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At least 1,045 records · Page 58

Emergent viscous hydrodynamics from a single quantum particle

We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single nonrelativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature T , a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the nonrelativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant γ , which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Furthermore, our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment.

Hydrodynamics↗

Operator dynamics in Floquet many-body systems

We study operator dynamics in many-body quantum systems, focusing on generic features of systems that are ergodic, spatially extended, and lack conserved densities. Quantum circuits of various types provide simple models for such systems. We focus on Floquet quantum circuits, comparing their behavior with what has been found previously for circuits that are random in time. Floquet circuits, which have discrete time-translation symmetry, represent an intermediate case between circuits that are random in time and lack any symmetry, and systems with a time-independent Hamiltonian and continuous time-translation invariance. By making this comparison, one of our aims is to identify signatures of time-translation symmetry in Floquet operator dynamics. To characterize behavior we examine a variety of quantities in solvable models and numerically: operator autocorrelation functions; the partial spectral form factor; the out-of-time-order correlator (OTOC); and the paths in operator space that make the dominant contributions to the ensemble-averaged autocorrelation functions. Our most striking result is that ensemble-averaged autocorrelation functions show behavior that is distinctively different in Floquet systems compared to systems in which successive time-steps are independent. Specifically, while average autocorrelation functions decay on a microscopic timescale for circuits that are random in time, in Floquet systems they have a late-time tail with a duration that grows parametrically with the size of the operator support. In the simplest models this tail is separated from the initial decay by a minimum, so that the average autocorrelation function has an intermediate-time peak. The existence of these tails provides a way to understand deviations of the spectral form factor from random matrix behavior at times shorter than the Thouless time. In contrast to this feature in autocorrelation functions, we find no new aspects to the behavior of OTOCs for Floquet models compared to random-in-time circuits. We show that this difference between averaged autocorrelation functions and OTOCs can be understood in terms of the paths in operator space that contribute to the two quantities: paths for the former retain a limited support at late times, while paths for the latter are dominated by operator spreading. Published by the American Physical Society 2025

Yoshimura, Takato (ORCID:0000000309159846)↗

Coarsening dynamics of Ising-nematic order in a frustrated Heisenberg antiferromagnet

We study the phase ordering dynamics of the classical antiferromagnetic 𝐽 1 −𝐽 2 (nearest-neighbor and next-nearest-neighbor couplings) Heisenberg model on the square lattice in the strong frustration regime (𝐽 2 /𝐽 1 > 1/2). While thermal fluctuations preclude any long-range magnetic order at finite temperatures, the system exhibits a long-range spin-driven nematic phase at low temperatures. The transition into the nematic phase is further shown to belong to the two-dimensional Ising universality class based on the critical exponents near the phase transition. Our large-scale stochastic Landau-Lifshitz-Gilbert simulations find a two-stage phase ordering when the system is quenched from a high-temperature paramagnetic state into the nematic phase. In the early stage, collinear alignments of spins lead to a locally saturated Ising-nematic order. Once domains of well-defined Ising order are developed, the late-stage relaxation is dominated by curvature-driven domain coarsening, as described by the Allen-Cahn equation. The characteristic size of Ising-nematic domains scales as the square root of time, similar to the kinetic Ising model described by the time-dependent Ginzburg-Landau theory. Our results confirm that the late-stage ordering kinetics of the spin-driven nematic, which is a vestigial order of the frustrated Heisenberg model, belongs to the dynamical universality class of a nonconserved Ising order. Interestingly, the system shows no violation of the superuniversality hypothesis under weak bond disorder. The dynamic scaling invariance is preserved in the presence of weak bond disorder. Here, we also discuss possible applications of our results to materials for which vestigial Ising-nematic order is realized.

Antiferromagnets↗

Detailed analysis of excited-state systematics in a lattice QCD calculation of 𝑔 𝐴

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations ≳ 1 fm are commonly used to combat these issues. In this work, focusing on g A , we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2–1 fm), combined with a multistate analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while, for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Global polarization of Λ and $\overline{Λ}$ hyperons in Au + Au collisions at $\sqrt{s_{NN}}$ = 19.6 and 27 GeV

