ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present the exact solution to the moment problem for the spin-1/2 isotropic antiferromagnetic XY chain with explicit forms for the moments with respect to the Neel state, the cumulant generating function, and the Resolvent Operator. We verify the correctness of the Horn-Weinstein Theorems, but the analytic structure of the generating function <e^{-tH}> in the complex t-plane is quite different from that assumed by the "t"-Expansion and the Connected Moments Expansion due to the vanishing gap. This function has a finite radius of convergence about t=0, and for large t has a leading descending algebraic series E(t)-E_0 ~ At^{-2}. The Resolvent has a branch cut and essential singularity near the ground state energy of the form G(s)/s ~ B|s+1|^{-3/4} exp(C|s+1|^{1/2}). Consequently extrapolation strategies based on these assumptions are flawed and in practise we find that the CMX methods are pathological and cannot be applied, while numerical evidence for two of the "t"-expansion methods indicates a clear asymptotic convergence behaviour with truncation order.
Energy in stars is provided by nuclear reactions, which, in many cases, produce radioactive nuclei. When stable nuclei are irradiated by a flux of protons or neutrons, capture reactions push stable matter out of stability into the regime of unstable species. The ongoing production of radioactive nuclei in the deep interior of the Sun via proton-capture reactions is recorded by neutrinos emitted during radioactive decay and detected on Earth. Radioactive nuclei that have relatively long half lives may also be detected in stars via spectroscopic observations and in stardust recovered from primitive meteorites via laboratory analysis. The vast majority of these stardust grains originated from Asymptotic Giant Branch (AGB) stars. This is the final phase in the evolution of stars initially less massive than ~10 solar masses, during which nuclear energy is produced by alternate hydrogen and helium burning in shells above the core. The long-lived radioactive nucleus 26Al is produced in massive AGB stars (>4:5 solar masses), where the base of the convective envelope reaches high temperatures. Several other long-lived radioactive nuclei, including 60Fe, 87Rb, and 99Tc, are produced in AGB stars when matter is exposed to a significant neutron flux leading to the synthesis of elements heavier than iron. Here, neutron captures occur on a timescale that is typically slower than beta-decay timescales, resulting slow neutron captures (the s-process). However, when radioactive nuclei with half lives greater than a few days are produced they may either decay or capture a neutron, thus branching up the path of neutron captures and defining the final s-process abundance distribution. This nucleosynthesis in AGB stars could produce some long-living radioactive nuclei in relative abundances that resemble those observed in the early solar system.
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is shown that the scalar field is dependent on a single unknown function of the same variable and that the scalar field potential has exponential form. The Einstein equations then take the form of a set of ODEs. Self-similarity also gives rise to a singularity at the scaling origin. We extend the work of [1], which determined the global structure of all solutions in the causal past of the singularity. We identified a class of solutions that evolves through the past null cone of the singularity. We give the global structure of these solutions and show that the singularity is censored in all cases.
We investigate the interactions of energetic hadronic particles (cosmic ray protons) with photons and baryons in protogalactic environments, where the target photons are supplied by the first generations of stars to form in the galaxy and the cosmological microwave background, while the target baryons are the interstellar and circumgalactic medium. We show that pair-production and photo-pion processes are the dominant interactions at particle energies above $10^{19}\;\! {\rm eV}$, while ${\rm pp}$-interaction pion-production dominates at the lower energies in line with expectations from, for example $\gamma$-ray observations of star-forming galaxies and dense regions of our own galaxy's interstellar medium. We calculate the path lengths for the interaction channels and determine the corresponding rates of energy deposition. We have found that protogalactic magnetic fields and their evolution can significantly affect the energy transport and energy deposition processes of cosmic rays. Within a Myr after the onset of star-formation the magnetic field in a protogalaxy could attain a strength sufficient to confine all but the highest energy particles within the galaxy. This enhances the cosmic ray driven self-heating of the protogalaxy to a rate of around $10^{-24}\;\! {\rm erg} \;\!{\rm cm}^{-3}\;\! {\rm s}^{-1}$ for a galaxy with strong star-forming activity that yields 1 core collapse SN event per year. This heating power exceeds even that due to radiative emission from the protogalaxy's stellar populations. However, in a short window before the protogalaxy is fully magnetised, energetic particles could stream across the galaxy freely, delivering energy into the circumgalactic and intergalactic medium.
