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29 records · Page 2

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↗

Effect of Dipole Interactions on Blocking Temperature and Relaxation Dynamics of Superparamagnetic Iron-Oxide (Fe 3 O 4 ) Nanoparticle Systems

The effects of dipole interactions on magnetic nanoparticle magnetization and relaxation dynamics were investigated using five nanoparticle (NP) systems with different surfactants, carrier liquids, size distributions, inter-particle spacing, and NP confinement. Dipole interactions were found to play a crucial role in modifying the blocking temperature behavior of the superparamagnetic nanoparticles, where stronger interactions were found to increase the blocking temperatures. Consequently, the blocking temperature of a densely packed nanoparticle system with stronger dipolar interactions was found to be substantially higher than those of the discrete nanoparticle systems. The frequencies of the dominant relaxation mechanisms were determined by magnetic susceptibility measurements in the frequency range of 100 Hz–7 GHz. The loss mechanisms were identified in terms of Brownian relaxation (1 kHz–10 kHz) and gyromagnetic resonance of Fe 3 O 4 (~1.12 GHz). It was observed that the microwave absorption of the Fe 3 O 4 nanoparticles depend on the local environment surrounding the NPs, as well as the long-range dipole–dipole interactions. These significant findings will be profoundly important in magnetic hyperthermia medical therapeutics and energy applications.

36 MATERIALS SCIENCE↗

Non-Markovian relaxation spectroscopy of fluxonium qubits

Recent studies have shown that parasitic two-level systems (TLS) in superconducting qubits, which are a leading source of decoherence, can have relaxation times longer than the qubits themselves. However, the standard techniques used to characterize qubit relaxation is only valid for measuring T 1 under the Born-Markov approximation and could mask environmental memory effects in practice. Here, we introduce two-timescale relaxometry, a technique to probe the qubit and environment relaxation simultaneously and efficiently. We apply it to high-coherence fluxonium qubits over a frequency range of 0.1-0.4 GHz, and reveal a discrete spectrum of TLS with millisecond lifetimes. Our analysis of the spectrum is consistent with a random distribution of TLS in the aluminum oxide tunnel barrier of the Josephson junction chain of the fluxonium, with a spectral and volumetric density and average electric dipole similar to previous TLS studies at much higher frequencies. Our study suggests that investigating and mitigating TLS in the junction chain is crucial to the development of various types of noise-protected qubits in circuit QED.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Clearing up the Strong $CP$ problem

The absence of a neutron electric dipole moment (EDM) constrains the quantum chromodynamics (QCD) theta angle to be less than one part in ten billion, posing the Strong $CP$ problem. We revisit two classes of proposed solutions. First, we show that when $P$ or $CP$ is realized as a gauged discrete symmetry - as can arise in quantum gravity - the vacuum necessarily preserves $CP$, contrary to recent claims that discrete-symmetry solutions fail. Gauged discrete models face model-building challenges, such as avoiding contributions to the neutron EDM after spontaneous $P$ or $CP$ breaking, but in principle have no fundamental obstructions. Second, we critically examine recent arguments that the Strong $CP$ problem is illusory, demonstrating that a nonzero neutron EDM at finite $\barθ$ follows directly from well-understood QCD dynamics. Taken together, our results reinforce the reality of the Strong $CP$ problem and highlight gauged discrete-symmetry realizations of $P$ or $CP$ as plausible solutions.

FOS: Physical sciences↗

Primary $\gamma$-ray intensities and $\gamma$-strength functions from discrete two-step $\gamma$-ray cascades in radiative proton-capture experiments