In relativistic heavy-ion collisions, a global spin polarization, 𝑃 H , of Λ and $\overline{Λ}$ hyperons along the direction of the system angular momentum was discovered and measured across a broad range of collision energies and demonstrated a trend of increasing 𝑃 H with decreasing $\sqrt{s_{NN}}$. A splitting between Λ and $\overline{Λ}$ polarization may be possible due to their different magnetic moments in a late-stage magnetic field sustained by the quark-gluon plasma which is formed in the collision. The results presented in this study find no significant splitting at the collision energies of $\sqrt{s_{NN}}$ = 19.6 and 27 GeV in the BNL Relativistic Heavy Ion Collisions Beam Energy Scan Phase II using the STAR detector, with an upper limit of 𝑃 $\overline{Λ}$ – 𝑃 Λ < 0.24% and 𝑃 $\overline{Λ}$ – 𝑃 Λ < 0.35%, respectively, at a 95% confidence level. We derive an upper limit on the naive extraction of the late-stage magnetic field of 𝐵 < 9.4 × 10 12 T and 𝐵 < 1.4 × 10 13 T at $\sqrt{s_{NN}}$ = 19.6 and 27 GeV, respectively, although more thorough derivations are needed. Differential measurements of 𝑃 H were performed with respect to collision centrality, transverse momentum, and rapidity. With our current acceptance of |𝑦| < 1 and uncertainties, we observe no dependence on transverse momentum and rapidity in this analysis. Furthermore, these results challenge multiple existing model calculations following a variety of different assumptions which have each predicted a strong dependence on rapidity in this collision-energy range.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Modeling iterative reconstruction and displacement field in the large scale structure

The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time matter perturbations will be a key to unlock the full potential of these datasets, and the area of initial condition reconstruction is attracting growing attention. Iterative reconstruction developed by Marcel Schmittfull et al. is a technique designed to reconstruct the displacement field from the observed galaxy distribution. The nonlinear displacement field and initial linear density field are highly correlated. Therefore, reconstructing the nonlinear displacement field enables us to extract the primordial cosmological information better than from the late time density field at the level of the two-point statistics. This paper will test to what extent the iterative reconstruction can recover the true displacement field and construct a perturbation theory model for the postreconstructed field. We model the iterative reconstruction process with Lagrangian perturbation theory (LPT) up to third order for dark matter in real space and compare it with N-body simulations. Here we find that the simulated iterative reconstruction does not converge to the nonlinear displacement field, and the discrepancy mainly appears in the shift term, i.e., the term correlated directly with the linear density field. On the contrary, our 3LPT model predicts that the iterative reconstruction should converge to the nonlinear displacement field. We discuss the sources of discrepancy, including numerical noise/artifacts on small scales, and present an ad hoc phenomenological model that improves the agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Model-independent versus model-dependent interpretation of the SDSS-III BOSS power spectrum: Bridging the divide

The traditional clustering analyses of galaxy redshift surveys compress the clustering data into a set of late-time physical variables in a model-independent way. This approach has recently been extended by an additional shape variable encoding early-time physics information. Here we apply this new technique, ShapeFit, to SDSS-III BOSS data and show that it matches the constraining power of alternative, model-dependent approaches, which directly constrain the model’s parameters adopting a cosmological model ab initio. ShapeFit is ~30 times faster, model independent, naturally splits early- and late-time variables, and enables a better control of observational systematics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Interpretable AI forecasting for numerical relativity waveforms of quasicircular, spinning, nonprecessing binary black hole mergers

We present a deep-learning artificial intelligence model (AI) that is capable of learning and forecasting the late-inspiral, merger and ringdown of numerical relativity waveforms that describe quasicircular, spinning, nonprecessing binary black hole mergers. We used the NRHybSur3dq8 surrogate model to produce train, validation and test sets of ℓ = |m| = 2 waveforms that cover the parameter space of binary black hole mergers with mass ratios q ≤ 8 and individual spins |s$^{z}_ {(1,2)}$| ≤ 0.8. These waveforms cover the time range t ∊ [-5000 M, 130 M], where t = 0M marks the merger event, defined as the maximum value of the waveform amplitude. We harnessed the ThetaGPU supercomputer at the Argonne Leadership Computing Facility to train our AI model using a training set of 1.5 million waveforms. We used 16 NVIDIA DGX A100 nodes, each consisting of 8 NVIDIA A100 Tensor Core GPUs and 2 AMD Rome CPUs, to fully train our model within 3.5 h. Our findings show that artificial intelligence can accurately forecast the dynamical evolution of numerical relativity waveforms in the time range t ∊ [-100 M, 130 M]. Sampling a test set of 190,000 waveforms, we find that the average overlap between target and predicted waveforms is ≳99% over the entire parameter space under consideration. We also combined scientific visualization and accelerated computing to identify what components of our model take in knowledge from the early and late-time waveform evolution to accurately forecast the latter part of numerical relativity waveforms. This work aims to accelerate the creation of scalable, computationally efficient and interpretable artificial intelligence models for gravitational wave astrophysics