In this manuscript of the habilitation \`a diriger des recherches (HDR), the author presents some of his work over the last ten years. The main topic of this thesis is cosmic shear, the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure.   I review the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then I give an overview of weak-lensing measurements, and present observational results from the Canada-France Hawai'i Lensing Survey (CFHTLenS), as well as the implications for cosmology. I conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations.
By adopting a generalised parton model approach at leading order in QCD, including spin and intrinsic parton motion effects, we study the Collins azimuthal asymmetries for pions within a large-$p_T$ jet produced at mid-rapidity in polarised hadronic collisions. Using available information on the quark transversity distributions and the pion Collins functions, as extracted from semi-inclusive deeply inelastic scattering and $e^+e^-\to h_1 h_2\, X$ processes, we compute estimates for the Collins asymmetries in kinematical configurations presently investigated at RHIC by the STAR Collaboration. Collins-like asymmetries, involving linearly polarised gluons, are also considered. Our predictions, compared against available preliminary data, show a very good agreement, even if some discrepancies, to be further scrutinized both theoretically and experimentally, appear in the transverse momentum dependence of the Collins asymmetry. These results are in favour of the predicted universality of the Collins function and of a mild, if any, evolution with the hard scale of the asymmetries.
Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., gamma-ray bursts (GRBs), active galactic nuclei (AGNs), and Galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations of relativistic electron-ion (electron-positron) jets injected into a stationary medium show that particle acceleration occurs within the downstream jet. In the presence of relativistic jets, instabilities such as the Buneman instability, other two-streaming instability, and the Weibel (filamentation) instability create collisionless shocks, which are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation from deflected electrons in small-scale magnetic fields has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation, a case of diffusive synchrotron radiation, may be important to understand the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.
An effective $\alpha$ particle equation is derived for cases where an $\alpha$ particle is formed on top of a doubly magic nucleus. As an example, we consider $^{212}$Po with the $\alpha$ on top of the $^{208}$ Pb core. We will consider the core nucleus infinitely heavy, so that the $\alpha$ particle moves with respect to a fixed center, i.e., recoil effects are neglected. The fully quantal solution of the problem is discussed. The approach is inspired by the THSR (Tohsaki-Horiuchi-Schuck-R\"{o}pke) wave function concept that has been successfully applied to light nuclei. Shell model calculations are improved by including four-particle ($\alpha$-like) correlations that are of relevance when the matter density becomes low. In the region where the $\alpha$-like cluster penetrates the core nucleus, the intrinsic bound state wave function transforms at a critical density into an unbound four-nucleon shell model state. Exploratory calculations for $^{212}$Po are presented. Such preformed cluster states are only hardly described by shell model calculations. Reasons for different physics behavior of an $\alpha$-like cluster with respect to a deuteron-like cluster are discussed.
Nuclear theory today aims for a comprehensive theoretical framework that can describe all nuclei. I discuss recent progress in this pursuit and the associated challenges as we move forward.
The recent observation of Weyl fermions in the itinerant 4d ferromagnetic perovskite SrRuO3 points to this material being a good platform for exploring novel physics related to a pair of Weyl nodes in epitaxial heterostructures. In this letter, we report the thickness-dependent magnetotransport properties of ultra-high-quality epitaxial SrRuO3 films grown under optimized conditions on SrTiO3 substrates. Signatures of Weyl fermion transport, i.e., unsaturated linear positive magnetoresistance accompanied by a quantum oscillation having a {\pi} Berry phase, were observed in films with thicknesses as small as 10 nm. Residual resistivity increased with decreasing film thickness, indicating disorder near the interface between SrRuO3 and the SrTiO3 substrate. Since this disorder affects the magnetic and electrical properties of the films, the Curie temperature decreases and the coercive field increases with decreasing thickness. Thickness-dependent magnetotransport measurements revealed that the threshold residual resistivity ratio (RRR) to observe Weyl fermion transport is 21. These results provide guidelines for realizing quantum transport of Weyl fermions in SrRuO3 near heterointerfaces.
