ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. Our techniques rely on a universality principle for the Gaussian Wiener chaos, recently proved by the authors together with Gesine Reinert, as well as on some combinatorial estimates. Unlike other related results in the probabilistic literature, we do not require that the law of the entries has a density with respect to the Lebesgue measure. In particular, our results apply to the ensemble of Bernoulli random matrices.
We present our XMM-Newton RGS observations of X Comae, an AGN behind the Coma cluster. We detect absorption by NeIX and OVIII at the redshift of Coma with an equivalent width of 3.3+/-1.8 eV and 1.7+/-1.3 eV, respectively (90% confidence errors or 2.3 sigma and 1.9 sigma confidence detections determined from Monte Carlo simulations). The combined significance of both lines is 3.0 sigma, again determined from Monte Carlo simulations. The same observation yields a high statistics EPIC spectrum of the Coma cluster gas at the position of X Comae. We detect emission by NeIX with a flux of 2.5+/-1.2 x 10^-8 photons cm^-2 s^-1 arcmin^-2 (90% confidence errors or 3.4 sigma confidence detection). These data permit a number of diagnostics to determine the properties of the material causing the absorption and producing the emission. Although a wide range of properties is permitted, values near the midpoint of the range are T = 4 x 10^6 K, n_H = 6 x 10^-6 cm^-3 corresponding to an overdensity with respect to the mean of 32, line of sight path length through it 41 Z/Zsolar^-1 Mpc where Z/Zsolar is the neon metallicity relative to solar. All of these properties are what has been predicted of the warm-hot intergalactic medium (WHIM), so we conclude that we have detected the WHIM associated with the Coma cluster.
The flow of kaons, i.e., the average kaon transverse momentum as a function of rapidity, and the associated flow parameter in heavy-ion collisions at SIS/GSI energies is investigated in the relativistic transport model. It is found that the pattern of kaon flow at the final stage is sensitive to the kaon potential used in the model and is thus a useful probe of the kaon potential in a nuclear medium.
The VSOP mission is a Japanese-led project to study radio sources with sub-milliarcsecond angular resolution using an orbiting 8-m telescope, HALCA and global arrays of Earth-based telescopes. Approximately 25% of the observing time has been devoted to a survey of compact AGN at 5 GHz which are stronger than 1 Jy -- the VSOP AGN Survey. This paper, the second in a series, describes the data calibration, source detection, self-calibration, imaging and modeling, and gives examples illustrating the problems specific to space VLBI. The VSOP Survey web-site which contains all results and calibrated data is described.
Aims: To provide a significantly improved probability distribution for the H-test for periodicity in X-ray and $\gamma$-ray arrival times, which is already extensively used by the $\gamma$-ray pulsar community. Also, to obtain an analytical probability distribution for stacked test statistics in the case of a search for pulsed emission from an ensemble of pulsars where the significance per pulsar is relatively low, making individual detections insignificant on their own. This information is timely given the recent rapid discovery of new pulsars with the Fermi-LAT t $\gamma$-ray telescope. Methods: Approximately $10^{14}$ realisations of the H-statistic ($H$) for random (white) noise is calculated from a random number generator for which the repitition cycle is $\gg 10^{14}$. From these numbers the probability distribution $P(>H)$ is calculated. Results: The distribution of $H$ is is found to be exponential with parameter $\lambda=0.4$ so that the cumulative probability distribution $P(>H)=\exp{(-\lambda H)}$. If we stack independent values for $H$, the sum of $K$ such values would follow the Erlang-K distribution with parameter $\lambda$ for which the cumulative probability distribution is also a simple analytical expression. Conclusion: Searches for weak pulsars with unknown pulse profile shapes in the Fermi-LAT, Agile or other X-ray data bases should benefit from the {\it H-test} since it is known to be powerful against a broad range of pulse profiles, which introduces only a single statistical trial if only the {\it H-test} is used. The new probability distribution presented here favours the detection of weaker pulsars in terms of an improved sensitivity relative to the previously known distribution.