79 ASTRONOMY AND ASTROPHYSICS↗

Early dark sector, the Hubble tension, and the swampland

We consider the interplay of the Early Dark Energy (EDE) model, the Swampland Distance Conjecture (SDC), and cosmological parameter tensions. EDE is a proposed resolution of the Hubble tension relying upon a near-Planckian scalar field excursion, while the SDC predicts an exponential sensitivity of masses of other fields to such an excursion, m ∝ e –c |ΔΦ|/Mpl with c ~ 0(1). Meanwhile, EDE is in tension with large-scale structure (LSS) data, due to shifts in the standard ΛCDM parameters necessary to fit the cosmic microwave background (CMB). One might hope that a proper treatment of the model, e.g., accounting for the SDC, may ameliorate the tension with LSS. Motivated by these considerations, we introduce the Early Dark Sector (EDS) model, wherein the mass of dark matter is exponentially sensitive to super-Planckian field excursions of the EDE scalar. The EDS model exhibits new phenomenology in both the early and late universe, the latter due to an EDE-mediated dark matter self-interaction. This dark matter-philic "fifth force", while constrained to be small, remains active in the late universe and is not screened in virialized halos. We find that the new interaction with dark matter partially resolves the LSS tension. However, the marginalized posteriors are nonetheless consistent with f EDE = 0 at 95% CL once the Dark Energy Survey Year 3 measurement of S 8 is included. We study constraints on the model from Atacama Cosmology Telescope data, and find a factor of two improvement on the error bar on the SDC parameter c, along with an increased preference for the EDE component. Here, we discuss the implications of these constraints for the SDC, and find the tightest observational constraints to date on a swampland parameter, suggesting that an EDE description of cosmological data is in tension with the SDC.

79 ASTRONOMY AND ASTROPHYSICS↗

Novel features of attractors and transseries in nonconformal Bjorken flows

In this work we investigate the impact of conformal symmetry breaking on hydrodynamization of a far-from-equilibrium fluid. We find a new kind of transseries solutions for the nonconformal hydrodynamic equations of a longitudinal boost invariant expanding plasma. The new transseries solutions unveil a rich physical structure which arises due to the interplay of different physical scales. In the perfect fluid case the nonconformal speed of sound slows down the cooling of the temperature due to the emergence of logarithmic corrections that depends on the mass of the particle. Further, these terms propagate into the perturbative and nonperturbative sectors of the transseries once viscous corrections are included. The logarithmic mass contributions increase the asymptotic value of the Knudsen number while decreasing the damping rate of the transient nonhydrodynamic modes and thus, yielding to an extremely slow hydrodynamization process where flow lines merge to their forward attractor at extremely late times. The early time free streaming expansion is modified and receives logarithmic mass corrections induced by the shear-bulk couplings. The global flow structure and numerical analyses carried out in our work demonstrate the existence of local attraction at early and late times for the shear viscous tensor and bulk viscous pressure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Lagrangian displacement field estimators in cosmology

The late-time nonlinear Lagrangian displacement field is highly correlated with the initial field, so reconstructing it could enable us to extract primordial cosmological information. Our previous work carefully studied the displacement field reconstructed from the late-time density field using the iterative method proposed and found that it does not fully converge to the true, underlying displacement field (e.g., ~8 % offset at k ~ 0.2 h Mpc –1 at z = 0.6 ). We also constructed the Lagrangian perturbation theory model for the reconstructed field, but the model could not explain the discrepancy between the true and the reconstructed fields in the previous work. Here, the main sources of the discrepancy were speculated to be a numerical artifact in the displacement estimator due to the discreteness of the sample. In this paper, we develop two new estimators of the displacement fields to reduce such a numerical discreteness effect, the normalized momentum estimator and the rescaled resumed estimator. We show that the discrepancy reported is not due to the numerical artifacts. We conclude that the method cannot fully reconstruct the shape of the nonlinear displacement field at the redshift we studied, while it is still an efficient baryon acoustic oscillation reconstruction method. In parallel, by properly accounting for the UV-sensitive term in a reconstruction procedure with an effective field theory approach, we improve the theoretical model for the reconstructed displacement field, by almost 5 times, from ~15% to the level of a few percent at k ~ 0.2 h Mpc –1 at the redshift z = 0.6.

