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In thermalizing many-body quantum systems without conservation laws such as ergodic Floquet and random unitary circuits, local expectation values are predicted to decay to their equilibrium values exponentially quickly. In this work we derive a relationship between said exponential decay rate $\overline{g}$ and the operator spreading properties of a local unitary evolution. A hydrodynamical picture for operator spreading allows us to argue that, for random unitary circuits, $\overline{g}$ is encoded by the leading eigenvalue of a dynamical map obtained by enriching unitary dynamics with dissipation, in the limit of weak dissipation. We argue that the size of the eigenvalue does not depend on the details of this weak dissipation (given mild assumptions on properties of the ergodic dynamics), so long as it only suppresses large operators significantly. Our calculations are based on analytical results for random unitary circuits, but we argue that similar results hold for ergodic Floquet systems. These conjectures are in accordance with existing results which numerically obtain quantum many-body analogues of classical Ruelle-Pollicott resonances [T. Prosen J. Phys. A: Math. Gen. 35 L737 (2002), T. Mori, arXiv:2311.10304] by studying unitary evolutions subject to weak dissipation., Comment: 5.5 pages, 2 figures, 7 pages supplemental material

Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a scale set by the scattering length, finding the intuitive result that the diffusion constant scales as $D \propto 1/\rho$ at low densities $\rho$. Our numerical approach generalizes the Dissipation-Assisted Operator Evolution (DAOE) algorithm: in the spirit of the BBGKY hierarchy, we effectively approximate non-local operators by their ensemble averages, rather than discarding them entirely. This greatly reduces the operator entanglement entropy, while still giving accurate predictions for diffusion constants across all density scales. We further construct a minimal model for the transport crossover, yielding charge correlation functions which agree well with our numerical data. Our results clarify the dominant contributions to hydrodynamic correlation functions of conserved densities, and serve as a guide for generalizations to low temperature transport., Comment: 5 + 9 pages, 3 + 3 figures. Comments welcome!

The National Science Foundation's Daniel K. Inouye Solar Telescope (DKIST) will provide high-resolution, multi-line spectropolarimetric observations that are poised to revolutionize our understanding of the Sun. Given the massive data volume, novel inference techniques are required to unlock its full potential. Here, we provide an overview of our "SPIn4D" project, which aims to develop deep convolutional neural networks (CNNs) for estimating the physical properties of the solar photosphere from DKIST spectropolarimetric observations. We describe the magnetohydrodynamic (MHD) modeling and the Stokes profile synthesis pipeline that produce the simulated output and input data, respectively. These data will be used to train a set of CNNs that can rapidly infer the four-dimensional MHD state vectors by exploiting the spatiotemporally coherent patterns in the Stokes profile time series. Specifically, our radiative MHD model simulates the small-scale dynamo actions that are prevalent in quiet-Sun and plage regions. Six cases with different mean magnetic fields have been conducted; each case covers six solar-hours, totaling 109 TB in data volume. The simulation domain covers at least $25\times25\times8$ Mm with $16\times16\times12$ km spatial resolution, extending from the upper convection zone up to the temperature minimum region. The outputs are stored at a 40 s cadence. We forward model the Stokes profile of two sets of Fe I lines at 630 and 1565 nm, which will be simultaneously observed by DKIST and can better constrain the parameter variations along the line of sight. The MHD model output and the synthetic Stokes profiles are publicly available, with 13.7 TB in the initial release., Comment: Submitted to AAS Journals after revision. Comments welcome

Most currently deployed large language models (LLMs) undergo continuous training or additional finetuning. By contrast, most research into LLMs' internal mechanisms focuses on models at one snapshot in time (the end of pre-training), raising the question of whether their results generalize to real-world settings. Existing studies of mechanisms over time focus on encoder-only or toy models, which differ significantly from most deployed models. In this study, we track how model mechanisms, operationalized as circuits, emerge and evolve across 300 billion tokens of training in decoder-only LLMs, in models ranging from 70 million to 2.8 billion parameters. We find that task abilities and the functional components that support them emerge consistently at similar token counts across scale. Moreover, although such components may be implemented by different attention heads over time, the overarching algorithm that they implement remains. Surprisingly, both these algorithms and the types of components involved therein can replicate across model scale. These results suggest that circuit analyses conducted on small models at the end of pre-training can provide insights that still apply after additional pre-training and over model scale.

