively simple Markovian dissipative process. In the specific case where the two subsystems are ensembles of two-level atoms or spins, our generalized states define a notion of two-mode spin squeezing that is valid beyond the Gaussian limit and that enables true multiparameter estimation. We discuss how generalized Ramsey measurements allow one to reach the two-parameter quantum Cramér-Rao bound, and how the dissipative preparation scheme is compatible with current experiments.

Mamaev, Mikhail [Univ. of Chicago, IL (United Stat↗
DOE OSTI2023

A Sequential Quadratic Programming Algorithm for Nonsmooth Problems with Upper- \({\boldsymbol{\mathcal{C}^2}}\) Objective

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objective functions is proposed and analyzed. Upper- \({\boldsymbol{\mathcal{C}^2}}\) is a weakly concave property that exists in difference of convex (DC) functions and arises naturally in many applications, particularly certain classes of solutions to parametric optimization problems e.g., recourse of stochastic programming and projection onto closed sets. The algorithm can be viewed as an extension of sequential quadratic programming (SQP) to nonsmooth problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objectives or a simplified bundle method. It is globally convergent with bounded algorithm parameters that are updated with a trust-region criterion. The algorithm handles general smooth constraints through linearization and uses a line search to ensure progress. The potential inconsistencies from the linearization of the constraints are addressed through a penalty method. In conclusion, the capabilities of the algorithm are demonstrated by solving both simple upper- \({\boldsymbol{\mathcal{C}^2}}\) problems and a real-world optimal power flow problem used in current power grid industry practices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Online Learning and Pricing for Service Systems with Reusable Resources

We consider a price-based revenue management problem with finite reusable resources over a finite time horizon T. Customers arrive following a price-dependent Poisson process, and each customer requests one unit of c homogeneous reusable resources. If there is an available unit, the customer gets served within a price-dependent exponentially distributed service time; otherwise, the customer waits in a queue until the next available unit. In this paper, we assume that the firm does not know how the arrival and service rates depend on posted prices, and thus it makes adaptive pricing decisions in each period based only on past observations to maximize the cumulative revenue. Given a discrete price set with cardinality P, we propose two online learning algorithms, termed batch upper confidence bound (BUCB) and batch Thompson sampling (BTS), and prove that the cumulative regret upper bound is O˜(√PT) , which matches the regret lower bound. In establishing the regret, we bound the transient system performance upon price changes via a novel coupling argument, and also generalize bandits to accommodate subexponential rewards. Here, we also extend our approach to models with balking and reneging customers and discuss a continuous price setting. Our numerical experiments demonstrate the efficacy of the proposed BUCB and BTS algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Optimal resource allocation for flexible-grid entanglement distribution networks

We use a genetic algorithm (GA) as a design aid for determining the optimal provisioning of entangled photon spectrum in flex-grid quantum networks with arbitrary numbers of channels and users. After introducing a general model for entanglement distribution based on frequency-polarization hyperentangled biphotons, we derive upper bounds on fidelity and entangled bit rate for networks comprising one-to-one user connections. Simple conditions based on user detector quality and link efficiencies are found that determine whether entanglement is possible. We successfully apply a GA to find optimal resource allocations in four different representative network scenarios and validate features of our model experimentally in a quantum local area network in deployed fiber. Our results show promise for the rapid design of large-scale entanglement distribution networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement

This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm bounds for finite element and graph-based discretizations of Matérn-type priors and deconvolution forward models. For linear-Gaussian inverse problems, we develop a general theory to characterize the error in the approximation to the posterior. We also embed the computational framework into ensemble Kalman methods and MAP estimators for nonlinear inverse problems. Furthermore, our operator-norm bounds for prior discretizations guarantee the scalability and accuracy of these algorithms under mesh refinement.

Bayesian inverse problem↗
DOE OSTI2023

Analytic continuation of the relativistic three-particle scattering amplitudes

We investigate the relativistic scattering of three identical scalar bosons interacting via pair-wise interactions. Extending techniques from the nonrelativistic three-body scattering theory, we provide a detailed and general prescription for solving and analytically continuing integral equations describing the three-body reactions. We use these techniques to study a system with zero angular momenta described by a single scattering length leading to a bound state in a two-body subchannel. We obtain bound-state-particle and three-particle amplitudes in the previously unexplored kinematical regime; in particular, for real energies below elastic thresholds and complex energies in the physical and unphysical Riemann sheets. We extract positions of three-particle bound-states that agree with previous finite-volume studies, providing further evidence for the consistency of the relativistic finite-volume three-body quantization conditions. We also determine previously unobserved virtual bound states in this theory. Lastly, we find numerical evidence of the breakdown of the two-body finite-volume formalism in the vicinity of the left-hand cuts and argue for the generalization of the existing formalism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Spent Nuclear Fuel Mechanical Loads in the General Package Drop Scenario

The US Department of Energy Spent Fuel and Waste Science and Technology program is performing research to determine the mechanical loading conditions applied to spent nuclear fuel (SNF) during normal conditions of transportation to inform mechanical tests of SNF and close an important knowledge gap related to the practical disposition of SNF in the US. A recent multi-national collaborative test campaign measured SNF assembly impact response to the 30 cm horizontal package drop scenario, which is a common regulatory basis test of SNF package design. Researchers at Pacific Northwest National Laboratory (PNNL) are using the test data to validate explicit finite element models to calculate the mechanical loads and structural response of spent nuclear fuel assemblies in the as-tested 30 cm horizontal package drop scenario. Once the as-tested package drop model is validated, the next step is to apply the model to the general 30 cm drop scenario, which includes all impact angles, all fuel assembly types, and all burnup conditions. PNNL is developing a damage model that will incorporate the results of finite element parametric studies to establish trends in SNF mechanical loading to various input parameters, like impact orientation and burnup. The damage model will have the capability to estimate mechanical loads for any single set of input parameters, but it will first be used to describe the upper bounds of potential SNF loading in the 30 cm drop scenario. This paper describes PNNL’s progress toward developing the general solution to the problem of spent nuclear fuel mechanical loads in the 30 cm package drop scenario and it describes the next steps in closing the knowledge gap.

