ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the so-called Dickman subordinator, whose Levy measure has density 1/x restricted to the interval (0,1). The marginal density of this process, known as the Dickman function, appears in many areas of mathematics, from number theory to combinatorics. In this paper, we study renewal processes in the domain of attraction of the Dickman subordinator, for which we prove local renewal theorems. We then present applications to marginally relevant disordered systems, such as pinning and directed polymer models, and prove sharp second moment estimates on their partition functions.
The HOSTS (Hunt for Observable Signatures of Terrestrial Systems) survey searches for dust near the habitable zones (HZs) around nearby, bright main sequence stars. We use nulling interferometry in N band to suppress the bright stellar light and to probe for low levels of HZ dust around the 30 stars observed so far. Our overall detection rate is 18%, including four new detections, among which are the first three around Sun-like stars and the first two around stars without any previously known circumstellar dust. The inferred occurrence rates are comparable for early type and Sun-like stars, but decrease from 60 (+16/-21)% for stars with previously detected cold dust to 8 (+10/-3)% for stars without such excess, confirming earlier results at higher sensitivity. For completed observations on individual stars, our sensitivity is five to ten times better than previous results. Assuming a lognormal excess luminosity function, we put upper limits on the median HZ dust level of 13 zodis (95% confidence) for a sample of stars without cold dust and of 26 zodis when focussing on Sun-like stars without cold dust. However, our data suggest that a more complex luminosity function may be more appropriate. For stars without detectable LBTI excess, our upper limits are almost reduced by a factor of two, demonstrating the strength of LBTI target vetting for future exo-Earth imaging missions. Our statistics are so far limited and extending the survey is critical to inform the design of future exo-Earth imaging surveys.
In the Standard Model of elementary particles, quark-mixing is expressed in terms of a 3 x 3 unitary matrix V, the so called Cabibbo-Kobayashi-Maskawa (CKM) matrix. Significant unitarity checks are so far possible for the first row of this matrix. This article reviews the experimental and theoretical information on these matrix elements. On the experimental side, we find a 2.2 sigma to 2.7 sigma deviation from unitarity, which conflicts with the Standard Model.
Here we present the first results from the Siding Spring Southern Seyfert Spectroscopic Snapshot Survey (S7) which aims to investigate the physics of ~140 radio-detected southern active Galaxies with z<0.02 through Integral Field Spectroscopy using the Wide Field Spectrograph (WiFeS). This instrument provides data cubes of the central 38 x 25 arc sec. of the target galaxies in the waveband 340-710nm with the unusually high resolution of R=7000 in the red (530-710nm), and R=3000 in the blue (340-560nm). These data provide the morphology, kinematics and the excitation structure of the extended narrow-line region, probe relationships with the black hole characteristics and the host galaxy, measures host galaxy abundance gradients and the determination of nuclear abundances from the HII regions. From photoionisation modelling, we may determine the shape of the ionising spectrum of the AGN, discover whether AGN metallicities differ from nuclear abundances determined from HII regions, and probe grain destruction in the vicinity of the AGN. Here we present some preliminary results and modelling of both Seyfert galaxies observed as part of the survey.
The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with simple examples such as the SO(4) symmetry of the hydrogen atom and the isospin symmetry in nuclei. Two nuclear models, the shell model and the interacting boson model, are reviewed with particular emphasis on their use of group-theoretical techniques.
We show all-versus-nothing proofs of Bell's theorem in the one-dimensional transverse-field Ising model, which is one of the most important exactly solvable models in the field of condensed matter physics. Since this model can be simulated with nuclear magnetic resonance, our work might lead to a fresh approach to experimental test of the Greenberger-Horne-Zeilinger contradiction between local realism and quantum mechanics.
We construct crosscap states in the N = 2 Liouville theory from the modular bootstrap method. We verify our results by comparing it with the calculation from the minisuperspace approximation and by checking the consistency with the conformal bootstrap equation. Various overlaps with other known branes are studied. We further discuss the topological nature of the discrete terms in the crosscap wavefunction and their connection with the Landau-Ginzburg approach in a nontrivial dilaton background. We find that it can be mapped to the Landau-Ginzburg theory with a negative power superpotential by a simple change of variables, extending the known duality to the open string sector. Possible applications to the two-dimensional noncritical string theories and supersymmetric orientifolds in the higher dimension are also discussed.
We discuss the nature of the low-frequency quadrupole vibrations from small-amplitude to large-amplitude regimes. We consider full five-dimensional quadrupole dynamics including three-dimensional rotations restoring the broken symmetries as well as axially symmetric and asymmetric shape fluctuations. Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinates and collective momenta, we microscopically derive the collective Hamiltonian of Bohr and Mottelson, which describes low-frequency quadrupole dynamics. We show that the five-dimensional collective Schr\"odinger equation is capable of describing large-amplitude quadrupole shape dynamics seen as shape coexistence/mixing phenomena. We summarize the modern concepts of microscopic theory of large-amplitude collective motion, which is underlying the microscopic derivation of the Bohr-Mottelson collective Hamiltonian.
