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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Gravity Effects in Diffusive Coarsening of Bubble Lattices: von Neumann's Law

von Neumann modelled the evolution of two-dimensional soap froths as a purely diffusive phenomenon; the area growth of a given cell was found to depend only on the geometry of the bubble lattice. In the model, hexagons are stable, pentagons shrink and heptagons grow. The simplest equivalent to the area growth law is / approximately t(sub beta). The result depends on assuming (1) an incompressible gas; (2) bubble walls which meet at 120 deg and (3) constant wall thickness and curvature. Each assumption is borne out in experiments except the last one: bubble wall thickness between connecting cells varies in unit gravity because of gravity drainage. The bottom part of the soap membrane is thickened, the top part is thinned, such that gas diffusion across the membrane shows a complex dependence on gravity. As a result, experimental tests of von Neumann's law have been influenced by effects of gravity; fluid behavior along cell borders can give non-uniform wall thicknesses and thus alter the effective area and gas diffusion rates between adjacent bubbles. For area plotted as a function of time, Glazier (J.A. Glazier, S.P. Gross, and I. Stavans, Phys. Rev. A. 36, 306 (1987); J. Stavans, J.A, Glazier, Phys. Rev. Lett. 62, 1318 (1989).) suggest that in some cases their failure to observe von Neumann's predicted growth exponent ((sup beta)theor(sup =1; beta)exp(sup =0.70 + 0.10)) may have been the result of such "fluid drainage onto the lower glass plate". Additional experiments which varied plate spacing gave different beta exponents in a fashion consistent with this suggestion. During preliminary long duration experiments (approximately 100 h) aboard Spacelab-J, a low-gravity test of froth coarsening has examined (1) power law scaling of von Neumann's law (beta values) in the appropriate diffusive limits; (2) new bubble lattice dynamics such as greater fluid wetting behavior on froth membranes in low gravity; and (3) explicit relations for the gravity dependence of the second moment (or disorder parameter) governing the geometric spread in cell-sidedness around the mean of perfect hexagonal filling. By reducing the gravity-induced distortion in lattice wall thickness, the diffusion-limited regime of bubble coarsening becomes available for performing critical tests of network dynamics.

Noever, David A.↗
DOE OSTI2024

A retrospective review of von Neumann’s analysis of hidden variables in quantum mechanics

This article reviews the history of J. von Neumann’s analysis of hidden variables in quantum mechanics and the subsequent analysis by others. In his book The Mathematical Foundations of Quantum Mechanics , published in 1932, von Neumann performed an analysis of the consequences of introducing hidden parameters (hidden variables) into quantum mechanics. He arrived at two principal conclusions: first, hidden variables cannot be incorporated into the existing theory of quantum mechanics without major modifications, and second, if they did exist, the theory would have already failed in situations where it has been successfully applied. This analysis has been taken as an “incorrect proof” against the existence of hidden variables, possibly due to a mistranslation of the German word prufen . von Neumann’s so-called proof isn’t even wrong as such a proof does not exist, but it is an examination of the limitations imposed by internal consistency of the Hilbert space formulation of the theory. One of the earliest attempts to eliminate uncertainty, by D. Bohm, requires a major modification of quantum mechanics (observables are not represented by Hermitian operators), which supports von Neumann’s first principal conclusion. However, testing the Bohm theory requires constructing a physically impossible initial state. As such, the theory has no experimental consequences, so W. Pauli referred to it as an “uncashable check”. As there are no observable consequences, the Bohm theory is possibly a counterexample to von Neumann’s second conclusion that hidden variables in particular would have already led to a failure of the theory.

density matrix↗
DOE OSTI2022

Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras

We prove the existence of a universal recovery channel that approximately recovers states on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I von Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary von Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki–Masuda L p norms. We comment on applications to the quantum null energy condition.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Predicting the von Neumann entanglement entropy using a graph neural network

Calculating the von Neumann entanglement entropy from experimental data is challenging due to its dependence on the complete wavefunction, forcing reliance on approximations such as classical mutual information (MI). We propose a machine learning approach using a graph neural network to predict the von Neumann entropy directly from experimentally accessible bitstrings. We test this approach on a Rydberg ladder system and achieve a mean absolute error of $3.6\,\times 10^{-3}$ when evaluating within the training range on a dataset with entropy values ranging from 0 to 1.9. The model achieves a mean absolute percentage error of 1.44% and outperforms MI-based bounds. When tested beyond the training range, the model maintains reasonable accuracy. Furthermore, we demonstrate that fine-tuning the model with small datasets significantly improves performance on data outside the original training range.

graph neural networks↗
DOE OSTI2020

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman–von Neumann formulation of classical mechanics. The Koopman–von Neumann formulation implies that the conservation of the probability distribution function on phase space, as expressed by the Liouville equation, can be recast as an equivalent Schrödinger equation on Hilbert space with a Hermitian Hamiltonian operator and a unitary propagator. This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of this unitary evolution operator. Quantum simulation of classical dynamics is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Koopman–von Neumann Hamiltonian is sparse. Utilizing quantum walk techniques for state preparation and amplitude estimation for the calculation of observables leads to a quadratic improvement over classical probabilistic Monte Carlo algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

On the τ-Compactness of Products of τ -Measurable Operators Adjoint to Semi-Finite Von Neumann Algebras

