Algebraic approach to the vibrational excitations in methane
We present a description of the vibrational excitations of methane by means of an algebraic analysis of a model of coupled anharmonic oscillators.
Lemus, Renato↗
SEARCH · Engineering Papers
Results for “excitation algebra”
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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Second Linear Response Theory and the Analytic Calculation of Excited-State Properties
We present a method based on second linear response time-dependent density func- tional theory (TDDFT) to calculate permanent and transition multipoles of excited states, which are required to compute excited-state absorption/emission spectra, multi- photon optical processes, among others. In previous work, we examined computations based on second linear response theory in which linear response TDDFT was employed twice. In contrast, the present methodology only requires information from a single linear response calculation to compute the excited-state properties. These are eval- uated analytically through various algebraic operations involving electron repulsion integrals and excitation vectors. The present derivation focuses on full many-body wave functions instead of single orbitals, as in our previous approach. Here, we test the proposed method by applying it to several diatomic and triatomic molecules. This shows that the computed excited-state dipoles are consistent with respect to reference equation-of-motion coupled cluster calculations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Electron-Molecule Col1isions: Quantitative Approaches, and the Legacy of Aaron Temkin
This article, on electron-molecule collisions, is dedicated to the legacy of my good friend and sometime collaborator, Aaron Temkin on his retirement from the NASA-Goddard Space Flight Center after many years of work at the highest intellectual level in the theoretical treatment of electron-atom and electron-molecule scattering. Aaron's contributions to the manner in which we think about electron-molecule collisions is clear to all of us who have worked in this field. I doubt that the great progress that has occurred in the computational treatment of such complex collision problems could have happened without these contributions. For a brief historical account, see the discussion of Temkin's contribution to electron-molecule scattering in the first article of this volume by Dr. A. K. Bhatia. In this article, I will concentrate on the application of the so called, non-adiabatic R-matrix theory, to vibrational excitation and dissociative attachment, although I will also present some results applying the Linear Algebraic and Kohn-Variational methods to vibrational excitation. As a starting point for almost all computationally effective approaches to electron-molecule collisions, is the fixed nuclei approximation. That is, one recognizes, just as one does with molecular bound states, that there is a separation of electronic(fast) and nuclear(s1ow) degrees of freedom. This separation makes it possible to "freeze" the nuclei in space, calculate the collision parameters for the frozen molecule and then, somehow to add back the vibrations and rotations. The manner in which this is done, depends on the details of the collision problem. It is the work of Aaron and a number of other researchers that has provided the guidance necessary to resolve these issues.
Schneider, B.I.↗
Two-fermion negativity and confinement in the Schwinger model
We consider the fermionic (logarithmic) negativity between two fermionic modes in the Schwinger model. Recent results pointed out that fermionic systems can exhibit stronger entanglement than bosonic systems, exhibiting a negativity that decays only algebraically. The Schwinger model is described by fermionic excitations at short distances, while its asymptotic spectrum is the one of a bosonic theory. We show that the two-mode negativity detects this confining, fermion-to-boson transition, shifting from an algebraic decay to an exponential decay at distances of the order of the de Broglie wavelength of the first excited state. We derive analytical expressions in the massless Schwinger model and confront them with tensor network simulations. We also perform tensor network simulations in the massive model, which is not solvable analytically, and close to the Ising quantum critical point of the Schwinger model, where we show that the negativity behaves as its bosonic counterpart. Published by the American Physical Society 2024
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Integrating subsystem embedding subalgebras and coupled cluster Green’s function: a theoretical foundation for quantum embedding in excitation manifold
Here, in this study, we introduce a novel approach to coupled-cluster Green's function (CCGF) embedding by seamlessly integrating conventional CCGF theory with the state-of-the-art sub-system embedding sub-algebras coupled cluster (SES-CC) formalism. This integration focuses primarily on delineating the characteristics of the sub-system and the corresponding segments of the Green's function, defined explicitly by active orbitals. Crucially, our work involves the adaptation of the SES-CC paradigm, addressing the left eigenvalue problem through a distinct form of Hamiltonian similarity transformation. This advancement not only facilitates a comprehensive representation of the interaction between the embedded sub-system and its surrounding environment but also paves the way for the quantum mechanical description of multiple embedded domains, particularly by employing the emergent quantum flow algorithms. Our theoretical underpinnings further set the stage for a generalization to multiple embedded sub-systems. This expansion holds significant promise for the exploration and application of non-equilibrium quantum systems, enhancing the understanding of system–environment interactions. In doing so, the research underscores the potential of SES-CC embedding within the realm of quantum computations and multi-scale simulations, promising a good balance between accuracy and computational efficiency.
