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DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2021

Local wave-number model for inhomogeneous two-fluid mixing

We analyze the local wave-number (LWN) model, a two-point spectral closure model for turbulence, as applied to the Rayleigh-Taylor (RT) instability, the flow induced by the relaxation of a statically-unstable density stratification. Model outcomes are validated against data from 3D simulations of the RT instability. In the first part of the study we consider the minimal model terms required to capture inhomogeneous mixing and show that this version, with suitable model coefficients, is sufficient to capture the evolution of important mean global quantities including mix-width, turbulent mass flux velocity, and Reynolds stress, if the start time is chosen such that the earliest transitions are avoided. However, this simple model does not permit the expected finite asymptote of the density-specific-volume covariance b. In the second part of the study, we investigate two forms for a source term for the evolution of the spectrum of density-specific-volume covariance for the LWN model. The first includes an empirically motivated calibration of the source to achieve the final asymptotic state of constant b. Here, the second form does not require calibration but, in conjunction with enhanced diffusion and drag captures the full evolution of all the dynamical quantities, namely, the mix-layer growth, turbulent mass-flux velocity, Reynolds stress, as well as the desired behavior of b.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Spatially-resolved dynamic sampling of different phasic magnetic resonances of nanoparticle ensembles in a magnetotactic bacterium Magnetospirillum magnetotacticum

Abstract Nanoscaled magnetic particle ensembles are promising building blocks for realizing magnon based binary logic. Element-specific real-space monitoring of magnetic resonance modes with sampling rates in the GHz regime is imperative for the experimental verification of future complex magnonic devices. Here we present the observation of different phasic magnetic resonance modes using the element-specific technique of time-resolved scanning transmission x-ray microscopy within a chain of dipolarly coupled Fe 3 O 4 nanoparticles (40–50 nm particle size) inside a single cell of a magnetotactic bacterium Magnetospirillum magnetotacticum . The particles are probed with 25 nm resolution at the Fe L 3 x-ray absorption edge in response to a microwave excitation of 4.07 GHz. A plethora of resonance modes is observed within multiple particle segments oscillating in- and out-of-phase, well resembled by micromagnetic simulations.

time-resolved scanning transmission x-ray microsco↗
DOE OSTI2020

Phase-matching analysis in high-order harmonic generation with nonzero orbital angular momentum Laguerre-Gaussian beams

Through high-order harmonic generation driven by intense ultrashort vortex infrared or midinfrared lasers, a nonzero orbital angular momentum can be imprinted onto extreme ultraviolet (XUV) or soft-x-ray (SXR) light pulses. Here we simulate the generation of vortex XUV harmonics in the gas medium as well as their propagation in vacuum till reaching the far field. In this work, we find that the intensity and phase of generated high harmonics are very sensitive to the position of gas jet with respect to the laser focus. The topological charge of the $\textit{q}$th harmonic is found to be $\textit{q}$ times that of the driving Laguerre-Gaussian beam. Each harmonic in the far field appears as a single ring in the transverse plane with an invariant diameter which is scalable with the fundamental topological charge only when the gas jet is placed after the laser focus. The underlying phase-matching mechanism is analyzed by examining the spatial map of the coherence length and by calculating the evolution of harmonic emission in the medium. We anticipate this work to stimulate interest in generating intense vortex XUV or SXR attosecond pulses for probing dynamics of molecules where special molecular features are difficult to be detected with linear or circular XUV or SXR pulses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Thermodynamic stability of a spin microemulsion in Rashba spin-orbit-coupled bosons

Recent finite-temperature numerical simulations have unveiled a quantum “spin” microemulsion analog, found by raising the temperature of a stripe supersolid phase in a Rashba spin-orbit coupled Bose gas. This microemulsion state is a highly correlated, isotropic normal fluid where atoms self-arrange based on their internal pseudospin into patterns that resemble bicontinuous microemulsions. This finding leaves several open questions regarding the broader accessibility of this phase in experiments. Here, we use equilibrium finite-temperature numerical simulations based on a coherent-state path integral representation to perform a computational investigation into the thermodynamic stability of the spin microemulsion state. Numerical simulations emphasize the requirement of a nearly, but not perfectly, isotropic spin-orbit coupling in order to achieve the microemulsion phase in cold-atom experiments. Moreover, the microemulsion state exists independent of miscibility of the pseudospin components and for a wide range of pseudospin population imbalance, suggesting a high degree of flexibility in choosing the atom and hyperfine states in an experimental realization. Lastly, we demonstrate this feasibility by mimicking a Rashba spin-orbit-coupled 87 Rb experiment in an isotropic harmonic trap, where we confirm the microemulsion's existence via its density profile and equilibrium quasimomentum distribution.