The non-linear dynamics of General Relativity leave their imprint on remnants of black hole mergers in the form of a recoil ``kick''. The kick has profound astrophysical implications across the black hole mass range from stellar to super-massive. However, a robust measurement of the kick for generic binaries from gravitational-wave observations has proved so far to be extremely challenging. In this \emph{letter}, we demonstrate the prospects of measuring black hole kicks through a multiband gravitational-wave network consisting of space mission LISA, the current earth-based detector network and a third-generation detector. For two distinct cases of remnant black hole kick (68 km/s, 1006 km/s) emerging from near identical pre-merger configuration of GW190521 -- the first confirmed intermediate-mass black hole -- we find that the multiband network will recover with 90\% credible level the projection of the kick vector relative to the orbital plane within tens of km/s accuracy. Such precise measurement of the kick offer a new set of multi-messenger follow-ups and unprecedented tests of astrophysical formation channels., Comment: 11 pages, 4 figures, 2 tables

The Black Hole Explorer (BHEX) is a mission concept that can dramatically improve state-of-the-art astronomical very long baseline interferometry (VLBI) imaging resolution by extending baseline distances to space. To support these scientific goals, a high data rate downlink is required from space to ground. Laser communications is a promising option for realizing these high data rate, long-distance space-to-ground downlinks with smaller space/ground apertures. Here, we present a scalable laser communications downlink design and current lasercom mission results., Comment: Submitted to SPIE Astronomical Telescopes + Instrumentation, 2024

We study entanglement growth in a harmonic oscillator chain subjected to the weak measurement of observables which have been smeared-out over a length scale $R$. We find that entanglement grows diffusively ($S \sim t^{1/2}$) for a large class of initial Gaussian states provided the measurement scale $R$ is sufficiently large. At late times $t \gtrsim \mathcal{O}(L^{2})$ the entropy relaxes towards an area-law value which we compute exactly. We propose a modified quasi-particle picture which accounts for all of these main features and agrees quantitatively well with our essentially exact numerical results. The quasiparticles are associated with the modes of a non-Hermitian effective Hamiltonian. At small wave-vector $k$, the quasiparticles transport entropy with a finite velocity, but have a lifetime scaling as $1/k^2$; the concurrence of these two conditions leads directly to the observed $t^{1/2}$ growth.

Doped semiconductors are a central and crucial component of all integrated circuits. By using a combination of white light and a focused laser beam, and exploiting hBN defect states, heterostructures of hBN/Graphene/hBN are photodoped in-operando, reproducibly and reversibly. We demonstrate device geometries with spatially-defined doping type and magnitude. After each optical doping procedure, magnetotransport measurements including quantum Hall measurements are performed to characterize the device performance. In the unipolar (p+-p-p+ and n-n+-n) configurations, we observe quantization of the longitudinal resistance, proving well-defined doped regions and interfaces that are further analyzed by Landauer-Buttiker modeling. Our unique measurements and modeling of these optically doped devices reveal a complete separation of the p- and n-Landau level edge states. The non-interaction of the edge states results in an observed "insulating" state in devices with a bi-polar p-n-p configuration that is uncommon and has not been measured previously in graphene devices. This insulating state could be utilized in high-performance graphene electrical switches. These quantitative magnetotransport measurements confirm that these doping techniques can be applied to any 2D materials encapsulated within hBN layers, enabling versatile, rewritable circuit elements for future computing and memory applications.

