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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 OSTI2024

Unified understanding of the impact of semiflexibility, concentration, and molecular weight on macromolecular-scale ring diffusion

Conformationally fluctuating, globally compact macromolecules such as polymeric rings, single-chain nanoparticles, microgels, and many-arm stars display complex dynamic behaviors due to their rich topological structure and intermolecular organization. Synthetic rings are hybrid objects with conformations that display both ideal random walk and compact globular features, which can serve as models of genomic DNA. To date, emphasis has been placed on the effect of ring molecular weight on their unusual behaviors. Here, we combine simulations and a microscopic force-level theory to build a unified understanding for how key aspects of ring dynamics depend on different tunable molecular properties including backbone rigidity, monomer concentration, degree of traditional entanglement, and molecular weight. Our large-scale molecular dynamics simulations of ring melts with very different backbone stiffnesses reveal unanticipated behaviors which agree well with our generalized theory. This includes a universal master curve for center-of-mass diffusion constants as a function of molecular weight scaled by a chemistry and thermodynamic state-dependent critical molecular weight that generalizes the concept of an entanglement cross-over for linear chains. The key physics is how backbone rigidity and monomer concentration induced changes of the entanglement length, interring packing, degree of interpenetration, and liquid compressibility slow down space-time dynamic-force correlations on macromolecular scales. A power law decay of the center-of-mass diffusion constant with inverse molecular weight squared is the first consequence, followed by an ultraslow activated hopping transport regime. Our results set the stage to address slow dynamics and kinetic arrest in different families of compact synthetic and biological polymeric systems.

Science & Technology - Other Topics↗

DOE OSTI2023

Atomic Dynamics of Multi‐Interfacial Migration and Transformations

Redox-induced interconversions of metal oxidation states typically result in multiple phase boundaries that separate chemically and structurally distinct oxides and suboxides. Directly probing such multi-interfacial reactions is challenging because of the difficulty in simultaneously resolving the multiple reaction fronts at the atomic scale. Using the example of CuO reduction in H 2 gas, a reaction pathway of CuO → monoclinic m-Cu 4 O 3 → Cu 2 O is demonstrated and identifies interfacial reaction fronts at the atomic scale, where the Cu 2 O/m-Cu 4 O 3 interface shows a diffuse-type interfacial transformation; while the lateral flow of interfacial ledges appears to control the m-Cu 4 O 3 /CuO transformation. Together with atomistic modeling, it is shown that such a multi-interface transformation results from the surface-reaction-induced formation of oxygen vacancies that diffuse into deeper atomic layers, thereby resulting in the formation of the lower oxides of Cu 2 O and m-Cu 4 O 3 , and activate the interfacial transformations. In conclusion, these results demonstrate the lively dynamics at the reaction fronts of the multiple interfaces and have substantial implications for controlling the microstructure and interphase boundaries by coupling the interplay between the surface reaction dynamics and the resulting mass transport and phase evolution in the subsurface and bulk.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Spatially resolved charge-transfer kinetics at the quantum dot–microbe interface using fluorescence lifetime imaging microscopy

Integrating the optoelectronic properties of quantum dots (QDs) with biological enzymatic systems to form microbe-semiconductor biohybrids offers promising prospects for both solar-to-chemical conversion and light-modulated biochemical processes. Developing these nano–bio hybrid systems necessitates a deep understanding of charge-transfer dynamics at the nano–bio interface. Photoexcited carrier transfer from QDs to microbes is driven by complex interactions, with emerging insights into the relevant thermodynamic and kinetic factors. The heterogeneities of both microbes and QD ensembles pose significant challenges in mechanistic understanding, which is critical for designing advanced nano–bio hybrids. We used fluorescence lifetime imaging microscopy to analyze charge transfer between a CdSe QD film andShewanella oneidensismicrobes. We correlated the spatiotemporal fluorescence data with an analytical model. Our analysis revealed two distinct distributions of QD de-excitation pathways. The characteristics of these distributions: 1) a faster transfer rate ( k ¯ E T 1 = 1.5 10 9 s - 1 ), with a lower acceptor number ( N ¯ a 1 = 0.03 ) and 2) a slower transfer rate ( k ¯ E T 2 = 4.1 10 8 s - 1 ) with a higher acceptor number ( N ¯ a 2 = 0.18 ). We assign these distributions to the indirect and direct electron transfer mechanisms, respectively. Our findings demonstrate how spectroscopic imaging can uncover fundamental electron transfer mechanisms at complex interfaces, offering valuable design principles for future nano–bio hybrids.