Complex Langevin dynamics↗
DOE OSTI2021

The imaginary part of the heavy-quark potential from real-time Yang-Mills dynamics

We extract the imaginary part of the heavy-quark potential using classical-statistical simulations of real-time Yang-Mills dynamics in classical thermal equilibrium. The r-dependence of the imaginary part of the potential is extracted by measuring the temporal decay of Wilson loops of spatial length r. We compare our results to continuum expressions obtained using hard thermal loop theory and to semi-analytic lattice perturbation theory calculations using the hard classical loop formalism. We find that, when plotted as a function of m D r, where m D is the hard classical loop Debye mass, the imaginary part of the heavy-quark potential shows little sensitivity to the lattice spacing at small m D r ≲ 1 and agrees well with the semi-analytic hard classical loop result. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. This work sets the stage for extracting the imaginary part of the heavy-quark potential in an expanding non-equilibrium Yang Mills plasma.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Faster Randomized Dynamical Decoupling

We present a randomized dynamical decoupling (DD) protocol that can substantially improve the performance of any given deterministic DD scheme for suppressing coherent noise by using no more than two additional pulses. Our construction is implemented by probabilistically applying sequences of pulses, which, when combined, effectively eliminate the error terms that scale linearly with the system-environment coupling strength. As a result, we show that a randomized protocol using a few pulses can outperform deterministic DD protocols that require considerably more pulses. Furthermore, we prove that the randomized protocol provides an improvement compared to deterministic DD sequences that aim to reduce the error in the system’s Hilbert space, such as Uhrig DD, which had been previously regarded to be optimal. To rigorously evaluate the performance, we introduce new analytical methods suitable for analyzing higher-order DD protocols that might be of independent interest. Here, we also present numerical simulations confirming the significant advantage of using randomized protocols compared to widely used deterministic protocols.

Quantum algorithms & computation↗
DOE OSTI2021

Discrete Time-Crystalline Order Enabled by Quantum Many-Body Scars: Entanglement Steering via Periodic Driving

The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein et al. Science 371, 1355 (2021)] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

FuSED Users Manual, 5.24

The Fusion of Simulation, Experiment, and Data (FuSED) team provides a set of tools for solving inverse problems in structural dynamics and thermal physics, and also sensor placement optimization via Optimal Experimental Design (OED). These methods are used for designing experiments, model calibration, and verification/validation analysis of systems. This document provides a user’s guide to the input for the three apps that are supported for these methods. Details of input specifications, output options, and optimization parameters are included.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Similarity of capacitive radio-frequency discharges in nonlocal regimes

Similarity transformations are essential for correlating discharges at different scales, which are mostly utilized with local field or local energy approximations. In this work, we report the fully kinetic results from particle-in-cell/Monte Carlo collision simulations that unambiguously demonstrate the similarity of radio frequency (rf) discharges in nonlocal regimes where the electron energy relaxation length is much larger than the gap dimension. It is found that at a constant rf voltage amplitude, discharges will be similar if the gas pressure, inverse of gap distance, and rf driving frequency are all changed by the same scaling factor. The scaling relations of fundamental parameters are illustrated for rf discharges in the alpha-mode with secondary electron emission ignored, and the temporal electron kinetics are shown to have invariance in similar discharges. The results explicitly validate the scaling laws in nonlocal kinetic regimes, indicating promising application potentials of the similarity transformations across a wide range of kinetic regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Predicted Reaction Mechanisms, Product Speciation, Kinetics, and Detonation Properties of the Insensitive Explosive 2,6-Diamino-3,5-dinitropyrazine-1-oxide (LLM-105)

2,6-Diamino-3,5-dinitropyrazine-1-oxide (LLM-105) is a relatively new and promising insensitive high-explosive (IHE) material that remains only partially characterized. IHEs are of interest for a range of applications and from a fundamental science standpoint, as the root causes behind insensitivity are poorly understood. In this work, we adopt a multitheory approach based on reactive molecular dynamic simulations performed with density functional theory, density functional tight-binding, and reactive force fields to characterize the reaction pathways, product speciation, reaction kinetics, and detonation performance of LLM-105. We compare and contrast these predictions to 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a prototypical IHE, and 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (HMX), a more sensitive and higher performance material. The combination of different predictive models allows access to processes operative on progressively longer timescales while providing benchmarks for assessing uncertainties in the predictions. We find that the early reaction pathways of LLM-105 decomposition are extremely similar to TATB; they involve intra- and intermolecular hydrogen transfer. Additionally, the detonation performance of LLM-105 falls between that of TATB and HMX. We find agreement between predictive models for first-step reaction pathways but significant differences in final product formations. Predictions of detonation performance result in a wide range of values, and one-step kinetic parameters show the similar reaction rates at high temperatures for three out of four models considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Automated Development of Molten Salt Machine Learning Potentials: Application to LiCl