We show that charge noise $S_Q$ in Josephson qubits can be produced by fluctuating two level systems (TLS) with electric dipole moments in the substrate using a flat density of states. At high frequencies the frequency and temperature dependence of the charge noise depends on the ratio $J/J_c$ of the electromagnetic flux $J$ to the critical flux $J_c$. It is not widely appreciated that TLS in small qubits can easily be strongly saturated with $J/J_c\gg 1$. Our results are consistent with experimental conclusions that $S_Q\sim 1/f$ at low frequencies and $S_Q\sim f$ at high frequencies.
The ground state of spin-1 Haldane chains is characterized by the so-called string order. We show that the same hidden order is also present in ordinary one-dimensional band insulators. We construct a family of Hamiltonians which connects adiabatically band insulators to two topologically non-equivalent spin models, the Haldane chain and the antiferromagnetic spin-1/2 ladder. We observe that the localized spin-1/2 edge-state characteristic of spin-1 chains is smoothly connected to a surface-bound state of band insulators and its emergence is not related to any bulk phase transition. Furthermore, we show that the string order is absent in any dimensions higher than one.
We calculate the finite-temperature conductance of clean, weakly interacting one-dimensional quantum wires subject to Rashba spin-orbit coupling and a magnetic field. For chemical potentials near the center of the Zeeman gap ($\mu = 0$), two-particle scattering causes the leading deviation from the quantized conductance at finite temperatures. On the other hand, for $|\mu| > 0$, three-particle scattering processes become more relevant. These deviations are a consequence of the strongly nonlinear single-particle spectrum, and are thus not accessible using Luttinger liquid theory. We discuss the observability of these predictions in current experiments on InSb nanowires and in "spiral liquids", where a spontaneous ordering of the nuclear spins at low temperatures produces an effective Rashba coupling.
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total variation, uniformly with respect to the initial distribution. Our approach is based on probabilistic and coupling methods, contrary to the classical approach based on spectral theory results. Our general criteria apply in the case where $\infty$ is entrance and 0 either regular or exit, and are proved to be satisfied under several explicit assumptions expressed only in terms of the speed and killing measures. We also obtain exponential ergodicity results on the $Q$-process. We provide several examples and extensions, including diffusions with singular speed and killing measures, general models of population dynamics, drifted Brownian motions and some one-dimensional processes with jumps.
A revised rotation-vibration line list for the combined hydrogen cyanide (HCN) / hydrogen isocyanide (HNC) system is presented. The line list uses {\it ab initio} transition intensities calculated previously (Harris et al., ApJ, 2002, 578, 657) and extensive datasets of recently measured experimental energy levels (Mellau, J. Chem. Phys. and J. Mol. Spectrosc. 2010-2011). The resulting line list has significantly more accurate wavelengths than previous ones for these systems. An improved value for the separation between HCN and HNC is adopted leading to an approximately 25%\ lower predicted thermal population of HNC as a function of temperature in the key 2000 to 3000 K region. Temperature-dependent partition functions and equilibrium constants are presented. The line lists are validated by comparison with laboratory spectra and are presented in full as supplementary data to the article and at \url{www.exomol.com}.
Recently, there has been increasing interest to leverage the competence of neural networks to analyze data. In particular, new clustering methods that employ deep embeddings have been presented. In this paper, we depart from centroid-based models and suggest a new framework, called Clustering-driven deep embedding with PAirwise Constraints (CPAC), for non-parametric clustering using a neural network. We present a clustering-driven embedding based on a Siamese network that encourages pairs of data points to output similar representations in the latent space. Our pair-based model allows augmenting the information with labeled pairs to constitute a semi-supervised framework. Our approach is based on analyzing the losses associated with each pair to refine the set of constraints. We show that clustering performance increases when using this scheme, even with a limited amount of user queries. We demonstrate how our architecture is adapted for various types of data and present the first deep framework to cluster 3D shapes.