Background: Reaction rates of radiative capture reactions can play a crucial role in the nucleosynthesis of heavy nuclei in explosive stellar environments. These reaction rates depend strongly on $\gamma$-ray decay widths in the reaction products, which are, for nonresonant capture reactions at high excitation energies, derived from the $\gamma$-ray strength function and the nuclear level density. Recently, the ratio method was applied to primary $\gamma$ rays observed from ($\textit{d, p}$) reactions and nuclear resonance fluorescence measurements to extract the dipole strength in atomic nuclei and to test the generalized Brink-Axel hypothesis. Purpose: The purpose of this work is to apply the ratio method to primary $\gamma$-ray intensities of the 63,65 Cu($\textit{p},\gamma$) reactions to extract $\gamma$-ray strength information on the nuclei 64,66 Zn. Here, the impact of spin distribution, total $\gamma$-ray decay widths, level densities, and width fluctuations on the application of the ratio method will be discussed. Additionally, by comparing the relative $\gamma$-ray strength at different excitation energies, conclusions on the validity of the generalized Brink-Axel hypothesis can be made. Method: The radiative proton capture reaction measurements have been performed at the HORUS $\gamma$-ray spectrometer of the University of Cologne at one excitation energy for each reaction. Primary $\gamma$-ray intensities have been determined by normalizing secondary $\gamma$-ray transitions in two-step cascades using their absolute branching ratio. The ratio method was applied to the measured primary $\gamma$-ray intensities as well as to previous measurements by Erlandsson et al. at different excitation energies. Results: The relative strength function curve for 64 Zn from our measurement shows no significant deviation from the previous measurement at a different excitation energy. The same is true for 66 Zn where both measurements were at almost the same excitation energy. Absolute $\gamma$-strength function values have been obtained by normalizing the relative curves to quasiparticle random phase approximation calculations because of the absence of experimental data in the respective energy region. Conclusion: The generalized Brink-Axel hypothesis, i.e., the independence of the strength function on the excitation energy, seems to hold in the studied energy region and nuclei. The method to obtain primary $\gamma$-ray intensities from two-step cascade spectra was shown to be a valuable and sensitive tool although its uncertainties are connected to the knowledge of the low-energy level scheme of the investigated nucleus. The scaling in the ratio method should be taken with care, because the relative strength is not a simple sum of $f_{E1}$ and $f_{M1}$ but a somewhat complex linear combination dependent on the excitation energy of the nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Sub Coulomb barrier d+ 208 Pb scattering in the time-dependent basis function approach

We employ the non-perturbative time-dependent basis function (tBF) approach to study the scattering of the deuteron on 208 Pb below the Coulomb barrier. We obtain the bound and discretized scattering states of the projectile, which form the basis representation of the tBF approach, by diagonalizing a realistic Hamiltonian in a large harmonic oscillator basis. We find that the higher-order inelastic scattering effects are noticeable for sub barrier scatterings with the tBF method. We have successfully reproduced experimental sub Coulomb barrier elastic cross section ratios with the tBF approach by considering only the electric dipole (E1) component of the Coulomb interaction between the projectile and the target during scatterings. Here, we find that the correction of the polarization potential to the Rutherford trajectory is dominant in reproducing the data at very low bombarding energies, whereas the role of internal transitions of the deuteron projectile induced by the E1 interaction during the scattering becomes increasingly significant at higher bombarding energies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A coupled vacancy diffusion-dislocation dynamics model for the climb-glide motion of jogged screw dislocations

Here, we develop a novel model to study the climb/glide motion of jogged screw dislocations within the discrete dislocation dynamics (DDD) framework. We present results for the dependence of the climb velocity on the applied stress and on the jog size and distribution statistics. We show that the model predictions are consistent with experimental data in both γ-TiAl and Zircaloy-4. The ranges of the applied stress and jog spacing that determine the dominance of one of three dislocation mechanisms are identified. These are the jog dragging, dipole dragging, and dipole bypass mechanisms, respectively. The overall dislocation motion in the jog dragging regime is composed of glide of screw segments and climb of jogs, controlling the plastic strain and the creep rate, respectively. Based on current simulations and on a detailed examination of the predicted jog heights compared to experiments, we advance the hypothesis that a combination of jog dragging and dipole bypass mechanisms is necessary to reproduce the high creep rate observed in some experiments.

36 MATERIALS SCIENCE↗

A parametric analysis of oilfield design factors affecting the detectability and characterization of electrically conductive hydrofracks