We prove the Abelian/non-Abelian Correspondence with bundles for target spaces that are partial flag bundles, combining and generalising results by Ciocan-Fontanine-Kim-Sabbah, Brown, and Oh. From this we deduce how genus-zero Gromov-Witten invariants change when a smooth projective variety X is blown up in a complete intersection defined by convex line bundles. In the case where the blow-up is Fano, our result gives closed-form expressions for certain genus-zero invariants of the blow-up in terms of invariants of X. We also give a reformulation of the Abelian/non-Abelian Correspondence in terms of Givental's formalism, which may be of independent interest.
In this paper, by the umbral calculus method, we give a remarkable congruence involving Appell polynomials. Some applications on derangement polynomials are also presented.
We prove that the moduli space of stable sheaves of rank 2 with a certain Chern classes on a smooth quadric $Q$ in $\PP_3$, is isomorphic to $\PP_3$. Using this identification, we give a new proof that a certain Brill-Noether locus on a non-hyperelliptic curve of genus 4, is isomorphic to the Donagi-Izadi cubic threefold.
We show that three-dimensional General Relativity, augmented with two vector fields, allows for a non-relativistic limit, different from the standard limit leading to Newtonian gravity, that results into a well-defined action which is of the Chern-Simons type. We show that this three-dimensional `Extended Bargmann Gravity', after coupling to matter, leads to equations of motion allowing a wider class of background geometries than the ones that one encounters in Newtonian gravity. We give the supersymmetric generalization of these results and point out an important application in the context of calculating partition functions of non-relativistic field theories using localization techniques.
Spin relaxation can be greatly enhanced in narrow channels of two-dimensional electron gas due to ballistic spin resonance, which is mediated by spin-orbit interaction for trajectories that bounce rapidly between channel walls. The channel orientation determines which momenta affect the relaxation process, so comparing relaxation for two orientations provides a direct determination of spin-orbit anisotropy. Electrical measurements of pure spin currents are shown to reveal an order of magnitude stronger relaxation for channels fabricated along the [110] crystal axis in a GaAs electron gas compared to [-110] channels, believed to result from interference between structural and bulk inversion asymmetries.
The accretion-induced collapse (AIC) of a white dwarf to form a neutron star can leave behind a rotationally supported disk with mass of up to ~ 0.1 M_sun. The disk is initially composed of free nucleons but as it accretes and spreads to larger radii, the free nucleons recombine to form helium, releasing sufficient energy to unbind the remaining disk. Most of the ejected mass fuses to form Ni56 and other iron group elements. We present spherically symmetric radiative transfer calculations of the transient powered by the radioactive heating of this ejecta. For an ejecta mass of 1e-2 M_sun (3e-3 M_sun), the lightcurve peaks after <~ 1 day with a peak bolometric luminosity ~ 2e41 erg/s (~ 5e40 erg/s), i.e., a "kilonova"; the decay time is ~ 4 (2) days. Overall, the spectra redden with time reaching U-V ~ 4 after ~ 1 day; the optical colors (B-V) are, however, somewhat blue. Near the peak in the lightcurve, the spectra are dominated by Doppler broadened Nickel features, with no distinct spectral lines present. At ~ 3-5 days, strong Calcium lines are present in the infrared, although the Calcium mass fraction is only ~ 1e-4.5. If rotationally supported disks are a common byproduct of AIC, current and upcoming transient surveys such as the Palomar Transient Factory should detect a few AIC per year for an AIC rate of ~ 1e-2 of the Type Ia rate. We discuss ways of distinguishing AIC from other rapid, faint transients, including .Ia's and the ejecta from binary neutron star mergers.