With nucleons occupying an oscillator shell $\eta$, there are $2^{\eta/2}$ number of $SU(3)$ algebras; $\eta/2$ is the integer part of $\eta/2$. Analyzing the first non trivial situation with four $SU(3)$ algebras in $(sdg)$ space, demonstrated recently is that they generate quite different quadrupole properties though they all generate the same spectrum. More complex situation is with eight $SU(3)$ algebras in $(sdgi)$ space. In the present work, quadrupole properties generated by these eight algebras are analyzed first using the more analytically tractable interacting boson model. In addition, shell model and the closely related deformed shell model are used with three examples of nucleons in $sdgi$ space. It is found that in general six of the $SU(3)$ algebras generate prolate shape and two oblate shape. Out of all these, one of the $SU(3)$ algebra generates quite small quadrupole moments for the low-lying states.
We have performed a specific observational test to measure the effect that the zodiacal light can have on measurements of the spatial fluctuations of the near-IR background. Previous estimates of possible fluctuations caused by zodiacal light have often been extrapolated from observations of the thermal emission at longer wavelengths and low angular resolution, or from IRAC observations of high latitude fields where zodiacal light is faint and not strongly varying with time. The new observations analyzed here target the COSMOS field, at low ecliptic latitude where the zodiacal light intensity varies by factors of $\sim2$ over the range of solar elongations at which the field can be observed. We find that the white noise component of the spatial power spectrum of the background is correlated with the modeled zodiacal light intensity. Roughly half of the measured white noise is correlated with the zodiacal light, but a more detailed interpretation of the white noise is hampered by systematic uncertainties that are evident in the zodiacal light model. At large angular scales ($\gtrsim100"$) where excess power above the white noise is observed, we find no correlation of the power with the modeled intensity of the zodiacal light. This test clearly indicates that the large scale power in the infrared background is not being caused by the zodiacal light.
We review the recent status of big bounce genesis as a new possibility of using dark matter particle's mass and interaction cross section to test the existence of a bounce universe at the early stage of evolution in our currently observed universe. To study the dark matter production and evolution inside the bounce universe, called big bounce genesis for short, we propose a model independent approach. We shall present the motivation for proposing big bounce as well the model independent predictions which can be tested by dark matter direct searches. A positive finding shall have profound impact on our understanding of the early universe physics.
We study the origin of gamma rays from the supernova remnant (SNR) RX J1713.7-3946. Using an analytical model, we calculate the distribution of cosmic rays (CRs) around the SNRs. Motivated by the results of previous studies, we assume that the SNR is interacting with two-phase interstellar medium (ISM), where dense clumps are surrounded by tenuous interclump medium. We also assume that only higher-energy protons (~> TeV) can penetrate the dense clumps. We find that pi^0-decay gamma rays produced by protons reproduce the observed gamma-ray spectrum peaked at ~TeV. On the other hand, it has recently been indicated that the observed ISM column density (N_p), the X-ray surface brightness (I_X), and the gamma-ray surface brightness (I_g) at grid points across the SNR form a plane in the three-dimensional (3D) space of (N_p, I_X, I_g). We find that the planar configuration is naturally reproduced if the ISM or the CR electron-to-proton ratio is not spherically uniform. We show that the shift of the observed data in the 3D space could be used to identify which of the quantities, the ISM density, the CR electron-to-proton ratio, or the magnetic field, varies in the azimuthal direction of the SNR.
OH absorption against PSR B1718-35 at (l,b) =351.688,+0.671 has been discovered at 1665 and 1667 MHz using the Green Bank Telescope. The absorption appears to arise at the interface of an HII region and a molecular cloud which are likely associated with the high mass star forming region NGC 6334. Beam dilution is found to be the cause of differences in the opacity of the OH against the Galactic background continuum emission and against the pulsar. The OH cloud is approximately 3 by 1.3 pc and is located behind the HII region.