Baltimore City Public Schools includes approximately 30 high schools, and the characteristics of each school's graduates vary systematically according to schools' admissions policies, curricular areas of focus, and resource availability, which depend on school size, management type, and leaders' priorities. This report summarizes trends in college-related outcomes among City Schools graduates over a ten-year timespan, from 2011 to 2020. The data presented centers on core activities in accessing college, from applying for admission and financial aid, to college enrollment and, ultimately, degree completion. The authors acknowledge that pursuing postsecondary education is but one path to independent adulthood. Many young adults wish to engage in other types of training and preparation that are not represented in this report, such as apprenticeships, on-the-job training, and military service. However, research concludes that individuals with at least some college education have higher lifetime earnings (Kim & Tamborini, 2019), better health outcomes (Kaplan et al., 2017), and greater civic engagement (Campbell, 2009). Moreover, higher education attainment in the aggregate yields benefits for the local economy (Koropeckyj et al., 2017) and greater well-being for the community (Baum et al., 2013). The authors thus offer the data in this report as one means of monitoring opportunity for Baltimore youth and Baltimore City as a whole.

Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits -- a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focussing on the \emph{spectral form factor}, i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions., Comment: 22 pages, 12 figures

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general \textit{syntax} of structural recursion, coupled with two different frameworks for understanding their \textit{semantics} -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art large language models (LLMs) to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function., Comment: arXiv admin note: text overlap with arXiv:2305.14699

Charge and energy are expected to diffuse in interacting systems of fermions at finite temperatures, even in the absence of disorder, with the interactions inducing a crossover from the coherent and ballistic streaming of quasi-particles at early times, to incoherent diffusive behavior at late times. The relevant crossover timescales and the transport coefficients are both controlled by the strength of interactions. In this work we develop a numerical method to simulate such systems at high temperatures, applicable in a wide range of interaction strengths, by adapting Dissipation-assisted Operator Evolution (DAOE) to fermions. Our fermion DAOE, which approximates the exact dynamics by systematically discarding information from high $n$-point functions, is tailored to capture non-interacting dynamics exactly, thus providing a good starting point for the weakly interacting problem. Applying our method to a microscopic model of weakly interacting fermions, we numerically demonstrate that the crossover from ballistic to diffusive transport happens at a time $t_D\sim1/\Delta^{2}$ and that the diffusion constant similarly scales as $D \sim 1/\Delta^2$, where $\Delta$ is the interaction strength. We substantiate this scaling with a Fermi's golden rule calculation in the operator spreading picture, interpreting $t_D$ as the fermion-fermion scattering time and lifetime of the single-particle Green's function.

The operator growth hypothesis (OGH) is a technical conjecture about the behaviour of operators -- specifically, the asymptotic growth of their Lanczos coefficients -- under repeated action by a Liouvillian. It is expected to hold for a sufficiently generic closed many-body system. When it holds, it yields bounds on the high frequency behavior of local correlation functions and measures of chaos (like OTOCs). It also gives a route to numerically estimating response functions. Here we investigate the generalisation of OGH to open quantum systems, where the Liouvillian is replaced by a Lindbladian. For a quantum system with local Hermitian jump operators, we show that the OGH is modified: we define a generalisation of the Lanczos coefficient and show that it initially grows linearly as in the original OGH, but experiences exponentially growing oscillations on scales determined by the dissipation strength. We see this behavior manifested in a semi-analytically solvable model (large-q SYK with dissipation), numerically for an ergodic spin chain, and in a solvable toy model for operator growth in the presence of dissipation (which resembles a non-Hermitian single-particle hopping process). Finally, we show that the modified OGH connects to a fundamental difference between Lindblad and closed systems: at high frequencies, the spectral functions of the former decay algebraically, while in the latter they decay exponentially. This is an experimentally testable statement, which also places limitations on the applicability of Lindbladians to systems in contact with equilibrium environments., Comment: 9 pages, 6 figures

