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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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62 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Bidirectional Classical Stochastic Processes with Measurements and Feedback

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Hahne, G. E.↗
DOE OSTI2020

Annihilation-to-nothing: a quantum gravitational boundary condition for the Schwarzschild black hole

The interior of a static Schwarzschild metric can be written in terms of two functions, similar to some models of anisotropic cosmology. With a suitable choice of canonical variables, we solve the Wheeler-DeWitt equation (WDW) inside the horizon of a Schwarzschild black hole. By imposing classicality near the horizon, and requiring boundedness of the wave function, we get a rather generic solution of the WDW equation, whose steepest-descent solution, i.e., the ridge of the wave function, coincides nicely with the classical trajectory. However, there is an ambiguity in defining the arrow of time which leads to two possible interpretations—(i) if there is only one arrow of time, one can infer that the steepest-descent of the wave function follows the classical trajectory throughout: coming from the event horizon and going all the way down to the singularity, while (ii) if there are two different arrows of time in two separate regimes, it can be inferred that the steepest-descent of the wave function comes inwards from the event horizon in one region while it moves outwards from the singularity in the other region, and there exists an annihilation process of these two parts of the wave function inside the horizon. Additionally, adopting the second interpretation could shed light on the information loss paradox: as time goes on, probabilities for histories that include black holes and singularities decay to zero and eventually only trivial geometries dominate.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Islands in asymptotically flat 2D gravity

The large-$\textit{N}$ limit of asymptotically flat two-dimensional dilaton gravity coupled to $\textit{N}$ free matter fields provides a useful toy model for semiclassical black holes and the information paradox. Analyses of the asymptotic information flux as given by the entanglement entropy show that it follows the Hawking curve, indicating that information is destroyed in these models. Recently, motivated by developments in AdS/CFT, a semiclassical island rule for entropy has been proposed. We define and compute the island rule entropy for black hole formation and evaporation in the large-$\textit{N}$ RST model of dilaton gravity and show that, in contrast, it follows the unitary Page curve. The relation of these two observations, and interesting properties of the dilaton gravity island rule, are discussed.

2D Gravity↗
DOE OSTI2020

Optical measure of disorder: Why Urbach analysis works for amorphous silicon but fails for amorphous carbon

We investigate the basis for the Paradox where the Urbach-slope disorder parameter disagrees with the Raman width in amorphous diamond-like carbon (DLC) materials (lower Urbach-Eo yet greater Raman width). We examined the bandgap and Urbach-slope measurement issues. While significant errors are identified, ultimately these cannot resolve the Paradox. This resolution involves large changes in shape of DLC's absorption band resulting from large energy shifts. To solidify the understanding of band energy shifts, we examined their properties using a-Si:H, well known for its agreement between Raman and Urbach-slope disorder parameters. Using Tauc-Lorentz (T-L) dispersion functions, the Urbach method works for a-Si:H because small changes in shape occur, as measured by (i) peak position, (ii) peak width, (iii) peak amplitude, and (iv) and gap energies. Moreover, for a-Si:H, a 5th condition (v) there is no other feature below the principal band to interfere with its fall. All 5 of these conditions fail for DLCs. Because T-L dispersions accommodate asymmetry, we traced the Paradox to a steepening of the band shape as it pushes toward lower energy. This steepening is unrelated to disorder, but to a boundary value problem where energy cannot be negative. We conclude that Urbach analysis is invalid for DLC materials, but the T-L width is a good measure instead. We also examined another disorder measure, where π bonds should be considered as disorder relative to the σ bonds in an idealized “amorphous diamond” sp 3 network: superconvergence can be used to quantify these π transitions. Finally, further molecular orbital calculations are needed to properly interpret the changes in T-L widths.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The paradox of the tight spiral pass in American football: A simple resolution

An American football is a rotationally symmetric object, which, when well-thrown, spins rapidly around its symmetry axis. In the absence of aerodynamic effects, the football would be a torque-free gyroscope and the symmetry/spin axis would remain pointing in a fixed direction in space as the football moved on its parabolic path. When a pass is well-thrown through the atmosphere, however, the symmetry axis remains—at least approximately—tangent to the path of motion. The rotation of the symmetry axis must be due to aerodynamic torque; yet, that torque, at first glance, would seem to have precisely the opposite effect. In this work, we explain the action of aerodynamics on the ball's orientation at second glance.