Science & Technology - Other Topics↗

DOE OSTI2024

Secondary structure determines electron transport in peptides

Proteins play a key role in biological electron transport, but the structure–function relationships governing the electronic properties of peptides are not fully understood. Despite recent progress, understanding the link between peptide conformational flexibility, hierarchical structures, and electron transport pathways has been challenging. Here, we use single-molecule experiments, molecular dynamics (MD) simulations, nonequilibrium Green’s function-density functional theory (NEGF-DFT), and unsupervised machine learning to understand the role of secondary structure on electron transport in peptides. Our results reveal a two-state molecular conductance behavior for peptides across several different amino acid sequences. MD simulations and Gaussian mixture modeling are used to show that this two-state molecular conductance behavior arises due to the conformational flexibility of peptide backbones, with a high-conductance state arising due to a more defined secondary structure (beta turn or 3 10 helices) and a low-conductance state occurring for extended peptide structures. These results highlight the importance of helical conformations on electron transport in peptides. Conformer selection for the peptide structures is rationalized using principal component analysis of intramolecular hydrogen bonding distances along peptide backbones. Molecular conformations from MD simulations are used to model charge transport in NEGF-DFT calculations, and the results are in reasonable qualitative agreement with experiments. Projected density of states calculations and molecular orbital visualizations are further used to understand the role of amino acid side chains on transport. Overall, our results show that secondary structure plays a key role in electron transport in peptides, which provides broad avenues for understanding the electronic properties of proteins.

Science & Technology - Other Topics↗

DOE OSTI2025

Experimental and theoretical evidence of universality in superfluid vortex reconnections

The minimum separation between reconnecting vortices in fluids and superfluids obeys a universal scaling law with respect to time. The prereconnection and the postreconnection prefactors of this scaling law are different, a property related to irreversibility and to energy transfer and dissipation mechanisms. In the present work, we determine the temperature dependence of these prefactors in superfluid helium from experiments and a numeric model which fully accounts for the coupled dynamics of the superfluid vortex lines and the thermal normal fluid component. At all temperatures, we observe a pre- and postreconnection asymmetry similar to that observed in other superfluids and in classical viscous fluids, indicating that vortex reconnections display a universal behavior independent of the small-scale regularizing dynamics. We also numerically show that each vortex reconnection event represents a sudden injection of energy in the normal fluid. Finally we argue that in a turbulent flow, these punctuated energy injections can sustain the normal fluid in a perturbed state, provided that the density of superfluid vortices is large enough.

Reconnections↗

DOE OSTI2024

Osmotic and phoretic competition explains chemotaxic assembly and sorting

Microscale objects responding to chemical gradients by migrating toward or away from a preferred species is a simple yet constitutive mechanism by which transport occurs in biological organisms. Synthetic chemotaxis provides key physical descriptions of simplified systems that can be used in biological models, or in the creation of advanced responsive material systems. In this article, we provide a quantitative framework for understanding synthetic chemotaxis of microparticles which involves a competition between phoresis and osmosis. We present separate quantitative measurements of phoresis and osmosis acting on individual taxing particles, finding that phoresis follows the long-predicted v ∼ 1 / r 2 scaling while the osmotic contribution depends on the geometry and details of the system, and must be solved on a case-by-case basis. Through this, we are able to develop a more accurate picture of particle transport at the single particle level. Equipped with this approach, we go on to describe how high concentrations of particles in a symmetric chemical gradient grow close-packed hives that reach a steady-state size tunable through light intensity or particle size. Last, we demonstrate that mixed particles experiencing the same chemical gradient will selectively migrate toward or away depending on the nature of the particle surface, thereby locally sorting out a particular species. We anticipate these results will be important in describing both biological and synthetic chemotaxis in phoretic systems and should bring a wealth of studies that take advantage of competing osmotic flows to illicit unexpected dynamic active behavior.

