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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Mechanical form factors and densities of nonrelativistic fermions

The hadron physics community has been actively debating the interpretation of so-called mechanical properties of hadrons. Nonrelativistic quantum-mechanical systems like the hydrogen atom have been appealed to in these debates as analogies. Since such appeals are likely to continue, it is important to have Galilei-covariant expressions for matrix elements of the energy-momentum tensor. In this work, I obtain Galilei-covariant breakdowns of such matrix elements into mechanical form factors, with a special focus on spin-half states. I additionally study the spatial densities associated with these form factors, using the pilot wave interpretation to guide their breakdown into contributions from internal structure and from quantum-mechanical effects such as wave packet dispersion. For completeness, I also obtain nonrelativistic Breit frame densities.

form factors↗
DOE OSTI2021

Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, involving a small dimensionless parameter 0 < ε &NestedLessLess; 1 inversely proportional to the speed of light. In the massless and nonrelativistic regime, the solution exhibits rapid motion in space and is highly oscillatory in time. Specifically, the wavelength of the propagating waves in time is at O(ε), while in space, it is at O(1) with the wave speed at O(ε -1 ). We adopt one leap-frog, two semi-implicit, and one conservative Crank-Nicolson finite difference methods to numerically discretize the Dirac equation in one dimension and establish rigorously the error estimates which depend explicitly on the time step τ, mesh size h, and the small parameter ε. The error bounds indicate that, to obtain the “correct” numerical solution in the massless and nonrelativistic regime, i.e., 0 < ε &NestedLessLess; 1, all these finite difference methods share the same ε-scalability as time step τ = O(ε 3/2 ) and mesh size h = O(ε 1/2 ). A large number of numerical results are reported to verify the error estimates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Interacting quantum and classical waves: Resonant and non-resonant energy transfer to electrons immersed in an intense electromagnetic wave

Dynamics of electrons subjected to a constant amplitude classical electromagnetic (EM) wave is investigated as a fundamental, representative problem in the physics of interacting quantum and classical waves. In the nonrelativistic regime (electrons as Schrödinger waves), the electron energy acquires a constant and a time dependent part. Driven by EM waves, both parts scale strongly with the amplitude, but we expect no resonant enhancement since the parallel electron “speed” of nonrelativistic electrons could never match the wave phase velocity. In the relativistic regime (electron as a Klein–Gordon wave), however, a class of electron waves (with parallel speed matching the EM phase speed) are resonantly excited to extremely high energies. Such a direct resonant energy transfer from intense electromagnetic waves constitutes a mechanism that could, in principle, power the most energetic of cosmic rays (this mechanism will work on protons just as well). Some predictions of the theory will, hopefully, be tested in laboratory laser experiments. In conclusion, the nonrelativistic calculations will also be examined in the context of recent experiments using photon-induced near-field electron microscopy in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Mass of a weakly measured photon

Bohmian mechanics has garnered significant attention as an interpretation of quantum theory since the paradigmatic experiments which inferred the average trajectories of photons in the nonrelativistic regime. These experiments were largely motivated by Wiseman's formulation of Bohmian mechanics, which grounded these trajectories in weak measurements. Recently, Wiseman's framework was extended to the relativistic regime by expressing the velocity field of single photons in terms of weak values of the photon energy and momentum. Here, we propose an operational, weak value-based definition for the Bohmian “local mass” of relativistic single particles. For relativistic wave functions satisfying the scalar Klein-Gordon equation, this mass coincides with the effective mass defined by de Broglie in his relativistic pilot-wave theory, a quantity closely connected with the quantum potential that is responsible for Bohmian trajectory self-bending and the anomalous photoelectric effect. Here, we demonstrate the relationship between the photon trajectories and the mass in an interferometric setup.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Cold freeze out of superheavy dark matter and Hubble tension

We present a unified framework, the "X miracle", in which dark matter consists of superheavy, nonthermal X particles whose relic abundance is determined not by the conventional weak-scale, semi-relativistic ("hot") freeze-out of WIMPs, but by annihilation or decay occurring within the smallest and earliest gravitationally bound objects. Unlike thermal WIMPs, which decouple at velocities of order 0.3c with relic abundance ρ∞ set by weak-scale interactions, X particles are produced nonthermally with an initial overabun dance ρ ini >> ρ ∞ . They become nonrelativistic extremely early, redshift to ultra-cold velocities, allowing collapse into compact bound structures characterized by a novel quantum gravitational scale, r X = 4$\hbar$ 2 $/Gm^3_X$ = 10 −13 m $\hbar$$/m_Xc$, much larger than the Compton wavelength. The framework predicts a particle mass of 10 12 GeV and an enhanced cross section of 10 −21 m 3 /s. Overlapping particle wavefunctions in these compact structures drive annihilation or decay into additional radiation, leading to a "cold" freeze-out that converts most of ρ ini into radiation while leaving a relic density ρ ∞ . Solutions to the Boltzmann equation indicate that an extreme ("big") depletion, with only one particle in a billion surviving, yields an additional radiation contribution $ΔN_{eff}$ ≈ 0.4, which could help alleviate the Hubble tension. For particles of 10 12 GeV, the scenario predicts a dark coupling constant α X = 0.09 that is responsible for an instanton-induced decay process, consistent with current UHECR bounds. Early collapse at 10 −6 s may release binding energy as high-frequency (100kHz) gravitational waves or ultralight GUT-scale axions (10 −9 eV). Superheavy sterile neutrinos provide a natural particle realization, linking dark matter to neutrino mass and baryogenesis. If gravitationally produced, this framework favors high-scale inflation and effi cient reheating. The "X miracle" thus demonstrates that dark matter need not be weak-scale: gravitational dynamics can control freeze-out and evolution, producing multi-messenger observational signatures in UHECRs, axions, gravitational waves, and small-scale structures.

Xu, Zhijie Jay [Pacific Northwest National Laborat↗
DOE OSTI2022

Quantum simulations of hydrodynamics via the Madelung transformation

Developing numerical methods to simulate efficiently nonlinear fluid dynamics on universal quantum computers is a challenging problem. In this paper, a generalization of the Madelung transform is defined to solve quantum relativistic charged fluid equations interacting with external electromagnetic forces via the Dirac equation. The Dirac equation is discretized into discrete-time quantum walks which can be efficiently implemented on universal quantum computers. A variant of this algorithm is proposed to implement simulations using current noisy intermediate scale quantum (NISQ) devices in the case of homogeneous external forces. High resolution (up to N=2 17 grid points) numerical simulations of relativistic and nonrelativistic hydrodynamical shocks on current IBM NISQs are performed with this algorithm. Here, this paper demonstrates that fluid dynamics can be simulated on NISQs, and opens the door to simulating other fluids, including plasmas, with more general quantum walks and quantum automata.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