Let M be the von Neumann algebra of operators in a Hilbert space H and τ be an exact normal semi-finite trace on M. We obtain inequalities for permutations of products of τ-measurable operators. We apply these inequalities to obtain new submajorizations (in the sense of Hardy, Littlewood, and Pólya) of products of τ -measurable operators and a sufficient condition of orthogonality of certain nonnegative τ-measurable operators. We state sufficient conditions of the τ –compactness of products of self-adjoint τ -measurable operators and obtain a criterion of the τ -compactness of the product of a nonnegative τ-measurable operator and an arbitrary τ -measurable operator. We present an example that shows that the nonnegativity of one of the factors is substantial. We also state a criterion of the elementary nature of the product of nonnegative operators from M . All results are new for the *-algebra B(H) of all bounded linear operators in H endowed with the canonical trace τ = tr.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Approximate recoverability and relative entropy II: 2-positive channels of general von Neumann algebras

Abstract We generalize our results in paper I in this series to quantum channels between general von Neumann algebras, proving the approximate recoverability of states which undergo a small change in relative entropy through the channel. To this end, we derive a strengthened form of the quantum data processing inequality for the change in relative entropy of two states under a channel between two von Neumann algebras. Compared to the usual inequality, there is an explicit lower bound involving the fidelity between the original state and a recovery channel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

von Neumann algebras in JT gravity

We quantize JT gravity with matter on the spatial interval with two asymptotically AdS boundaries. We consider the von Neumann algebra generated by the right Hamiltonian and the gravitationally dressed matter operators on the right boundary. We prove that the commutant of this algebra is the analogously defined left boundary algebra and that both algebras are type II ∞ factors. These algebras provide a precise notion of the entanglement wedge away from the semiclassical limit. We comment on how the factorization problem differs between pure JT gravity and JT gravity with matter.

2D Gravity↗
DOE OSTI2023

The woman behind the curious invention of modern software: Klára Dán von Neumann’s handwritten letters confirm her legacy

The year 1945 marked not only the birth of the atomic age, but also the birth of modern computer programming. The first fully electronic computing machine, the ENIAC (Electronic Numerical Integrator And Computer), came online in December 1945. But programming the ENIAC was an excruciatingly difficult task. Klára Dán von Neumann, who joined the Laboratory at Los Alamos after WWII, helped to revolutionize the process, creating the very first modern computer programs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Organismic materials for beyond von Neumann machines

The elementary basis of intelligence in organisms with a central nervous system includes neurons and synapses and their complex interconnections forming neural circuits. In non-neural organisms such as slime mold with gel-like media, viscosity modulation enables adaptation to changing environments. At a larger scale, collective intelligence emerges via social interactions and feedback in animal colonies. Learning and memory are therefore multi-scale features that evolve as a result of constant interactions with the environment. There is growing interest in emulating such features of intelligence in computing machines and autonomous systems. Materials that can respond to their environment in a manner similar to organisms (referred to as "organismic materials") therefore may be of interest as hardware components in artificial intelligence machines. In this brief review, we present a class of semiconductors called correlated oxides as candidates for learning machines. The term "correlated" refers to the fact that electrons in such lattices strongly interact and the ground state is not what is predicted by classical band theory. Such materials can undergo insulator-metal transitions at near ambient conditions under external stimuli such as thermal or electrical fields, strain, and chemical doping. Depending on the mechanism driving the transition, intermediate states can be metastable with different volatilities, and the time scales of phase change can be controlled over many orders of magnitude. The change in electronic properties can be sharp or gradual, leading to digital or analog behavior. These properties enable the realization of artificial neurons and synapses and emulate the associative and non-associative learning characteristics found in various organisms. We examine microscopic properties concerning electronic and structural transitions leading to collective behavior and theoretical treatments of the ground state and dynamical response, showcasing VO 2 as a model system. Next, we briefly review algorithms designed from the plasticity demonstrated by phase changing systems. Finally, we conclude the brief review with suggestions for future research toward realizing non-von Neumann machines.

42 ENGINEERING↗
NASA NTRS2005

Explicit Von Neumann Stability Conditions for the c-tau Scheme: A Basic Scheme in the Development of the CE-SE Courant Number Insensitive Schemes

As part of the continuous development of the space-time conservation element and solution element (CE-SE) method, recently a set of so call ed "Courant number insensitive schemes" has been proposed. The key advantage of these new schemes is that the numerical dissipation associa ted with them generally does not increase as the Courant number decre ases. As such, they can be applied to problems with large Courant number disparities (such as what commonly occurs in Navier-Stokes problem s) without incurring excessive numerical dissipation.

Chang, Sin-Chung↗
DOE OSTI2019

Integrable nonlinear evolution of the qubit

Highlights: •We study the nonlinear generalization of the von Neumann equation. •We discuss the nonlinear von Neumann equation for the qubit states. •We analyze solutions to the Riccati system corresponding to evolution of a qubit. -- Abstract: The nonlinear generalization of the von Neumann equation is studied. The global version of this equation preserves convexity of the space of states. The particular case of the evolution of pure states refers to the nonlinear Schrödinger equation discovered by Gisin. The concrete realization of the nonlinear von Neumann equation is investigated in detail for the density matrix representing the qubit states. Such equation reduces to the integrable classical Riccati system of nonlinear ordinary differential equations. An interesting property of the nonlinear dynamics described by this system is the global asymptotical stability of stationary solutions related to evolution from mixed states to pure states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