97 MATHEMATICS AND COMPUTING↗
Heavy-Duty Vehicle Air Drag Coefficient Estimation: From an Algebraic Perspective
When a heavy-duty vehicle (HDV) operates at the nominal highway speed, over two-thirds of its total resistive force comes from the air drag, contributing to more than half of its fuel consumption. One effective countermeasure to reduce the fuel consumption of HDVs is platooning, which employs connectivity and automated driving technologies to link two or more HDVs in convoy. Platooning allows HDVs to drive closer together and yields improved fuel economy and less CO2 emission thanks to the reduced air drag. Maximizing the energy benefits of an HDV platoon requires quantifying the drag interaction between vehicles. In practice, modeling the drag reduction in a platoon boils down to identifying the relationship between the air drag coefficient C d and the inter-vehicle distance d. Existing approaches to identify C d (d) include vehicle field tests, wind tunnel experiments, and computational fluid dynamics simulation, which can howbeit be time-consuming and cost prohibitive. In contrast, this paper proposes an algebraic approach, which relies on onboard-measurable variables, to estimate the air drag coefficient of an HDV in a platoon. Its algebraic nature avoids the classical persistence of excitation condition for parameter identification and can yield the identified parameter almost instantaneously. Simulation results demonstrate its effectiveness and the improved estimation speed over a recursive least squares identifier.
Wang, Zejiang↗
Numerical operator method
Algebraic solutions of difference equations - stability of sampled-data control systems - numerical method for determining transients in electric systems excited by complex signals
ELECTRIC NETWORK↗
Degenerate coupled-cluster theory
A size-extensive, converging, black-box, ab initio coupled-cluster (ΔCC) ansatz is introduced that computes the energies and wave functions of states from any degenerate or nondegenerate Slater-determinant references with any numbers of α- and β-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Møller–Plesset perturbation (ΔMP) theory. For ionized and electron-attached references, it is a coupled-cluster Green’s function, although the present theory is convergent toward the full-configuration-interaction limits, while the Feynman–Dyson many-body Green’s function (MBGF) theory generally is not. Its single-excitation instance is a projection Hartree–Fock theory as per the Thouless theorem, which may be useful for core ionizations, high-spin states, and possibly electron affinities. Additionally, a new multireference coupled-cluster theory for a general model space is developed. This quasidegenerate coupled-cluster (QCC) theory is exactly converging, but not black-box, and intended for strong correlation. Determinant-based, general-order algorithms of ΔCC and QCC theories are implemented and compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with ΔMP and MBGF theories up to the nineteenth order. An algebraic, optimal-scaling algorithm of the ΔCC theory is computer-synthesized at the levels of single excitations (ΔCCS) and of single and double excitations (ΔCCSD). As a result, the order of performance is QCC ≈ ΔCC > EOM-CC > CI at the same order or QCC ≈ ΔCC > ΔMP > MBGF at the same cost scaling.
Hirata, So [University of Illinois at Urbana-Champ↗
Analytical estimates of turbulent MHD transport coefficients
Turbulent transfer rates from small-scale MHD excitations to large-scale Fourier modes are calculated algebraically, using the method of Biskamp and Welter. Three cases are considered: two-dimensional Navier-Stokes flows, two-dimensional incompressible MHD, and the weakly three-dimensional Strauss equations. In all cases, an initially large spectral gap between the small-scale and large-scale excitations is assumed, and attention focusses on the initial values of the back-transfer rates. The sign of the transfer is determined by the sign of an analytically calculable eddy viscosity and/or anomalous resistivity. We are able to confirm the results of Biskamp and Welter for the case of two-dimensional MHD, but find some differences for the case of the Strauss equations. It is argued that the Strauss equations may not exhibit an inverse cascade phenomenon for the spatially periodic case unless their initial spectra are such that the behavior is essentially that of two-dimensional MHD.