The Fiedler vector of a graph, namely the eigenvector corresponding to the second smallest eigenvalue of a graph Laplacian matrix, plays an important role in spectral graph theory with applications in problems such as graph bi-partitioning and envelope reduction. Algorithms designed to estimate this quantity usually rely on a priori knowledge of the entire graph, and employ techniques such as graph sparsification and power iterations, which have obvious shortcomings in cases where the graph is unknown, or changing dynamically. In this paper, we develop a framework in which we construct a stochastic process based on a set of interacting random walks on a graph and show that a suitably scaled version of our stochastic process converges to the Fiedler vector for a sufficiently large number of walks. Like other techniques based on exploratory random walks and on-the-fly computations, such as Markov Chain Monte Carlo (MCMC), our algorithm overcomes challenges typically faced by power iteration based approaches. But, unlike any existing random walk based method such as MCMCs where the focus is on the leading eigenvector, our framework with interacting random walks converges to the Fiedler vector (second eigenvector). We also provide numerical results to confirm our theoretical findings on different graphs, and show that our algorithm performs well over a wide range of parameters and the number of random walks. Simulations results over time varying dynamic graphs are also provided to show the efficacy of our random walk based technique in such settings. As an important contribution, we extend our results and show that our framework is applicable for approximating not just the Fiedler vector of graph Laplacians, but also the second eigenvector of any time reversible Markov Chain kernel via interacting random walks.
In this paper easily applicable techniques are devised for detecting changepoints in autocorrelated Gaussian sequences. Our method proceeds by sequential evaluation of a CUSUM-type test statistic, which is compared to a predefined threshold. We assume that data is tested in sliding windows of fixed size. The distinguishing feature of this work is that, based on large deviations theory, we derive rather explicit equations that determine the threshold in such a way that the false alarm probability per window is approximately kept at the desired level. This criterion -- as opposed to the usual average run length -- allows to restrict not only the average number of false alarms but also their variability. Illustrative examples are provided, including the detection of a shift in mean in ARMA processes. The procedures are validated by means of a broad set of simulation experiments, and overall perform well.
We extend to quantum mechanics the technique of stochastic subordination, by means of which one can express any semi-martingale as a time-changed Brownian motion. As examples, we considered two versions of the q-deformed Harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules.
We report on the storage of orbital angular momentum of light in a cold ensemble of cesium atoms. We employ Bragg diffraction to retrieve the stored optical information impressed into the atomic coherence by the incident light fields. The stored information can be manipulated by an applied magnetic field and we were able to observe collapses and revivals due to the rotation of the stored atomic Zeeman coherence for times longer than 15 $\mu s$.
We derive the Teixeira, Wolk and Som method, for obtaining electrostatic solutions from given vacuum solutions, in its inverse form. Then we use it to obtain the geometrical mass $M_S$ in the Schwarzschild spacetime, and we find $M_S^2=M^2-Q^2$, where $M$ and $Q$ are, respectively, the mass and charge parameters of the Reissner-Nordstr\"om spacetime. We compare $M_S$ to the corresponding active gravitational mass and mass function.
We investigate the thermodynamics of model systems exhibiting two-scale fractal spectra. In particular, we present both analytical and numerical studies on the temperature dependence of the vibrational and electronic specific heats. For phonons, and for bosons in general, we show that the average specific heat can be associated to the average (power law) density of states. The corrections to this average behavior are log-periodic oscillations which can be traced back to the self-similarity of the spectral staircase. In the electronic case, even if the thermodynamical quantities exhibit a strong dependence on the particle number, regularities arise when special cases are considered. Applications to substitutional and hierarchical structures are discussed.
X-ray surveys contain sizable numbers of star forming galaxies, beyond the AGN which usually make the majority of detections. Many methods to separate the two populations are used in the literature, based on X-ray and multiwavelength properties. We aim at a detailed test of the classification schemes and to study the X-ray properties of the resulting samples. We build on a sample of galaxies selected at 1.4 GHz in the VLA-COSMOS survey, classified by Smolcic et al. (2008) according to their optical colours and observed with Chandra. A similarly selected control sample of AGN is also used for comparison. We review some X-ray based classification criteria and check how they affect the sample composition. The efficiency of the classification scheme devised by Smolcic et al. (2008) is such that ~30% of composite/misclassified objects are expected because of the higher X-ray brightness of AGN with respect to galaxies. The latter fraction is actually 50% in the X-ray detected sources, while it is expected to be much lower among X-ray undetected sources. Indeed, the analysis of the stacked spectrum of undetected sources shows, consistently, strongly different properties between the AGN and galaxy samples. X-ray based selection criteria are then used to refine both samples. The radio/X-ray luminosity correlation for star forming galaxies is found to hold with the same X-ray/radio ratio valid for nearby galaxies. Some evolution of the ratio may be possible for sources at high redshift or high luminosity, tough it is likely explained by a bias arising from the radio selection. Finally, we discuss the X-ray number counts of star forming galaxies from the VLA- and C-COSMOS surveys according to different selection criteria, and compare them to the similar determination from the Chandra Deep Fields. The classification scheme proposed here may find application in future works and surveys.
We present a statistical analysis of spectra of transfer matrices of classical lattice spin models; this continues the work on the eight-vertex model of the preceding paper. We show that the statistical properties of these spectra can serve as a criterion of integrability. It provides also an operational numerical method to locate integrable varieties. In particular, we distinguish the notions of integrability and criticality considering the two examples of the three-dimensional Ising critical point and the two-dimensional three-state Potts critical point. For complex spectra which appear frequently in the context of transfer matrices, we show that the notion of independence of eigenvalues for integrable models still holds.