Let $f$ be a newform of weight $2$ on $\Gamma_0(N)$ with Fourier $q$-expansion $f(q)=q+\sum_{n\geq 2} a_n q^n$, where $\Gamma_0(N)$ denotes the group of invertible matrices with integer coefficients, upper triangular mod $N$. Let $p$ be a prime dividing $N$ once, $p\parallel N$, a Steinberg prime. Then, it is well known that $a_p\in\{1,-1\}$. We denote by $K_f$ the field of coefficients of $f$. Let $\lambda$ be a finite place in $K_f$ not dividing $2p$ and assume that the mod $\lambda$ Galois representation attached to $f$ is irreducible. In this paper we will give necessary and sufficient conditions for the existence of another Hecke eigenform $f'(q)=q+\sum_{n\geq 2} a'_n q^n$ $p$-new of weight $2$ on $\Gamma_0(N)$ and a finite place $\lambda'$ of $K_{f'}$ such that $a_p=-a'_p$ and the Galois representations $\bar\rho_{f,\lambda}$ and $\bar\rho_{f',\lambda'}$ are isomorphic.
We study the entanglement spectra of many particle systems in states which are closely related to products of Slater determinants or products of permanents, or combinations of the two. Such states notably include the Laughlin and Jain composite fermion states which describe most of the observed conductance plateaus of the fractional quantum Hall effect. We identify a set of 'Entanglement Wave Functions' (EWF), for subsets of the particles, which completely describe the entanglement spectra of such product wave functions, both in real space and in particle space. A subset of the EWF for the Laughlin and Jain states can be recognized as Composite Fermion states. These states provide an exact description of the low angular momentum sectors of the real space entanglement spectrum (RSES) of these trial wave functions and a physical explanation of the branches of excitations observed in the RSES of the Jain states.
Let a_1,...,a_k satisfy a_1+...+a_k=1 and suppose a k-uniform hypergraph on n vertices satisfies the following property; in any partition of its vertices into k sets A_1,...,A_k of sizes a_1*n,...,a_k*n, the number of edges intersecting A_1,...,A_k is the number one would expect to find in a random k-uniform hypergraph. Can we then infer that H is quasi-random? We show that the answer is negative if and only if a_1=...=a_k=1/k. This resolves an open problem raised in 1991 by Chung and Graham [J. AMS '91].   While hypergraphs satisfying the property corresponding to a_1=...=a_k=1/k are not necessarily quasi-random, we manage to find a characterization of the hypergraphs satisfying this property. Somewhat surprisingly, it turns out that (essentially) there is a unique non quasi-random hypergraph satisfying this property. The proofs combine probabilistic and algebraic arguments with results from the theory of association schemes.
We have employed the Density Functional Theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyse the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropic-like to nematic-like states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition the system presents interface-like states which allow to continuously transform the nematic-like phase to the isotropic-like phase without undergoing a phase transition. Two different mechanisms for the disappearance of the capillary transition are identified. When the director of the nematic-like state is homogeneously planar-anchored with respect to the substrates, the capillary transition ends up in a critical point. This scenario is analogous to the observed in Ising models when confined in slit pores with opposing surface fields which have critical wetting transitions. When the nematic-like state has a linearly distorted director field, the capillary transition continuously transforms in a transition between two nematic-like states.
We present a multiscale modeling approach that concurrently couples quantum mechanical, classical atomistic and continuum mechanics simulations in a unified fashion for metals. This approach is particular useful for systems where chemical interactions in a small region can affect the macroscopic properties of a material. We discuss how the coupling across different scales can be accomplished efficiently, and we apply the method to multiscale simulations of an edge dislocation in aluminum in the absence and presence of H impurities.
We give an improvement of a result of Zverovich and Zverovich which gives a condition on the first and last elements in a decreasing sequence of positive integers for the sequence to be graphic, that is, the degree sequence of a finite graph.