Science & Technology - Other Topics↗

DOE OSTI2024

Associations between regional blood-brain barrier permeability, aging, and Alzheimer’s disease biomarkers in cognitively normal older adults

Background Increased blood-brain barrier permeability (BBBp) has been hypothesized as a feature of aging that may lead to the development of Alzheimer’s disease (AD). We sought to identify the brain regions most vulnerable to greater BBBp during aging and examine their regional relationship with neuroimaging biomarkers of AD. Methods We studied 31 cognitively normal older adults (OA) and 10 young adults (YA) from the Berkeley Aging Cohort Study (BACS). Both OA and YA received dynamic contrast-enhanced MRI (DCE-MRI) to quantify K trans values, as a measure of BBBp, in 37 brain regions across the cortex. The OA also received Pittsburgh compound B (PiB)-PET to create distribution volume ratios (DVR) images and flortaucipir (FTP)- PET to create partial volume corrected standardized uptake volume ratios (SUVR) images. Repeated measures ANOVA assessed the brain regions where OA showed greater BBBp than YA. In OA, K trans values were compared based on sex, Aβ positivity status, and APOE4carrier status within a composite region across the areas susceptible to aging. We used linear models and sparse canonical correlation analysis (SCCA) to examine the relationship between K trans and AD biomarkers. Results OA showed greater BBBp than YA predominately in the temporal lobe, with some involvement of parietal, occipital and frontal lobes. Within an averaged ROI of affected regions, there was no difference in K trans values based on sex or Aβ positivity, but OA who were APOE4carriers had significantly higher K trans values. There was no direct relationship between averaged K trans and global Aβ pathology, but there was a trend for an Ab status by tau interaction on K trans in this region. SCCA showed increased K trans was associated with increased PiB DVR, mainly in temporal and parietal brain regions. There was not a significant relationship between K trans and FTP SUVR. Discussion Our findings indicate that the BBB shows regional vulnerability during normal aging that overlaps considerably with the pattern of AD pathology. Greater BBBp in brain regions affected in aging is related to APOE genotype and may also be related to the pathological accumulation of Aβ.

Science & Technology - Other Topics↗

DOE OSTI2025

Non-equilibrium critical scaling and universality in a quantum simulator

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e. a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Measurement of the Neutron Electromagnetic Form Factor Ratio at High Momentum Transfer