Context. The largest grains (0.5-1 micron) in the interstellar size distribution are efficient in scattering near- and mid-infrared radiation. These wavelengths are therefore particularly well suited to probe the still uncertain high-end of the size distribution. Aims. We investigate the change in appearance of a typical low-mass molecular core from the Ks (2.2 micron) band to the Spitzer IRAC 3.6 and 8 micron bands, and compare with model calculations, which include variations of the grain size distribution. Methods. We combine Spitzer IRAC and ground-based near-infrared observations to characterize the scattered light observed at the near- and mid-infrared wavelengths from the core L260. Using a spherical symmetric model core, we perform radiative transfer calculations to study the impact of various dust size distributions on the intensity profiles across the core. Results. The observed scattered light patterns in the Ks and 3.6 micron bands are found to be similar. By comparison with radiative transfer models the two profiles place constraints on the relative abundance of small and large (more than 0.25 micron) dust grains. The scattered light profiles are found to be inconsistent with an interstellar silicate grain distribution extending only to 0.25 micron and large grains are needed to reach the observed fluxes and the flux ratios. The shape of the Ks band surface brightness profile limits the largest grains to 1-1.5 micron. Conclusions. In addition to observing coreshine in the Spitzer IRAC channels, the combination with ground-based near-infrared observations are suited to constrain the properties of large grains in cores.
Previous studies have shown that physically small, low-luminosity radio galaxies, which we refer to as galaxy scale jets (GSJ), could potentially have a significant effect upon the host galaxy's evolution. Using 6 arcsec resolution images taken from the first release of the LOFAR Two Metre Sky Survey (LoTSS DR1), we identified a representative sample of nine potential GSJ for which we obtained high-resolution, 2-4 GHz data using the Karl G. Jansky Very Large Array (VLA). Using these data we aim to verify the GSJ nature of these sources as well as investigating the potential role of feedback. Our VLA images reveal a diversity of structures, confirm the hosts for four of the sources and find that a fifth is the first known example of a galaxy-scale remnant showing that some radio galaxies never grow beyond the GSJ stage. We also derive spectral ages and the first estimates of the lobe expansion speeds of GSJ. We find our GSJ have maximum spectral ages of 60 Myr with most between about 5 and 20 Myr, consistent with being located along an evolutionary path joining compact sources and larger radio galaxies. We find lobe advance speeds a few times the local sound speed, with most GSJ predicted to be driving strong shocks into their environment and having a significant impact upon the host's evolution. Our discovery of a remnant GSJ, which will eventually transfer all of its energy directly into the local environment, represents an important and previously hidden aspect of AGN life cycles.
Recent spectroscopic observations have revealed the ubiquitous presence of blueward asymmetries of emission lines formed in the solar corona and transition region. These asymmetries are most prominent in loop footpoint regions, where a clear correlation of the asymmetry with the Doppler shift and line width determined from the single Gaussian fit is found. Such asymmetries suggest at least two emission components: a primary component accounting for the background emission and a secondary component associated with high-speed upflows. The latter has been proposed to play a vital role in the coronal heating process and there is no agreement on its properties. Here we slightly modify the initially developed technique of Red-Blue (RB) asymmetry analysis and apply it to both artificial spectra and spectra observed by the EUV Imaging Spectrometer onboard Hinode, and demonstrate that the secondary component usually contributes a few percent of the total emission, has a velocity ranging from 50 to 150 km s-1 and a Gaussian width comparable to that of the primary one in loop footpoint regions. The results of the RB asymmetry analysis are then used to guide a double Gaussian fit and we find that the obtained properties of the secondary component are generally consistent with those obtained from the RB asymmetry analysis. Through a comparison of the location, relative intensity, and velocity distribution of the blueward secondary component with the properties of the upward propagating disturbances revealed in simultaneous images from the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory, we find a clear association of the secondary component with the propagating disturbances.
Using the natural orbitals renormalization group (NORG) method, we have investigated the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator. We find that there is a local spin formed at the impurity site and the local spin is completely screened by electrons in the quantum spin Hall insulator. Meanwhile, the local spin is screened dominantly by a single active natural orbital. We then show that the Kondo screening mechanism becomes transparent and simple in the framework of natural orbitals formalism. We project the active natural orbital respectively into real space and momentum space to characterize its structure. And we confirm the spin-momentum locking property of the edge states based on the occupancy of a Bloch state in the edge to which the impurity couples. Furthermore, we study the dynamical property of the active natural orbital represented by the local density of states, from which we observe the Kondo resonance peak.