79 ASTRONOMY AND ASTROPHYSICS↗

Reviving MeV-GeV indirect detection with inelastic dark matter

Thermal relic dark matter below ∼ 10 GeV is excluded by cosmic microwave background data if its annihilation to visible particles is unsuppressed near the epoch of recombination. Usual model-building measures to avoid this bound involve kinematically suppressing the annihilation rate in the low-velocity limit, thereby yielding dim prospects for indirect detection signatures at late times. In this work, we investigate a class of cosmologically viable sub-GeV thermal relics with late-time annihilation rates that are detectable with existing and proposed telescopes across a wide range of parameter space. We study a representative model of inelastic dark matter featuring a stable state χ 1 and a slightly heavier excited state χ 2 whose abundance is thermally depleted before recombination. Since the kinetic energy of dark matter in the Milky Way is much larger than it is during recombination, χ 1 χ 1 → χ 2 χ 2 upscattering can efficiently regenerate a cosmologically long-lived Galactic population of χ 2 , whose subsequent coannihilations with χ 1 give rise to observable gamma-rays in the ∼ 1 MeV − 100 MeV energy range. We find that proposed MeV gamma-ray telescopes, such as e-ASTROGAM, AMEGO, and MAST, would be sensitive to much of the thermal relic parameter space in this class of models and thereby enable both discovery and model discrimination in the event of a signal at accelerator or direct detection experiments. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Heat transfer and transport property contrast effects on the compressible Rayleigh-Taylor instability

In extreme environments, the Rayleigh-Taylor instability (RTI) may occur under large variations in density and temperature and with fluid transport properties strongly dependent on temperature. Direct numerical simulations of the 3D fully compressible RTI are conducted, examining the idealized configuration of a hotter, less dense fluid pushing against a colder, denser fluid. Various temperature ratios and transport property configurations are explored to examine how heat conduction, large variations in transport properties, and sudden changes in transport properties can affect the evolution of the mixing layer. Nonuniform fluid expansion and contraction induced by heat transfer can significantly affect local density differences and overall instability growth, causing profile asymmetries about the initial interface for flow and mixing statistics. The departures from classical self-similar development of the instability along with misalignment between regions of mixing and regions of most intense turbulent activity caused by both heat transfer and transport property contrasts are examined. After sudden changes in fluid transport properties, which may occur as a result of rapid heating (e.g., in inertial confinement fusion), the flow quickly responds and begins to relax towards quasi-self-similar late-time evolution. For many dynamical quantities such as vorticity and dissipation, this late-time evolution resembles that of the configuration that already started with the final transport property magnitudes, suggesting that these quantities depend only on the transport properties and not on past flow history, provided that the density field distributions for the flows remain similar. On the other hand, the mixing evolution after the transport property change is unique, implying that both property magnitudes and previous history are impactful on the mixing. In conclusion, these simulations demonstrate how various temperature-related effects are extremely important to consider in compressible RTI flows with large temperature variations.

42 ENGINEERING↗

Measurement of pressure gradients near the interface in the viscous fingering instability

The viscous fingering instability, which forms when a less-viscous fluid invades a more-viscous one within a confined geometry, is an iconic system for studying pattern formation. For both miscible and immiscible fluid pairs the growth dynamics change after the initial instability onset and the global structures, typical of late-time growth, are governed by the viscosity ratio. Here we introduce an experimental technique to measure flow throughout the inner and outer fluids. This probes the existence of a new length scale associated with the local pressure gradients around the interface and allows us to compare our results to the predictions of a previously proposed model for late-time finger growth. Published by the American Physical Society 2024

Physics↗

Superspin renormalization and slow relaxation in random spin systems

We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-12 systems. Our formalism is suitable for systems with U(1) and Z2 symmetries, and we apply it to chains of randomly positioned spins with dipolar XX+YY interactions, as arise in Rydberg quantum simulators and other platforms. The formalism generates a sequence of effective Hamiltonians that provide approximate descriptions for dynamics on successively smaller energy scales. These effective Hamiltonians involve “superspins”: two-level collective degrees of freedom constructed from (anti)aligned microscopic spins. Conserved densities can then be understood as relaxing via coherent collective spin flips. For the well-studied simpler case of randomly interacting nearest-neighbor XX+YY chains, the superspins reduce to single spins. Our formalism also leads to a numerical method capable of simulating the dynamics up to an otherwise inaccessible combination of large system size and late time. Focusing on disorder-averaged infinite-temperature autocorrelation functions, in particular the spin survival probability Sp¯(t), we demonstrate quantitative agreement between our algorithm and exact diagonalization (ED) at low but nonzero frequencies. Such agreement holds for chains with nearest-neighbor, next-nearest-neighbor, and long-range dipolar interactions. Our results indicate decay of Sp¯(t) slower than any power law and feature no significant deviation from the ∼1/ln2(t) asymptote expected from the infinite-randomness fixed-point of the nearest-neighbor model. We also apply the RSRG-X formalism to two-dimensional long-range systems of moderate size and find slow late-time decay of Sp¯(t).