The inner structure of the nucleon (proton and neutron) remains a topic of great interest in nuclear and particle physics, after many decades of study. For example, understanding the quark-gluon dynamics inside the nucleon would shed light on how 99% of the nucleon mass is created. The neutron electromagnetic form factors, Gn E and Gn M , give important insights into the neutron structure. The Super BigBite Spectrometer (SBS) program at Jefferson Lab (JLab) seeks to extend the form factor measurements for both the proton and the neutron. The neutron electric form actor, Gn E , has been historically difficult to measure due to the short lifetime of the free neutron and the small value of Gn E . The GEn-II experiment is part of the SBS program and seeks to measure Gn E , significantly increasing the high momentum transfer coverage. A newly designed polarized 3He target increased the figure of merit by three times compared to previous measurements. The analysis of this data is especially challenging due to the unprecedented high-rate environment caused by the open nature of the spectrometer with a direct line of sight to the target. This required developing new Gas Electron Multiplier (GEM) particle trackers which can cover large areas demanded by this setup and handle particle rates up to 500 kHz/cm2. Rates this high over a large area is unprecedented in particle tracking systems and came with a number of challenges. Data taken in the SBS program was critical to understanding hardware and software solutions that improved the track reconstruction efficiency to be >97% with a position resolution of 70 ?m. In previous experiments the proton electromagnetic form factors, Gp E and Gp M were measured up to Q2 = 8.5 GeV2 and Q2 = 30 GeV2, respectively, while Gn E has only been measured up to Q2 = 3.4 GeV2. The GEn-II experiment has measured the neutron form factor ratio, Gn E/Gn M, at Q2 values of 2.90, 6.50, and 9.47 GeV2 by scattering a polarized electron beam with a polarized 3He target, used here as an effective polarized neutron target, and measuring the double spin asymmetry of the cross section. Previous Gn E measurements do not extend above Q2 = 3.4 GeV2, and therefore this analysis has extended the world data by almost three times. The background correction is especially difficult at the higher Q2 settings leading to large systematic errors. As very exploratory results from this early analysis of the data, we find for Q2 = 2.90 GeV2, Gn E = 0.0157 ±stat 0.0016 ±sys 0.0011, for Q2 = 6.50 GeV2, Gn E = 0.0067 ±stat 0.0019 ±sys 0.0005, and for Q2 = 9.46 GeV2, Gn E = 0.0046 ±stat 0.0023 ±sys 0.0005. These results are compared to predictions from the Dyson-Schwinger Equations (DSE) model and a Relativistic Constituent Quark Model (RCQM).

Jeffas, Sean↗

DOE OSTI2024

Coarse-graining Hamiltonian systems using WSINDy

Abstract Weak form equation learning and surrogate modeling has proven to be computationally efficient and robust to measurement noise in a wide range of applications including ODE, PDE, and SDE discovery, as well as in coarse-graining applications, such as homogenization and mean-field descriptions of interacting particle systems. In this work we extend this coarse-graining capability to the setting of Hamiltonian dynamics which possess approximate symmetries associated with timescale separation. A smooth $$\varepsilon$$ ε -dependent Hamiltonian vector field $$X_\varepsilon$$ X ε possesses an approximate symmetry if the limiting vector field $$X_0=\lim _{\varepsilon \rightarrow 0}X_\varepsilon$$ X 0 = lim ε → 0 X ε possesses an exact symmetry. Such approximate symmetries often lead to the existence of a Hamiltonian system of reduced dimension that may be used to efficiently capture the dynamics of the symmetry-invariant dependent variables. Deriving such reduced systems, or approximating them numerically, is an ongoing challenge. We demonstrate that WSINDy can successfully identify this reduced Hamiltonian system in the presence of large perturbations imparted in the $$\varepsilon >0$$ ε > 0 regime, while remaining robust to extrinsic noise. This is significant in part due to the nontrivial means by which such systems are derived analytically. WSINDy naturally preserves the Hamiltonian structure by restricting to a trial basis of Hamiltonian vector fields. The methodology is computationally efficient, often requiring only a single trajectory to learn the global reduced Hamiltonian, and avoiding forward solves in the learning process. In this way, we argue that weak-form equation learning is particularly well-suited for Hamiltonian coarse-graining. Using nearly-periodic Hamiltonian systems as a prototypical class of systems with approximate symmetries, we show that WSINDy robustly identifies the correct leading-order system, with dimension reduced by at least two, upon observation of the relevant degrees of freedom. While our main contribution is computational, we also provide a contribution to the literature on averaging theory by proving that first-order averaging at the level of vector fields preserves Hamiltonian structure in nearly-periodic Hamiltonian systems. This provides theoretical justification for our approach as WSINDy’s computations occur at the level of Hamiltonian vector fields. We illustrate the efficacy of our proposed method using physically relevant examples, including coupled oscillator dynamics, the Hénon–Heiles system for stellar motion within a galaxy, and the dynamics of charged particles.

97 MATHEMATICS AND COMPUTING↗