ShantanuT01/DACTYL-Pretraining huggingface dataset:
It is known that zigzag graphene edge is able to support edge states: there is a non-dispersive single-electron band localized near the zigzag edge. However, it is generally believed that no edge states exist near the armchair edge. In this paper we re-examine this notion. It is demonstrated that while, indeed, the pristine armchair edge does not support any localized states, they do appear if the edge is subjected to suitable modifications (e.g. chemical functionalization). We explicitly present two types of the edge modification which support the localized states. Unlike zigzag edge states, which have zero energy and show no dispersion, properties of the armchair localized states depend sensitively on the type of edge modification. Under suitable conditions they demonstrate pronounced dispersion. While the zigzag edge state wavefunction decays monotonously when we move away from the edge, the armchair edge state wavefunction shows non-monotonous decay. Such states may be observed in scanning tunneling spectroscopy experimentally.
The continuum random-phase approximation is extended to the one applicable to deformed nuclei. We propose two different approaches. One is based on the use of the three dimensional (3D) Green's function and the other is the small-amplitude TDHF with the absorbing-boundary condition. Both methods are based on the 3D Cartesian grid representation and applicable to systems without any symmetry on nuclear shape. The accuracy and identity of these two methods are examined with the BKN interaction. Using the full Skyrme energy functional in the small-amplitude TDHF approach, we study the isovector giant dipole states in the continuum for O-16 and for even-even Be isotopes.
Stellar loci are widely used for selection of interesting outliers, reddening determinations, and calibrations. However, hitherto the dependence of stellar loci on metallicity has not been fully explored and their intrinsic widths are unclear. In this paper, by combining the spectroscopic and re-calibrated imaging data of the SDSS Stripe 82, we have built a large, clean sample of dwarf stars with accurate colors and well determined metallicities to investigate the metallicity dependence and intrinsic widths of the SDSS stellar loci. Typically, one dex decrease in metallicity causes 0.20 and 0.02 mag decrease in colors u-g and g-r, and 0.02 and 0.02 mag increase in colors r-i and i-z, respectively. The variations are larger for metal-rich stars than for metal-poor ones, and for F/G/K stars than for A/M ones. Using the sample, we have performed two dimensional polynomial fitting to the u-g, g-r, r-i, and i-z colors as a function of color g-i and metallicity [Fe/H]. The residuals, at the level of 0.029, 0.008, 0.008 and 0.011 mag for the u-g, g-r, r-i, and i-z colors, respectively can be fully accounted for by the photometric errors and metallicity uncertainties, suggesting that the intrinsic widths of the loci are at maximum a few mmag. The residual distributions are asymmetric, revealing that a significant fraction of stars are binaries. In a companion paper, we will present an unbiased estimate of the binary fraction for field stars. Other potential applications of the metallicity dependent stellar loci are briefly discussed.
Window glass is a ternary mixture, while pyrex (after window glass, the most common form of commercial glass) is a quaternary. Building on our previous success in deriving the composition of window glass (sodium calcium silicate) without adjustable parameters, and borrowing from known reconstructed crystalline surfaces, we model pyrex as silica clusters with a specific ternary interface. Our global model explains the thermal expansivity contours of ternary sodium borosilicates, and it is consistent with the optimized resistance of pyrex to mechanical and thermal shocks. It suggests new directions for studying the nanoscopic structure of these remarkable materials.
We apply the connected moments expansion to simple quantum--mechanical examples and show that under some conditions the main equations of the approach are no longer valid. In particular we consider two--level systems, the harmonic oscillator and the pure quartic oscillator.
We present a Gutzwiller von Neumann dynamics (GvND) method for simulating equilibrium and nonequilibrium phenomena in strongly correlated electron systems. Our approach is a real-space formulation of the time-dependent Gutzwiller approximation method. Applying the GvND method to simulate interaction quenches in the Peierls-Hubbard model, we demonstrate the amplification of initial inhomogeneities, which in turn results in the collapse of quench-induced synchronized oscillation. Moreover, we find a dynamical phase transition separating two quasi-stationary regimes with rather distinct spatial distributions of physical quantities after the collapsed oscillation. In particular, in the strong-coupling regime, the system exhibits a dynamic phase separation in the quasi-stationary state. Our results thus underscore the importance of spatial fluctuations in the nonequilibrium dynamics of strongly correlated systems.