The in silico modeling of molten salts is critical for emerging "carbon-free" energy applications but is inhibited by the cost of quantum mechanically treating the high polarizabilities of molten salts. Here, we integrate configurational sampling using classical force fields with active learning to automate and accelerate the generation of Gaussian approximation potentials (GAP) for molten salts. This methodology reduces the number of expensive ab initio evaluations required for training set generation to O(100), enabling the facile parametrization of a molten LiCl GAP model that exhibits a 19 000-fold speedup relative to AIMD. The developed molten LiCl GAP model is applied to sample extended spatiotemporal scales, permitting new physical insights into molten LiCl's coordination structure as well as experimentally validated predictions of structures, densities, self-diffusion constants, and ionic conductivities. The developed methodology significantly lowers the barrier to the in silico understanding and design of molten salts across the periodic table.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Shear-induced lift force on spheres in a viscous linear shear flow at finite volume fractions

Several studies have shown a significant increase in drag on a distribution of solid spherical particles within a fluid with increasing particle volume fraction. As a result, many empirical drag laws accounting for the dependence on the Reynolds number and volume fraction can be found in the literature. This study investigates the possibility of a similar effect of the particle volume fraction on the mean hydrodynamic lift force on randomly distributed spherical particles in a linear shear flow. Particle-resolved direct numerical simulations are performed to evaluate the mean lift force, and the results are compared with the case of an isolated particle in a linear shear flow for the same Reynolds number and shear rate. The mean lift force acting on the particles appears to remain nearly the same as that on an isolated particle. However, due to the influence of neighboring particles, there is a substantial force variation in transverse directions on each individual particle, whose magnitude is comparable to the mean drag force. The distribution of drag force in a linear shear flow is shown to be nearly the same as in a uniform flow at the same volume fraction and Reynolds number. A simple stochastic model based on a Gaussian distribution is presented for the lift force variation, and its performance is compared to the prediction of the deterministic pairwise interaction extended point-particle model.

42 ENGINEERING↗
DOE OSTI2021

Time-resolved Rotational Velocities in the Upper Atmosphere of WASP-33 b

While steady empirical progress has been made in understanding the structure and composition of hot-planet atmospheres, direct measurements of velocity signatures, including winds, rotation, and jets, have lagged behind. Quantifying atmospheric dynamics of hot planets is critical for a complete understanding of their atmospheres, and such measurements may even illuminate other planetary properties, such as magnetic field strengths. In this manuscript we present the first detection of the Balmer lines Hα and Hβ in the atmosphere of the ultra-hot Jupiter WASP-33 b. Using atmospheric models that include the effects of atmospheric dynamics, we show that the shape of the average Balmer line transmission spectrum is consistent with rotational velocities in the planet’s thermosphere of v{sub rot}=10.1{sub −1.0}{sup +0.8} km s{sup −1}. We also measure a low-significance day- to nightside velocity shift of −4.6{sub −3.4}{sup +3.4} km s{sup −1} in the transmission spectrum, which is naturally explained by a global wind across the planet’s terminator. In a separate analysis the time-resolved velocity centroids of individual transmission spectra show unambiguous evidence of rotation, with a best-fit velocity of 10.0{sub −2.0}{sup +2.4} km s{sup −1}, consistent with the value of v {sub rot} derived from the shape of the average Balmer line transmission spectrum. Our observations and analysis confirm the power of time-resolved transmission spectra with a high signal-to-noise ratio to measure the velocity structures in exoplanet atmospheres. The high rotational and wind velocities we measure highlight the need for more detailed 3D global climate simulations of the rarefied upper atmospheres of ultra-hot gas giants.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Attosecond Probing of Coherent Vibrational Dynamics in CBr 4

