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Results for “Fluctuation theorems”

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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79 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quantum-gravitational null Raychaudhuri equation

Abstract We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by such fluctuations. For the gravitational field in its vacuum state, we find that quantum gravity contributes a correction to the null Raychaudhuri equation which is of the same sign as the classical terms. We thus derive a quantum-gravitational focusing theorem valid for linearized quantum gravity.

Physics↗
DOE OSTI2021

Stochastic density functional theory: Real- and energy-space fragmentation for noise reduction

Stochastic density functional theory (sDFT) is becoming a valuable tool for studying ground-state properties of extended materials. The computational complexity of describing the Kohn-Sham orbitals is replaced by introducing a set of random (stochastic) orbitals leading to linear and often sub-linear scaling of certain ground-state observables at the account of introducing a statistical error. Schemes to reduce the noise are essential, for example, for determining the structure using the forces obtained from sDFT. Recently, we have introduced two embedding schemes to mitigate the statistical fluctuations in the electron density and resultant forces on the nuclei. Both techniques were based on fragmenting the system either in real space or slicing the occupied space into energy windows, allowing for a significant reduction in the statistical fluctuations. For chemical accuracy, further reduction of the noise is required, which could be achieved by increasing the number of stochastic orbitals. However, the convergence is relatively slow as the statistical error scales as 1 / N χ according to the central limit theorem, where N χ is the number of random orbitals. In this paper, we combined the embedding schemes mentioned above and introduced a new approach that builds on overlapped fragments and energy windows. The new approach significantly lowers the noise for ground-state properties, such as the electron density, total energy, and forces on the nuclei, as demonstrated for a G-center in bulk silicon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green’s function methods: Theory and application to GW and GF2

One-particle Green’s function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green’s functions directly provide electronic energies and one-particle properties, such as dipole moment. However, the evaluation of two-particle properties, such as $\langle$S 2 $\rangle$ and $\langle$N 2 $\rangle$, can be challenging because they require a solution of the computationally expensive Bethe–Salpeter equation to find two-particle Green’s functions. We demonstrate that the solution of the Bethe–Salpeter equation can be completely avoided. Applying the thermodynamic Hellmann–Feynman theorem to self-consistent one-particle Green’s function methods, we derive expressions for two-particle density matrices in a general case and provide explicit expressions for GF2 and GW methods. Such density matrices can be decomposed into an antisymmetrized product of correlated one-electron density matrices and the two-particle electronic cumulant of the density matrix. Cumulant expressions reveal a deviation from ensemble representability for GW, explaining its known deficiencies. We analyze the temperature dependence of $\langle$S 2 $\rangle$ and $\langle$N 2 $\rangle$ for a set of small closed-shell systems. Interestingly, both GF2 and GW show a non-zero spin contamination and a non-zero fluctuation of the number of particles for closed-shell systems at the zero-temperature limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Electromagnetic energy transport by tearing fluctuations in a self-organized reversed-field pinch plasma

Fluctuation measurements reveal the outward electromagnetic energy flux needed to drive the dynamo electromotive force supporting magnetic self-organization in a reversed-field pinch plasma. The radial Poynting flux due to tearing mode fluctuations is measured with an insertable probe during magnetic relaxation. This flux corresponds to transient power levels much larger than the input power and comparable to the global equilibrium magnetic energy transient loss rate. The probe measurements of this flux are roughly as predicted by a simple Poynting's theorem model upon substitution of equilibrium measurement data.

Physics↗
DOE OSTI2025

Lattice QCD Study of Pion Electroproduction and Weak Production from a Nucleon

Quantum fluctuations in QCD influence nucleon structure and interactions, with pion production serving as a key probe of chiral dynamics. In this Letter, we present a lattice QCD calculation of multipole amplitudes at threshold, related to both pion electroproduction and weak production from a nucleon, using two gauge ensembles near the physical pion mass. We develop a technique for spin projection and construct multiple operators for analyzing the generalized eigenvalue problem in both the nucleon-pion system in the center-of-mass frame and the nucleon system with nonzero momentum. The numerical lattice results are then compared with those extracted from experimental data and predicted by low-energy theorems incorporating one-loop corrections. Published by the American Physical Society 2025

Gao, Yu-Sheng (ORCID:0009000406829247)↗
DOE OSTI2024

Characterizing non-Markovian and coherent errors in quantum simulation

Quantum simulation of many-body systems, particularly using ultracold atoms and trapped ions, presents a unique form of quantum control—it is a direct implementation of a multi-qubit gate generated by the Hamiltonian. As a consequence, it also faces a unique challenge in terms of benchmarking, because the well-established gate benchmarking techniques are unsuitable for this form of quantum control. Here we show that the symmetries of the target many-body Hamiltonian can be used not only to benchmark but to characterize experimental errors in the quantum simulation. We use our results to develop protocols to characterize these errors, which can be implemented using state-of-the-art technology. We consider two forms of errors: (i) unitary errors arising out of systematic errors in the applied Hamiltonian and (ii) canonical non-Markovian errors arising out of random shot-to-shot fluctuations in the applied Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally constant in time, can be used to characterize these errors. In the presence of errors, the expectation value of the target Hamiltonian shows a characteristic thermalization dynamics, when it satisfies the operator thermalization hypothesis (OTH). That is, an oscillation in the short time followed by relaxation to a steady-state value in the long time limit. We show that while the steady-state value can be used to characterize the coherent errors, the amplitude of the oscillations can be used to estimate the non-Markovian errors. We prove a sandwich theorem to establish a linear relation between the amplitude of the oscillations and the magnitude of the non-Markovian errors. Moreover, by varying the initial state, we show that the steady state values can be used to completely construct the generator of the coherent errors. Using these results, we develop two experimental protocols to characterize the unitary errors based on these results, one of which requires single-qubit addressing and the other one doesn't. We also develop a protocol to characterize non-Markovian errors. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A consistent, Bayesian, approach to the cross section probability distribution in the unresolved resonance region

The cross sections of neutron-induced reactions can be divided into three energy ranges: the resolved resonance region (RRR), the unresolved resonance region (URR), and the fast region. In general, the cross sections in the URR show significant fluctuations that cannot be predicted and cannot be experimentally resolved, thus, it is commonly assumed that the cross section at a specific energy is given by a probability distribution function (PDF) over a range of values that can span several orders of magnitude. The current methodology used to describe such behavior is to construct the PDF by stochastically generating resonance ladders and numerically measuring the PDF. The resonance ladders are sampled using known resonance statistical properties and average resonance widths and spacings extrapolated from the RRR. Although this is a standard and widely used technique, it is computationally very expensive, therefore, an alternative, analytical, approach would be preferable due to the considerable speed up of the computational time in real life applications. Moreover, the current methodology does not take into account existing experimental data, such for total and capture cross sections, that are available for many nuclei. Finally, this approach was developed to be used in reactor-scale applications and it is not suited for use in single-event applications. In this work we will rethink the entire approach to the PDF construction using a Bayesian mindset. This will allow us to provide a different definition of the PDF that allows a much faster calculation of the higher-temperature PDFs and a proper combination of theoretical and experimental PDFs following the probability theory. We will also show that our definition is well suited for single-event applications and we will make an explicit connection between our method and the standard approach. We do this by showing that the central limit theorem applies and our method leads to the same PDF obtained with the standard methodology, for a large number of events per history.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