We determine the critical strength of the effective electric coupling for the onset of Bose condensation of stable magnetic monopoles and antimonopoles in SU(2) Yang-Mills thermodynamics. Two scenarios are considered: infinitely fast and infinitely slow downward approach of the critical temperature. Our results support the claim that the first lepton family and the weak interactions emerge from pure SU(2) gauge dynamics of scale $\sim 0.5 $MeV.
We give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff.
A classical twisting lemma says that given a finitely generated torsion module $M$ over the Iwasawa algebra $\mathbb{Z}_p[[\Gamma ]]$ with $\Gamma \cong \mathbb{Z}_p, \ \exists$ a continuous character $\theta: \Gamma \rightarrow \mathbb{Z}_p^\times$ such that, the $ \Gamma^{n}$-Euler characteristic of the twist $M(\theta)$ is finite for every $n$. This twisting lemma has been generalized for the Iwasawa algebra of a general compact $p$-adic Lie group $G$. In this article, we consider a further generalization of the twisting lemma to $\mathcal{T}[[G]]$ modules, where $G$ is a compact $p$-adic Lie group and $\mathcal{T}$ is a finite extension of $\mathbb{Z}_p[[X]]$. Such modules naturally occur in Hida theory. We also indicate arithmetic application by considering the twisted Euler Characteristic of the big Selmer (respectively fine Selmer) group of a $\Lambda$-adic form over a $p$-adic Lie extension.
A possible existence of cosmologically large domains of antimatter or astronomical ``anti-objects'' is discussed. A brief review of different scenarios of baryogenesis predicting a noticeable amount of antimatter is given. Though both theory and observations indicate that the universe is most possibly uniformly charge asymmetric without any noticeable amount of antimatter, several natural scenarios are possible that allow for cosmologically (astronomically) interesting objects in close vicinity to us. The latter may be discovered by observation of cosmic ray antinuclei.
In this paper, we establish the Freidlin-Wentzell's large deviations for quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The proof is based on the weak convergence approach.
Real-world image denoising is a practical image restoration problem that aims to obtain clean images from in-the-wild noisy inputs. Recently, the Vision Transformer (ViT) has exhibited a strong ability to capture long-range dependencies, and many researchers have attempted to apply the ViT to image denoising tasks. However, a real-world image is an isolated frame that makes the ViT build long-range dependencies based on the internal patches, which divides images into patches, disarranges noise patterns and damages gradient continuity. In this article, we propose to resolve this issue by using a continuous Wavelet Sliding-Transformer that builds frequency correspondences under real-world scenes, called DnSwin. Specifically, we first extract the bottom features from noisy input images by using a convolutional neural network (CNN) encoder. The key to DnSwin is to extract high-frequency and low-frequency information from the observed features and build frequency dependencies. To this end, we propose a Wavelet Sliding-Window Transformer (WSWT) that utilizes the discrete wavelet transform (DWT), self-attention and the inverse DWT (IDWT) to extract deep features. Finally, we reconstruct the deep features into denoised images using a CNN decoder. Both quantitative and qualitative evaluations conducted on real-world denoising benchmarks demonstrate that the proposed DnSwin performs favorably against the state-of-the-art methods.
In this paper we present a probabilistic algorithm to compute the coefficients of modular forms of level one. Focus on the Ramanujan's tau function, we give out the explicit complexity of the algorithm. From a practical viewpoint, the algorithm is particularly well suited for implementations.
Heusler type compounds have long been recognized as potential thermoelectric (TE) materials. Here, the experimentally observed TE properties of Fe$_{2}$VAl are understood through electronic structure calculations in the temperature range of $300-800$ K. The observed value of $S$ is $\sim-$138 $\mu$V/K at 300 K. Then, the $|S|$ decreases with increase in temperature up to the highest temperature with the value of $\sim-$18 $\mu$V/K at 800 K. The negative sign of $S$ in the full temperature window signifies the dominating $n$-type character of the compound. The temperature dependent of electrical conductivity, $\sigma$ (thermal conductivity, $\kappa$) exhibits the increasing (decreasing) trend with the values of $\sim$1.2 $\times$ 10$^{5}$ $\Omega^{-1}$m$^{-1}$ ($\sim$23.7 W/m-K) and $\sim$2.2 $\times$ 10$^{5}$ $\Omega^{-1}$m$^{-1}$ ($\sim$15.3 W/m-K) at 300 K and 800 K, respectively. In order to understand these transport properties, the DFT based semi-classical Boltzmann theory is used. The contributions of multi-band electron and hole pockets are found to be mainly responsible for the temperature dependent trend of these properties. The decrement of $|S|$ and increment of $\sigma/\tau$ $\&$ $\kappa_{e}/\tau$ ($\tau$ is relaxation time) with temperature is directly related with the contribution of multiple hole pockets. Present study suggests that DFT based electronic calculations provide reasonably good explanations of experimental TE properties of Fe$_{2}$VAl in the high temperature range of $300-800$ K.