42 ENGINEERING↗
DOE OSTI2020

Replica wormholes and the entropy of Hawking radiation

The information paradox can be realized in anti-de Sitter spacetime joined to a Minkowski region. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirements of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as complexified wormholes connecting different copies of the black hole. As the replica number n → 1, the presence of these wormholes leads to the island rule for the computation of the fine-grained gravitational entropy. We discuss these replica wormholes explicitly in two-dimensional Jackiw-Teitelboim gravity coupled to matter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Semiclassical theory and the Koopman-van Hove equation *

Abstract The phase space Koopman-van Hove (KvH) equation can be derived from the asymptotic semiclassical analysis of partial differential equations. Semiclassical theory yields the Hamilton–Jacobi equation for the complex phase factor and the transport equation for the amplitude. These two equations can be combined to form a nonlinear semiclassical version of the KvH equation in configuration space. There is a natural injection of configuration space solutions into phase space and a natural projection of phase space solutions onto configuration space. Hence, every solution of the configuration space KvH equation satisfies both the semiclassical phase space KvH equation and the Hamilton–Jacobi constraint. For configuration space solutions, this constraint resolves the paradox that there are two different conserved densities in phase space. For integrable systems, the KvH spectrum is the Cartesian product of a classical and a semiclassical spectrum. If the classical spectrum is eliminated, then, with the correct choice of Jeffreys–Wentzel–Kramers–Brillouin (JWKB) matching conditions, the semiclassical spectrum satisfies the Einstein–Brillouin–Keller quantization conditions which include the correction due to the Maslov index. However, semiclassical analysis uses different choices for boundary conditions, continuity requirements, and the domain of definition. For example, use of the complex JWKB method allows for the treatment of tunneling through the complexification of phase space. Finally, although KvH wavefunctions include the possibility of interference effects, interference is not observable when all observables are approximated as local operators on phase space. Observing interference effects requires consideration of nonlocal operations, e.g. through higher orders in the asymptotic theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Accurate machine-learning predictions of coercivity in high-performance permanent magnets

Increased demand for high-performance permanent magnets in the electric vehicle and wind-turbine industries has prompted the search for cost-effective alternatives. Discovering magnetic materials with the desired intrinsic and extrinsic permanent magnet properties presents a significant challenge to researchers because of issues with the global supply of rare-earth elements, material stability, and a low maximum magnetic energy product BH max . While first-principles density functional theory (DFT) predicts materials’ magnetic moments, magnetocrystalline anisotropy constants, and exchange interactions, it cannot compute extrinsic properties such as coercivity (H c ). Although it is possible to calculate H c theoretically with micromagnetic simulations, the predicted value is larger than the experiment by almost an order of magnitude due to the Brown paradox. To circumvent these issues, we employ machine-learning (ML) methods on an extensive database obtained from experiments, DFT calculations, and micromagnetic modeling. The use of a large experimental dataset enables realistic H c predictions for materials such as Ce-doped Nd 2 ⁢Fe 14 ⁢B, comparing favorably against micromagnetically simulated coercivities. Remarkably, our ML model accurately identifies uniaxial magneto-crystalline anisotropy as the primary contributor to H c . With DFT calculations, we predict the Nd-site-dependent magnetic anisotropy behavior in Nd 2 ⁢Fe 14 ⁢B, confirming that Nd 4⁢g sites mainly contribute to uniaxial magnetocrystalline anisotropy, and also calculate the Curie temperature (T c ). Finally, both calculated results are in good agreement with the experiments. The coupled experimental dataset and ML modeling with DFT input predict H c with far greater accuracy and speed than was previously possible using micromagnetic modeling. Further, we reverse engineer the grain-boundary and intergrain exchange coupling with micromagnetic simulations by employing the ML predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