Zhao, Yi J↗

Positive Neutrino Masses with DESI DR2 via Matter Conversion to Dark Energy

The Dark Energy Spectroscopic Instrument (DESI) is a massively parallel spectroscopic survey on the Mayall telescope at Kitt Peak, which has released measurements of baryon acoustic oscillations determined from over 14 million extragalactic targets. We combine DESI Data Release 2 with CMB datasets to search for evidence of matter conversion to dark energy (DE), focusing on a scenario mediated by stellar collapse to cosmologically coupled black holes (CCBHs). In this physical model, which has the same number of free parameters as Λ⁢CDM, DE production is determined by the cosmic star formation rate density (SFRD), allowing for distinct early- and late-time cosmologies. Using two SFRDs to bracket current observations, we find that the CCBH model: accurately recovers the cosmological expansion history, agrees with early-time baryon abundance measured by BBN, reduces tension with the local distance ladder, and relaxes constraints on the summed neutrino mass ∑𝑚 𝜈 . For these SFRDs, we find a peaked positive ∑𝑚 𝜈 < 0.149 eV (95% confidence) and ∑𝑚 𝜈 = 0.106$^{+0.050}_{−0.069}$ eV, respectively, in good agreement with lower limits from neutrino oscillation experiments. A peak in ∑𝑚 𝜈 > 0 results from late-time baryon consumption in the CCBH scenario and is expected to be a general feature of any model that converts sufficient matter to dark energy during and after reionization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Biomass yield improvement in switchgrass through genomic prediction of flowering time

The seasonal timing of the transition from vegetative to reproductive growth has a major impact on biomass accumulation in switchgrass. Late-flowering switchgrass cultivars produce greater biomass, a critical trait for sustainable bioenergy production. Genomic prediction (GP) may allow rapid selection of late-flowering individuals with reduced time and expense for field evaluations. To evaluate GP, two flowering time traits (heading date and anthesis date) were collected on 1532 genotypes from four breeding populations: Midwest, Gulf, Atlantic, and Hybrid. These were sequenced using genotype-by-sequencing (530,792 single-nucleotide polymorphisms). Predictive ability of single-trait and multi-trait models were evaluated by cross-validation, by prediction of a progeny trial (n = 122), and through prediction of yield performance in a parallel experiment (n = 52). Predictive ability was not improved by sharing information among breeding groups. Overall, multi-trait models provided an advantage during cross-validation, but a smaller advantage during progeny prediction. Within populations, GP resulted in lower per-cycle progress than previously reported field evaluations (3.1 vs. 5.0 day –1 cycle –1 ). However, GP cycles are potentially much faster than field evaluations. When directly predicting biomass yield, the Hybrid training population had a predictive ability of 0.54–0.63. This reinforces the strong linkage between biomass yields in swards and flowering time. Furthermore, these results highlight the value of GP for rapid yield improvement in switchgrass, particularly in a breeding program designed to share information between biomass yield trials and low-cost flowering time evaluations.

09 BIOMASS FUELS↗

Iron XANES measurements of carbonates and phyllosilicates in CM chondrites: A record of redox conditions during aqueous alteration

Multiple generations of calcite and dolomite precipitated in CM chondrites during ice melting events that led to episodes of liquid water. Models and laboratory analysis have suggested a long-term transition from oxidizing to reducing conditions during aqueous alteration on the CM parent body. We found that synchrotron X-ray absorption near edge spectroscopy (XANES) can detect relative differences in the oxidation state of trace iron within these carbonates. In CM chondrites, previous work interpreted Mn abundance in calcite as an indicator of relatively early or late formation, and dolomite is understood to form relatively late. In the CM1 chondrite Meteorite Hills 01070, XANES maps reveal that Mn-poor calcite contains more oxidized iron relative to Mn-rich calcite. While these measurements of carbonates support increasing iron reduction with progressive aqueous alteration in MET 01070, comparison among different CM chondrites suggests a complex picture of redox evolution. In addition to carbonates, we performed XANES measurements of the phyllosilicate-rich matrix of Allan Hills 83,100. Pre-edge centroid analysis indicates that this CM1/2 has an oxidation state similar to typical CM2 chondrites. While additional measurements are warranted to confirm the full span of redox trends in CM carbonates, our data do not support a correlation between redox state and petrologic type.

Bailey, Elizabeth [Univ. of California, Santa Cruz↗