Montgomery, D.↗
Large N algebras and generalized entropy
We construct a Type II ∞ von Neumann algebra that describes the large N physics of single-trace operators in AdS/CFT in the microcanonical ensemble, where there is no need to include perturbative 1/N corrections. Using only the extrapolate dictionary, we show that the entropy of semiclassical states on this algebra is holographically dual to the generalized entropy of the black hole bifurcation surface. From a boundary perspective, this constitutes a derivation of a special case of the QES prescription without any use of Euclidean gravity or replicas; from a purely bulk perspective, it is a derivation of the quantum-corrected Bekenstein-Hawking formula as the entropy of an explicit algebra in the G → 0 limit of Lorentzian effective field theory quantum gravity. In a limit where a black hole is first allowed to equilibrate and then is later potentially re-excited, we show that the generalized second law is a direct consequence of the monotonicity of the entropy of algebras under trace-preserving inclusions. Finally, by considering excitations that are separated by more than a scrambling time we construct a “free product” von Neumann algebra that describes the semiclassical physics of long wormholes supported by shocks. We compute Rényi entropies for this algebra and show that they are equal to a sum over saddles associated to quantum extremal surfaces in the wormhole. Surprisingly, however, the saddles associated to “bulge” quantum extremal surfaces contribute with a negative sign.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The algebraic structure of gravitational scrambling
We introduce a new algebraic framework to describe gravitational scrambling, including the semiclassical limit of any out-of-time-order correlation function that is built out of operator insertions separated by approximately the scrambling time. In two dimensions, the scrambling algebra, which we call a modular-twisted product, is defined in terms of two copies of the Leutheusser-Liu half-sided modular inclusion of von Neumann algebras; these describe early- and late-time operators respectively. In limits where the separation between insertions is taken to be either significantly greater or smaller than the scrambling time, the modular-twisted product reduces, respectively, to free- and tensor-product algebras that were previously studied in [arXiv:2209.10454]. In a sense, the modular-twisted product interpolates between these two products. Including the Hamiltonian in the scrambling algebra leads to a Type II$_\infty$ von Neumann algebra with finite renormalized entropies that interpolate between single-QES and multi-QES phases. We also describe how to generalize the modular-twisted product algebra to higher dimensions, including spatially localized boundary excitations.
FOS: Physical sciences↗
Duality and form factors in the thermally deformed two-dimensional tricritical Ising model
The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional E_7 E 7 Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, \sigma(x) σ ( x ) and \sigma'(x) σ ′ ( x ) , in either phase are accompanied by associated disorder operators, \mu(x) μ ( x ) and \mu'(x) μ ′ ( x ) . Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For \sigma(x) σ ( x ) and \sigma'(x) σ ′ ( x ) , the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest \mathbb{Z}_2 ℤ 2 odd particles. Similarly, the equations for \mu(x) μ ( x ) and \mu'(x) μ ′ ( x ) have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for \sigma(x)/\sigma'(x) σ ( x ) / σ ′ ( x ) are fixed in terms of those for \mu(x)/\mu'(x) μ ( x ) / μ ′ ( x ) . We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the \Delta Δ -sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments.
Cortes Cubero, Axel↗
Third-sound propagation in thick films of superfluid He-4
Atkins' (1959) basic theory of third sound in thick films of superfluid He-4 is extended here to include a heat source for exciting third sound. A one-dimensional model obeying periodic boundary conditions is developed which can represent a variety of experimentally important configurations. General solutions for the model equations are found which give a complete description of third-sound waves in terms of displacement of the film surface, superfluid velocity, and temperature change as functions of space and time. Algebraic expressions for quantities that occur in general formulas are found for special excitation signals. The structure of third sound is calculated for the first time and the results are found to be inconsistent with previous findings. A direct method for accurately measuring the vaporization coefficient is also presented.