Sentiment is a pervasive feature in natural language text, yet it is an open question how sentiment is represented within Large Language Models (LLMs). In this study, we reveal that across a range of models, sentiment is represented linearly: a single direction in activation space mostly captures the feature across a range of tasks with one extreme for positive and the other for negative. Through causal interventions, we isolate this direction and show it is causally relevant in both toy tasks and real world datasets such as Stanford Sentiment Treebank. Through this case study we model a thorough investigation of what a single direction means on a broad data distribution. We further uncover the mechanisms that involve this direction, highlighting the roles of a small subset of attention heads and neurons. Finally, we discover a phenomenon which we term the summarization motif: sentiment is not solely represented on emotionally charged words, but is additionally summarized at intermediate positions without inherent sentiment, such as punctuation and names. We show that in Stanford Sentiment Treebank zero-shot classification, 76% of above-chance classification accuracy is lost when ablating the sentiment direction, nearly half of which (36%) is due to ablating the summarized sentiment direction exclusively at comma positions.

Despite a growing sample of precisely measured stellar rotation periods and ages, the strength of magnetic braking and the degree of departure from standard (Skumanich-like) spindown have remained persistent questions, particularly for stars more evolved than the Sun. Rotation periods can be measured for stars older than the Sun by leveraging asteroseismology, enabling models to be tested against a larger sample of old field stars. Because asteroseismic measurements of rotation do not depend on starspot modulation, they avoid potential biases introduced by the need for a stellar dynamo to drive starspot production. Using a neural network trained on a grid of stellar evolution models and a hierarchical model-fitting approach, we constrain the onset of weakened magnetic braking. We find that a sample of stars with asteroseismically-measured rotation periods and ages is consistent with models that depart from standard spindown prior to reaching the evolutionary stage of the Sun. We test our approach using neural networks trained on model grids produced by separate stellar evolution codes with differing physical assumptions and find that the choices of grid physics can influence the inferred properties of the braking law. We identify the normalized critical Rossby number ${\rm Ro}_{\rm crit}/{\rm Ro}_\odot = 0.91\pm0.03$ as the threshold for the departure from standard rotational evolution. This suggests that weakened magnetic braking poses challenges to gyrochronology for roughly half of the main sequence lifetime of sun-like stars., Comment: 26 pages, 10 figures

Humanity has wondered whether we are alone for millennia. The discovery of life elsewhere in the Universe, particularly intelligent life, would have profound effects, comparable to those of recognizing that the Earth is not the center of the Universe and that humans evolved from previous species. There has been rapid growth in the fields of extrasolar planets and data-driven astronomy. In a relatively short interval, we have seen a change from knowing of no extrasolar planets to now knowing more potentially habitable extrasolar planets than there are planets in the Solar System. In approximately the same interval, astronomy has transitioned to a field in which sky surveys can generate 1 PB or more of data. The Data-Driven Approaches to Searches for the Technosignatures of Advanced Civilizations_ study at the W. M. Keck Institute for Space Studies was intended to revisit searches for evidence of alien technologies in light of these developments. Data-driven searches, being able to process volumes of data much greater than a human could, and in a reproducible manner, can identify *anomalies* that could be clues to the presence of technosignatures. A key outcome of this workshop was that technosignature searches should be conducted in a manner consistent with Freeman Dyson's "First Law of SETI Investigations," namely "every search for alien civilizations should be planned to give interesting results even when no aliens are discovered." This approach to technosignatures is commensurate with NASA's approach to biosignatures in that no single observation or measurement can be taken as providing full certainty for the detection of life. Areas of particular promise identified during the workshop were (*) Data Mining of Large Sky Surveys, (*) All-Sky Survey at Far-Infrared Wavelengths, (*) Surveys with Radio Astronomical Interferometers, and (*) Artifacts in the Solar System., Comment: Final Report prepared for the W. M. Keck Institute for Space Studies (KISS), http://kiss.caltech.edu/workshops/technosignatures/technosignatures.html ; eds. Lazio, Djorgovski, Howard, & Cutler; The study leads gratefully acknowledge the outstanding support of Michele Judd, KISS Executive Director, and her dedicated staff, who made the study experience invigorating and enormously productive