Klymyshyn, Nicholas A.↗
DOE OSTI2021

A Rényi quantum null energy condition: proof for free field theories

The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory that has been proved quite generally. It can equivalently be phrased as a positivity condition on the second null shape derivative of the relative entropy S rel (ρ||σ) of an arbitrary state ρ with respect to the vacuum σ. The relative entropy has a natural one-parameter family generalization, the Sandwiched Rényi divergence S n (ρ||σ), which also measures the distinguishability of two states for arbitrary n &isin; [1/2, ∞). A Rényi QNEC, a positivity condition on the second null shape derivative of S n (ρ||σ), was conjectured in previous work. In this work, we study the Rényi QNEC for free and superrenormalizable field theories in spacetime dimension d > 2 using the technique of null quantization. In the above setting, we prove the Rényi QNEC in the case n > 1 for arbitrary states. We also provide counterexamples to the Rényi QNEC for n < 1.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Phase transitions from the fifth dimension

We study the cosmological transition of 5D warped compactifications, from the high-temperature black-brane phase to the low-temperature Randall-Sundrum I phase. The transition proceeds via percolation of bubbles of IR-brane nucleating from the black-brane horizon. The violent bubble dynamics can be a powerful source of observable stochastic gravitational waves. While bubble nucleation is non-perturbative in 5D gravity, it is amenable to semiclassical treatment in terms of a “bounce” configuration interpolating between the two phases. We demonstrate how such a bounce configuration can be smooth enough to maintain 5D effective field theory control, and how a simple ansatz for it places a rigorous lower-bound on the transition rate in the thin-wall regime, and gives plausible estimates more generally. When applied to the Hierarchy Problem, the minimal Goldberger-Wise stabilization of the warped throat leads to a slow transition with significant supercooling. We demonstrate that a simple generalization of the Goldberger-Wise potential modifies the IR-brane dynamics so that the transition completes more promptly. Supercooling determines the dilution of any (dark) matter abundances generated before the transition, potentially at odds with data, while the prompter transition resolves such tensions. We discuss the impact of the different possibilities on the strength of the gravitational wave signals. Via AdS/CFT duality the warped transition gives a theoretically tractable holographic description of the 4D Composite Higgs (de)confinement transition. Our generalization of the Goldberger-Wise mechanism is dual to, and concretely models, our earlier proposal in which the composite dynamics is governed by separate UV and IR RG fixed points. The smooth 5D bounce configuration we introduce complements the 4D dilaton/radion dominance derivation presented in our earlier work.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

The Markov gap for geometric reflected entropy

The reflected entropy S R (A : B) of a density matrix ρ AB is a bipartite correlation measure lower-bounded by the quantum mutual information I(A : B). In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-N 2 gap between S R and I. We provide an information-theoretic interpretation of this gap by observing that S R - I is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity S R - I the Markov gap. We then prove that for time-symmetric states in pure AdS 3 gravity, the Markov gap is universally lower bounded by log(2)ℓ AdS /2G N times the number of endpoints of the cross-section. We provide evidence that this lower bound continues to hold in the presence of bulk matter, and comment on how it might generalize above three bulk dimensions. Finally, we explore the Markov recovery problem controlling S R - I using fixed area states. This analysis involves deriving a formula for the quantum fidelity — in fact, for all the sandwiched Rényi relative entropies — between fixed area states with one versus two fixed areas, which may be of independent interest. We discuss, throughout the paper, connections to the general theory of multipartite entanglement in holography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Ultrafast Relaxations in Ruthenium Polypyridyl Chromophores Determined by Stochastic Kinetics Simulations

Maximizing the efficiency of solar energy conversion using dye assemblies rests on understanding where the energy goes following absorption. Transient spectroscopies in solution are useful for this purpose, and the time-resolved data are usually analyzed with a sum of exponentials. This treatment assumes that dynamic events are well separated in time, and that the resulting exponential prefactors and phenomenological lifetimes are related directly to primary physical values. Such assumptions break down for coincident absorption, emission, and excited state relaxation that occur in transient absorption and photoluminescence of tris(2,2'-bipyridine)ruthenium(2+) derivatives, confounding the physical meaning of the reported lifetimes. Here, we use inductive modeling and stochastic chemical kinetics to develop a detailed description of the primary ultrafast photophysics in transient spectroscopies of a series of Ru dyes, as an alternative to sums of exponential analysis. Commonly invoked three-level schemes involving absorption, intersystem crossing (ISC), and slow nonradiative relaxation and incoherent emission to the ground state cannot reproduce the experimentally measured spectra. The kinetics simulations reveal that ultrafast decay from the singlet excited state manifold to the ground state competes with ISC to the triplet excited state, whose efficiency was determined to be less than unity. The populations predicted by the simulations are used to estimate the magnitudes of transition dipoles for excited state excitations and evaluate the influence of specific ligands. The mechanistic framework and methodology presented here are entirely general, applicable to other dye classes, and can be extended to include charge injection by molecules bound to semiconductor surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