Most of the globular clusters in the main body of the Galactic halo were formed almost simultaneously. However, globular cluster formation in dwarf spheroidal galaxies appears to have extended over a significant fraction of a Hubble time. This suggests that the factors which suppressed late-time formation of globulars in the main body of the Galactic halo were not operative in dwarf spheroidal galaxies. Possibly the presence of significant numbers of ``young'' globulars at R_{GC} > 15 kpc can be accounted for by the assumption that many of these objects were formed in Sagittarius-like (but not Fornax-like) dwarf spheroidal galaxies, that were subsequently destroyed by Galactic tidal forces. It would be of interest to search for low-luminosity remnants of parental dwarf spheroidals around the ``young'' globulars Eridanus, Palomar 1, 3, 14, and Terzan 7. Furthermore multi-color photometry could be used to search for the remnants of the super-associations, within which outer halo globular clusters originally formed. Such envelopes are expected to have been tidally stripped from globulars in the inner halo.
Training a modern deep neural network on massive labeled samples is the main paradigm in solving the scene classification problem for remote sensing, but learning from only a few data points remains a challenge. Existing methods for few-shot remote sensing scene classification are performed in a sample-level manner, resulting in easy overfitting of learned features to individual samples and inadequate generalization of learned category segmentation surfaces. To solve this problem, learning should be organized at the task level rather than the sample level. Learning on tasks sampled from a task family can help tune learning algorithms to perform well on new tasks sampled in that family. Therefore, we propose a simple but effective method, called RS-MetaNet, to resolve the issues related to few-shot remote sensing scene classification in the real world. On the one hand, RS-MetaNet raises the level of learning from the sample to the task by organizing training in a meta way, and it learns to learn a metric space that can well classify remote sensing scenes from a series of tasks. We also propose a new loss function, called Balance Loss, which maximizes the generalization ability of the model to new samples by maximizing the distance between different categories, providing the scenes in different categories with better linear segmentation planes while ensuring model fit. The experimental results on three open and challenging remote sensing datasets, UCMerced\_LandUse, NWPU-RESISC45, and Aerial Image Data, demonstrate that our proposed RS-MetaNet method achieves state-of-the-art results in cases where there are only 1-20 labeled samples.
We prove an effective restriction theorem for stable vector bundles $E$ on a smooth projective variety: $E|_D$ is (semi)stable for all irreducible divisors $D \in |kH|$ for all $k$ greater than an explicit constant.   As an application, we show that Mercat's conjecture in any rank greater than $2$ fails for curves lying on K3 surfaces.   Our technique is to use wall-crossing with respect to (weak) Bridgeland stability conditions which we also use to reprove Camere's result on slope stability of the tangent bundle of $\mathbb{P}^n$ restricted to a K3 surface.
The issue of spontaneous breaking of Lorentz and CPT invariance is studied in the open bosonic string using a truncation scheme to saturate the string-field action at successively higher levels. We find strong evidence for the existence of extrema of the action with nonzero expectation values for certain fields. The Lorentz- and CPT-preserving solution previously suggested in the literature is confirmed through level 12 in the action. A family of Lorentz-breaking, CPT-preserving solutions of the equations of motion is found to persist and converge through level 18 in the action. Two sequences of solutions spontaneously breaking both Lorentz invariance and CPT are discussed. The analysis at this level involves the analytical form of over 20,000 terms in the static potential.
We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.
The interplay between the orbital and spin currents in (e,e') excitations of light nuclei is discussed. The microscopic analysis of E1 and M2 resonances was performed within the particle-core coupling approximation (PCC) of the shell model. The comparison of the theoretical results with the available experimental data has shown that the studies of relative contributions of the orbital and different spin components of the nuclear current into the excitation of EJ and MJ resonances could be useful for the identification of their configurational structure.
We investigate how a spherically symmetric scalar field can modify the Schwarzschild vacuum solution when there is no exchange of energy-momentum between the scalar field and the central source of the Schwarzschild metric. This system is described by means of the gravitational decoupling by Minimal Geometric Deformation (MGD-decoupling), which allows us to show that, under the MGD paradigm, the Schwarzschild solution is modified in such a way that a naked singularity appears.
In this paper, using $f(R)$ theory of gravity we explicitly calculate cosmological evolution in the presence of a perfect fluid source in four and five dimensional, space time in which this cosmological evolution in self-creation is presented by Reddy et al 2009 Int. J. Theor. Phys. 48 10. An exact cosmological model is presented using a relation between Einstein gravity field equation components due to a metric with the same component from $f(R)$ theory of gravity. Some physics and kinematical properties of the model are also discussed.