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors of the non-Hermitian operators that generate the dynamics, i.e., quantum channels (Markov chains). However, since these operators are non-Hermitian, their spectra are an unreliable guide to dynamical relaxation timescales or to stability against perturbations. We propose an alternative dynamical criterion for a steady state to be in a stable phase, which we name uniformity: informally, our criterion amounts to requiring that, under sufficiently small local perturbations of the dynamics, the unperturbed and perturbed steady states are related to one another by a finite-time dissipative evolution. We show that this criterion implies many of the properties one would want from any reasonable definition of a phase. We prove that uniformity is satisfied in a canonical classical cellular automaton, and provide numerical evidence that the gap determines the relaxation rate between nearby steady states in the same phase, a situation we conjecture holds generically whenever uniformity is satisfied. We further conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability., Comment: v2: Added section on relationship to previous literature

Recent findings suggest that shell protein distribution and morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. We explore how the morphology and component patterning are coupled through the competition of mean and Gaussian bending energies in multicomponent elastic shells that form three component irregular polyhedra. We observe two softer components with lower bending rigidities allocate on the edges and vertices while the harder component occupies the faces. When subjected to a non-zero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the Gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains $\approx 2$. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments and, moreover, can be realized in synthetic vesicles.

The NANOGrav 15-year data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15-year observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values, or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach sub-parsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations., Comment: Accepted by Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org. Edited to fix two equation typos (Eq.13 & 21), and minor text typos

The 15-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons., Comment: 74 pages, 31 figures, 4 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15-year pulsar-timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. The correlations follow the Hellings-Downs pattern expected for a stochastic gravitational-wave background. The presence of such a gravitational-wave background with a power-law-spectrum is favored over a model with only independent pulsar noises with a Bayes factor in excess of $10^{14}$, and this same model is favored over an uncorrelated common power-law-spectrum model with Bayes factors of 200-1000, depending on spectral modeling choices. We have built a statistical background distribution for these latter Bayes factors using a method that removes inter-pulsar correlations from our data set, finding $p = 10^{-3}$ (approx. $3\sigma$) for the observed Bayes factors in the null no-correlation scenario. A frequentist test statistic built directly as a weighted sum of inter-pulsar correlations yields $p = 5 \times 10^{-5} - 1.9 \times 10^{-4}$ (approx. $3.5 - 4\sigma$). Assuming a fiducial $f^{-2/3}$ characteristic-strain spectrum, as appropriate for an ensemble of binary supermassive black-hole inspirals, the strain amplitude is $2.4^{+0.7}_{-0.6} \times 10^{-15}$ (median + 90% credible interval) at a reference frequency of 1/(1 yr). The inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from a population of supermassive black-hole binaries, although more exotic cosmological and astrophysical sources cannot be excluded. The observation of Hellings-Downs correlations points to the gravitational-wave origin of this signal., Comment: 30 pages, 18 figures. Published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

This digest provides descriptive, aggregated statistics related to the experiences of six cohorts of kindergartners who were enrolled in Baltimore City Public Schools (City Schools) from the 2014-15 school year through the 2019-20 school year which is the most recent available. Multiple indicators of kindergarten readiness and outcomes, including Kindergarten Readiness Assessment (KRA), attendance, kindergarten grade repetition, and the Dynamic Indicators of Basic Early Literacy Skills (DIBELS) assessment were used. Researchers analyzed the data trends over time to understand children's kindergarten experiences in City Schools over the last six years. In addition, they examined to what extent children's kindergarten experiences are related to their 3rd grade outcomes, measured by the Partnership for Assessment of Readiness for College and Careers (PARCC) English Language Arts (ELA) and mathematics assessments.