Jackson, H. W.↗
Analytic gradients for coupled-cluster energies that include noniterative connected triple excitations - Application to cis- and trans-HONO
An efficient formulation of the analytic energy gradient for the single and double excitation coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations is presented. The formulation has a small computational cost, and the algebraic manipulations may be applied generally to the analytic gradient of Moller-Plesset perturbation theory energies. The new formulation has been implemented in an efficient set of programs that utilize highly vectorized algorithms and has been used to investigate the equilibrium structures, harmonic vibrational frequencies, IR intensities, and energy separation of cis- and trans-HONO.
Lee, Timothy J.↗
Efficiency and Accuracy of Time-Accurate Turbulent Navier-Stokes Computations
The accuracy and efficiency of two types of subiterations in both explicit and implicit Navier-Stokes codes are explored for unsteady laminar circular-cylinder flow and unsteady turbulent flow over an 18-percent-thick circular-arc (biconvex) airfoil. Grid and time-step studies are used to assess the numerical accuracy of the methods. Nonsubiterative time-stepping schemes and schemes with physical time subiterations are subject to time-step limitations in practice that are removed by pseudo time sub-iterations. Computations for the circular-arc airfoil indicate that a one-equation turbulence model predicts the unsteady separated flow better than an algebraic turbulence model; also, the hysteresis with Mach number of the self-excited unsteadiness due to shock and boundary-layer separation is well predicted.
Rumsey, Christopher L.↗
Modular flow of excited states
We develop new techniques for studying the modular and the relative modular flows of general excited states. We show that the class of states obtained by acting on the vacuum (or any cyclic and separating state) with invertible operators from the algebra of a region is dense in the Hilbert space. This enables us to express the modular and the relative modular operators, as well as the relative entropies of generic excited states in terms of the vacuum modular operator and the operator that creates the state. In particular, the modular and the relative modular flows of any state can be expanded in terms of the modular flow of operators in vacuum. We illustrate the formalism with simple examples including states close to the vacuum, and coherent and squeezed states in generalized free field theory.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A rocket tomography measurement of the N2(+) 3914 A emission rates within an auroral arc
A rocket tomography experiment designed to measure the two-dimensional distribution of the N2(+) 3914 A volume emission rates within an auroral arc is described. A simple filter photometer on board a sounding rocket, which was launched during the ARIES auroral campaign, was used to measure the 3914 A aruoral brightnesses at elevation angles ranging from 0 to 360 deg in the plane of the rocket trajectory. The measured auroral brightnesses have been tomographically inverted to recover the local 3914 A volume emissioin rates as a function of both altitude and latitude within the arc. The tomographic inversion procedure, which is based upon a maximum probability algebraic reconstruction approach, is described, and the implications of the results for studies of auroral excitation processes are briefly discussed.
Mcdade, I. C.↗
Quantum Electrodynamics Coupled-Cluster at Scale: High-Performance Implementation for Complex Systems
Coupled-cluster theory (CC) is a highly accurate and versatile method for simulating complex interactions within quantum systems. The extension of CC theory to model mixed electron-photon processes with quantum electrodynamics (QED) has improved our capability to predict cavity-modified chemistry, a field where photons are used as cost-effective and eco-friendly alternatives to catalyze/inhibit chemical reactions. However, calculations with CC methods, even without incorporating QED effects, are often prohibitively expensive. Simulations of larger systems require scalable infrastructures that exist for traditional CC methods but not for QED-CC methods. As such, we present a GPU-enabled, high-performance, open-source implementation of the quantum electrodynamics coupled-cluster method with single and double excitations (QED-CCSD) within the ExaChem quantum chemistry software package. ExaChem relies on the Tensor Algebra for Many-body Methods (TAMM) infrastructure: a parallel heterogeneous tensor library designed to achieve scalable performance on modern heterogeneous supercomputing platforms. Furthermore, we discuss theoretical foundations, algorithmic details, and numerical benchmarks to showcase the larger systems that ExaChem can simulate and how the integration of photonic degrees-of-freedom alters their ground-state properties.
Basis sets↗