A coherent vibrational wavepacket is launched and manipulated in the symmetric stretch (a1) mode of CBr 4 , by impulsive stimulated Raman scattering (ISRS) from nonresonant 400 nm laser pump pulses with various peak intensities on the order of tens of 10 12 W/cm 2 . Extreme ultraviolet (XUV) attosecond transient absorption spectroscopy (ATAS) records the wavepacket dynamics as temporal oscillations in XUV absorption energy at the bromine M 4,5 3d 3/2,5/2 edges around 70 eV. The results are augmented by nuclear timedependent Schrödinger equation simulations. Slopes of the (Br 3d 3/2,5/2 ) –1 10a 1 * core-excited state potential energy surface (PES) along the a 1 mode are calculated to be –9.4 eV/Å from restricted open-shell Kohn–Sham calculations. Using analytical relations derived for the small-displacement limit and the calculated slopes of the core-excited state PES, a deeper insight into the vibrational dynamics is obtained by retrieving the experimental excursion amplitude of the vibrational wavepacket and the amount of population transferred to the vibrational first-excited state as a function of pump-pulse peak intensity. Experimentally, the results show that XUV ATAS is capable of resolving oscillations in the XUV absorption energy on the order of a few to tens of meV with tens of femtosecond time precision. This corresponds to change in C–Br bond length on the order of 10 –4 to 10 –3 Å. The results and the analytic relationships offer a clear physical picture, on multiple levels of understanding, of how the pump-pulse peak intensity controls the vibrational dynamics launched by nonresonant ISRS in the small-displacement limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Hydrogen Diffusion in Slit Pores: Role of Temperature, Pressure, Confinement, and Roughness

Diffusion of hydrogen (H 2 ) is important to understand the leakage risk and transport behavior for H 2 geologic storage. We applied molecular dynamics simulations to investigate the influencing factors of H2 diffusion in the slit pores of calcite, hematite, and quartz, owing to their abundance. It is revealed that the H2 self-diffusion coefficient increases with the temperature, regardless of the type of pore minerals. The diffusion of H 2 in the 20 nm slit pores falls into the bulk diffusion regime when the pressure is 10 MPa. The self-diffusion of H 2 decreases with pressure in all three types of slit pores, following a power law model with the exponents ranging from -0.825 to -0.964. Furthermore, the impact of confinement on H 2 diffusion is more pronounced for the slit pores with stronger interactions with H 2 -like calcite. The role of surface roughness in H 2 diffusion depends on the slit aperture. The rough surface enhances H 2 diffusion in the larger slit pores due to the enlarged effective pore space, whereas it weakens H 2 diffusion in the small slit pores due to stronger adsorption. These findings will fill the knowledge gap on the coupling effect of different factors influencing H 2 diffusion.

08 HYDROGEN↗
DOE OSTI2021

Dynamics and energy coupling of gas puff Z-pinches on a fast linear transformer driver

Gas puff Z-pinch experiments with annular Ar and Ne gas shells have been conducted on the Compact Experimental System for Z-pinch and Ablation Research (CESZAR) linear transformer driver (LTD) with 500 kA current and 160 ns rise time. Here, we present results from the first systematic gas puff Z-pinch experiments using a fast (≤ 200 ns) LTD as a driver, in which we show that 7% of the stored energy in the capacitors is coupled to plasma kinetic energy as estimated via self-emission and laser schlieren images. 0D and 1D simulations—which do not allow instability growth and thus reach greater maximum average velocities—using initial conditions inferred from experimental implosion trajectories predict coupling in excess of 10% of the stored energy. Additionally, the Ar and Ne implosions were comparably massed and thus achieved similar maximum kinetic energies, though the Ne pinches were more stable and the x-ray pulses were longer and produced higher yield: 2–5 ns and 0.21–0.52 J (0.15–0.37 J/cm) of Ar K-shell and 12–25 ns and 2.2–3.9 J (1.6–2.6 J/cm) of Ne K-shell, respectively. The difference in stability is most likely attributed to variations in initial conditions such as density distribution and gas breakdown initiation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Nuclear two point correlation functions on a quantum computer

The calculation of dynamic response functions is expected to be an early application benefiting from rapidly developing quantum hardware resources. The ability to calculate real-time quantities of strongly correlated quantum systems is one of the most exciting applications that can easily reach beyond the capabilities of traditional classical hardware. Response functions of fermionic systems at moderate momenta and energies corresponding roughly to the Fermi energy of the system are a potential early application because the relevant operators are nearly local, and the energies can be resolved in moderately short real time, reducing the spatial resolution and gate depth required. This is particularly the case in quasielastic electron and neutrino scattering from nuclei, a topic of great interest in the nuclear and particle physics communities and directly related to experiments designed to probe neutrino properties. In this paper we use current quantum hardware and error mitigation protocols to calculate response functions for a highly simplified nuclear model through calculations of a 2-point real time correlation function for a modified Fermi-Hubbard model in two dimensions with three distinguishable nucleons on four lattice sites.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