Electrical responses in the vicinity of energized steel-cased well sources offer significant potential for monitoring induced fractures. However, the high complexity of well-fracture-host models spanning multiple length scales compels analysts to simplify their numerical models due to enormous computational costs. This consequently limits our understanding regarding monitoring capabilities and the limitations of electrical measurements on realistic hydraulically fracturing systems. In this paper, we use the hierarchical finite element approach to construct geoelectric models in which geometrically complex fractures and steel-cased wells are discretely represented in 3D conducting media without sacrificing the model realism and computation efficiency. We have discovered systematic numerical analyses of the electrical responses to evaluate the influences of borehole material conductivity and the source type as well as the effects of well geometry, conductivity contrast, source location, fracture growth, and fracture propagation. Furthermore, the numerical results indicate that the borehole material property has a strong control on the electrical potentials along the production and monitoring wells. The monopole source located at a steel-cased well results in a current density distribution that decays away from the source location throughout the well length, whereas the dipole source produces a current density that dominates mainly along the dipole length. Moreover, the conductivity contrast between the fractures and host does not change the overall pattern of the electrical potentials but varies its amplitude. The fracture models near different well systems indicate that the well geometry controls the entire distribution of potentials, while the characteristics of the voltage difference profiles along the wells before and after fracturing are insensitive to the well geometry and the well in which the source is located. Further, the hydraulic-fracturing models indicate that the voltage differences along the production well before and after fracturing have strong sensitivity to fracture growth and fracture set propagation.

58 GEOSCIENCES↗

Non-invertible duality interfaces in field theories with exotic symmetries

In recent years, the concept of global symmetry has generalized considerably. Two dramatic examples of this generalization are the exotic symmetries that govern theories with fractons and non-invertible symmetries, which do not fuse according to a group law. Only recently has the interplay between these two been examined. In this paper, we provide further examples of the interplay in the XY plaquette model, XY cube model, 1+1 d theory with global dipole symmetry, and the 2+1 d Lifshitz theory. They are analogs of the duality symmetries in 2d CTFs and are constructed by first gauging a finite subgroup of the momentum symmetry on half of spacetime and then performing a duality transformation. We analyze the fusion rules of the symmetries and find that they are condensation defects from an analog of higher gauging exotic symmetries. We also address their dependence on the UV cutoff when relevant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Correlated solvent coordinates accelerate multi-donor proton-coupled electron transfer

The rate of charge transfer within a discrete donor–acceptor (D/A) pair is well-described by semi-classical electron transfer theory, but the effects of multiple equivalent redox sites remain less understood. We report a series of ground-state intramolecular proton-coupled electron transfer (PCET) complexes designed to isolate the effects of donor number, N, while holding geometry, coupling, and driving forces constant. The [Ru(L) 3−N (OH) N ] 2+ complexes incorporate one, two, or three identical phenolic electron donors linked to Ru through rigid phenanthroline bridges (OH = 2,4-di-tert-butyl-6-(1-methyl-1H-imidazo[4,5-f][1,10]phenanthrolin-2-yl)phenol). Upon flash photolysis and oxidative quenching with methyl viologen (MV 2+ ), the transient Ru(III) oxidizes an appended phenol by PCET with the hydrogen-bonded imidazole nitrogen atom functioning as the base. The rate increased by 3.4-fold and 5.7-fold (1.7-fold and 1.9-fold after statistical correction) for two- and three-donor complexes compared to the single-donor system. The supra-statistical acceleration is attributed to a reduced effective outer sphere reorganization energy (λ m ) modeled by a partially shared solvent reaction coordinate, in which a subset of solvent dipoles is already oriented to stabilize charge from any donor. The final phenoxyl radical state is localized due to the transfer of a proton, and the recombination reaction with the viologen radical is not accelerated. These results demonstrate the effects of solvent dynamics on intramolecular PCET rates, offering a new strategy for the design of synthetic charge transfer systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Odd-Parity Magnetism Driven by Antiferromagnetic Exchange

Realizing odd-parity, time-reversal-preserving, nonrelativistic spin splitting is a central goal for spintronics applications. We propose a group-theory-based microscopic framework to induce odd-parity spin splitting from coplanar antiferromagnetic (AFM) states without spin-orbit coupling (SOC). We develop phenomenological models for 421 conventional period-doubling AFM systems in nonsymmorphic space groups and construct minimal microscopic models for 119 of these. We find that these AFM states can attain three possible competing ground states. These ground states all break symmetries in addition to those broken by the usual AFM order. Specifically, they give rise to either odd-parity spin-splitting, nematic order, or scalar odd-parity order related to multiferroicity. Our microscopic theories reveal that the odd-parity spin-splitting energy scale is generically large and further reveal that the scalar odd-parity order gives a nonzero Berry curvature dipole without SOC. We identify 67 materials in the Magndata database for which our theory applies. We provide density-functional theory (DFT) calculations on Fe-based materials that reveal an ℎ-wave spin splitting consistent with our symmetry arguments and apply our microscopic model to determine the nonrelativistic Edelstein response for CeNiAsO.

Antiferromagnets↗