Background: The isotropic harmonic oscillator supplemented by a strong spin-orbit interaction has been the cornerstone of nuclear structure since its inception more than seven decades ago. In this paper we introduce---or rather re-introduced---the "Dirac Oscillator", a fully relativistic basis that has all the desired attributes of the ordinary harmonic oscillator while naturally incorporating a strong spin-orbit coupling.   Purpose: To assess---to our knowledge for the first time---the power and flexibility of the Dirac Oscillator basis in the solution of nuclear structure problems within the framework of covariant density functional theory.   Methods: Self-consistent calculations of binding energies and ground-state densities for a selected set of doubly-magic magic are performed using the Dirac-oscillator basis and are then compared against results obtained with the often-used Runge-Kutta method.   Results: Results obtained using the Dirac oscillator basis reproduced with high accuracy those derived using the Runge-Kutta method and suggest a clear path for a generalization to systems with axial symmetry.   Conclusions: Although the three-dimensional harmonic oscillator with spin-orbit corrections has been the staple of the nuclear shell model since the beginning, the Dirac oscillator is practically unknown among the nuclear physics community. In this paper we illustrate the power and flexibility of the Dirac oscillator and suggest extensions to the study of systems without spherical symmetry as required in constrained calculations of nuclear excitations.
A theory is proposed for kinetic effects in isotropic Heisenberg antiferromagnets at temperatures above the Neel point. A metod based on the analysis of a set of Feynman diagrams for the kinetic coefficients is developed for studying the critical dynamics. The scaling behavior of the generalized coefficient of spin diffusion and relaxation constant in the paramagnetic phase is studied in terms of the approximation of coupling modes. It is shown that the kinetic coefficients in an antiferromagnetic system are singular in the fluctuation region. The corresponding critical indices for diffusion and relaxation processes are calculated. The scaling dimensionality of the kinetic coefficients agrees with the predictions of dynamic scaling theory and a renormalization group analysis. The proposed theory can be used to study the momentum and frequency dependence of the kinetic parameters, and to determine the form of the scaling functions. The role of nonlocal correlations and spin-liquid effects in magnetic systems is briefly discussed.
HD 5980 is a unique system containing one massive star (star A) that is apparently entering the luminous blue variable phase, and an eclipsing companion (star B) that may have already evolved beyond this phase to become a Wolf-Rayet star. In this paper we present the results from FUSE observations obtained in 1999, 2000, and 2002 and one far-UV observation obtained by ORFEUS/BEFS in 1993 shortly before the first eruption of HD 5980. The eight phase-resolved spectra obtained by FUSE in 2002 are analyzed in the context of a wind-eclipse model. This analysis shows that the wind of the eruptor obeyed a very fast velocity law in 2002, which is consistent with the line-driving mechanism. Large amplitude line-profile variations on the orbital period are shown to be due to the eclipse of star B by the wind of star A, although the eclipse due to gas flowing in the direction of star B is absent. This can only be explained if the wind of star A is not spherically symmetric, or if the eclipsed line radiation is "filled-in" by emission originating from somewhere else in the system, e.g., in the wind-wind collision region. Except for a slightly lower wind speed, the ORFEUS/BEFS spectrum is very similar to the spectrum obtained by FUSE at the same orbital phase: there is no indication of the impending eruption. However, the trend for decreasing wind velocity suggests the occurrence of the "bi-stability" mechanism, which in turn implies that the restructuring of the circumbinary environment caused by the transition from "fast, rarefied wind" to "slow, dense wind" was observed as the eruptive event. The underlying mechanism responsible for the long-term decrease in wind velocity that precipitated this change remains an open issue.
An integral part of the Unified Model for Active Galactic Nuclei (AGNs) is an axisymmetric obscuring medium, which is commonly depicted as a torus of gas and dust surrounding the central engine. However, a robust, dynamical model of the torus is required in order to understand the fundamental physics of AGNs and interpret their observational signatures. Here we explore self-similar, dusty disk-winds, driven by both magnetocentrifugal forces and radiation pressure, as an explanation for the torus. Using these models, we make predictions of AGN infrared (IR) spectral energy distributions (SEDs) from 2-100 microns by varying parameters such as: the viewing angle; the base column density of the wind; the Eddington ratio; the black hole mass; and the amount of power in the input spectrum emitted in the X-ray relative to that emitted in the UV/optical. We find that models with N_H,0 = 10^25 cm^-2, L/L_Edd = 0.1, and M_BH >= 10^8 Msun are able to adequately approximate the general shape and amount of power expected in the IR as observed in a composite of optically luminous Sloan Digital Sky Survey (SDSS) quasars. The effect of varying the relative power coming out in X-rays relative to the UV is a change in the emission below ~5 micron from the hottest dust grains; this arises from the differing contributions to heating and acceleration of UV and X-ray photons. We see mass outflows ranging from ~1-4 Msun/yr, terminal velocities ranging from ~1900-8000 km/s, and kinetic luminosities ranging from ~1x10^42-8x10^43 erg/s. Further development of this model holds promise for using specific features of observed IR spectra in AGNs to infer fundamental physical parameters of the systems.
Scalar boson stars and Dirac stars are solitonic solutions of the Einstein{Klein-Gordon and Einstein- Dirac classical equations, respectively. Despite the different bosonic vs: fermionic nature of the matter field, these solutions to the classical field equations have been shown to have qualitatively similar features [1]. In particular, for spinning stars the most fundamental configurations can be in both cases toroidal, unlike spinning Proca stars that are spheroidal [2]. In this paper we gauge the scalar and Dirac fields, by minimally coupling them to standard electromagnetism. We explore the impact of the gauge coupling on the resulting solutions. One of the most relevant difference concerns the gyromagnetic ratio, which for the scalar stars takes values around 1, whereas for Dirac stars takes values around 2.
This note establishes an interior quantitative lower bound for nonnegative supersolutions of fully nonlinear uniformly parabolic equations. The result may be interpreted as a nonlinear, quantitative version of a growth lemma established by Krylov and Safonov for nonnegative supersolutions of linear uniformly parabolic equations in nondivergence form. Our approach is different, and follows from an application of the Fabes-Stroock estimate. The result is the parabolic analogue of an elliptic regularity estimate established by Caffarelli, Souganidis, and Wang in the stochastic homogenization of fully nonlinear uniformly elliptic equations.
Doubled $\alpha'$-geometry is the simplest higher-derivative gravitational theory with exact global duality symmetry. We use the double metric formulation of this theory to compute on-shell three-point functions to all orders in $\alpha'$. A simple pattern emerges when comparing with the analogous bosonic and heterotic three-point functions. As in these theories, the amplitudes factorize. The theory has no Gauss-Bonnet term, but contains a Riemann-cubed interaction to second order in $\alpha'$.
I give an introduction to the theory of meson-antimeson mixing, aiming at students who plan to work at a flavour physics experiment or intend to do associated theoretical studies. I derive the formulae for the time evolution of a neutral meson system and show how the mass and width differences among the neutral meson eigenstates and the CP phase in mixing are calculated in the Standard Model. Special emphasis is laid on CP violation, which is covered in detail for K mixing, Bd mixing and Bs mixing. I explain the constraints on the apex (rho-bar,eta-bar) of the unitarity triangle implied by epsilon_K, Delta m_{B_d}, Delta m_{B_d}/(Delta m_{B_s}) and various mixing-induced CP asymmetries such as a_CP(Bd-bar -> J/psi K_short)(t). The impact of a future measurement of CP violation in flavour-specific Bd decays is also shown.
RR Lyrae stars pulsating in the fundamental mode have long been used to measure interstellar reddening, based on their observed uniformity of $B-V$ color at minimum light after small corrections for metallicity and period are applied. However, little attention has been paid to the first overtone pulsators (RRc or RR1). We present new $V-I$ observations of field RRc stars, supplemented with published data from uncrowded RRc in globular clusters. Preliminary results indicate the RRc colors are correlated with period, but appear to be independent of the stars' metallicity. The scatter around the period-color relation is slightly larger than a comparable relation for RRab. Thus, RRc can be useful indicators of line of sight reddening toward old stellar systems, particularly when multiple stars are available as in Oosterhoff II globular clusters and metal-poor galaxies.