The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a consistent perturbative framework for describing the statistical distribution of cosmological large-scale structure. In a previous EFTofLSS calculation that involved the one-loop power spectra and tree-level bispectra, it was shown that the $k$-reach of the prediction for biased tracers is comparable for all investigated masses if suitable higher-derivative biases, which are less suppressed for more massive tracers, are added. However, it is possible that the non-linear biases grow faster with tracer mass than the linear bias, implying that loop contributions could be the leading correction to the bispectra. To check this, we include the one-loop contributions in a fit to numerical data in the limit of strongly enhanced higher-order biases. We show that the resulting one-loop power spectra and higher-derivative plus leading one-loop bispectra fit the two- and three-point functions respectively up to $k\simeq 0.19\ h\ \rm{Mpc}^{-1}$ and $k\simeq 0.14\ h\ \rm{Mpc}^{-1}$ at the percent level. We find that the higher-order bias coefficients are not strongly enhanced, and we argue that the gain in perturbative reach due to the leading one-loop contributions to the bispectra is relatively small. Thus, we conclude that higher-derivative biases provide the leading correction to the bispectra for tracers of a very wide range of masses.
We study the evaporative cooling of magnetically trapped atomic hydrogen on the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is described by the coupled differential equations, considering both the evaporation and dipolar spin relaxation processes. The numerical time-evolution calculations quantitatively agree with the recent experiment of Bose-Einstein condensation with atomic hydrogen. It is demonstrated that the balance between evaporative cooling and heating due to dipolar relaxation limits the number of condensates to 9x10^8 and the corresponding condensate fraction to a small value of 4% as observed experimentally.
The illuminating role of differential forms in electromagnetism is seldom discussed in the classroom. It is the aim of this article to bring forth some of the relevant insights that can be learnt from a differential forms approach to E\&M. The article is self-contained in that no previous knowledge of forms is needed to follow it through. The effective polarization of the classical vacuum due to a uniform gravitational field and of the quantum vacuum in the Casimir effect are used to illustrate the power and easiness of interpretation of differential forms in dealing with electromagnetism in nontrivial situations. We hope that this article motivates the physics teacher to bring the subject of differential forms to the classroom.
We study the equilibration and relaxation processes within the time-dependent Hartree-Fock approach using the Wigner distribution function. On the technical side we present a geometrically unrestricted framework which allows us to calculate the full six-dimensional Wigner distribution function. With the removal of geometrical constraints, we are now able to extend our previous phase-space analysis of heavy-ion collisions in the reaction plane to unrestricted mean-field simulations of nuclear matter on a three-dimensional Cartesian lattice. From the physical point of view we provide a quantitative analysis on the stopping power in TDHF. This is linked to the effect of transparency. For the medium-heavy $^{40}$Ca+$^{40}$Ca system we examine the impact of different parametrizations of the Skyrme force, energy-dependence, and the significance of extra time-odd terms in the Skyrme functional. For the first time, transparency in TDHF is observed for a heavy system, $^{24}$Mg+$^{208}$Pb.
We prove limit theorems for the weighted quadratic variation of trifractional Brownian motion and $n$-th order fractional Brownian motion. Furthermore, a sufficient condition for the $L^P$-convergence of the weighted quadratic variation for Gaussian processes is obtained as a byproduct. As an application, we give a statistical estimator for the self-similarity index of trifractional Brownian motion. These theorems extend results of Baxter, Gladyshev, and Norvai\v{s}a.
Let $\pi\colon\mathcal{X}\to B$ be a family over a smooth connected analytic variety $B$, not necessarily compact, whose general fiber $X$ is smooth of dimension $n$, with irregularity $\geq n+1$ and such that the image of the canonical map of $X$ is not contained in any quadric of rank $\leq 2n+3$. We prove that if the Albanese map of $X$ is of degree $1$ onto its image then the fibers of $\pi\colon\mathcal{X}\to B$ are birational under the assumption that all the $1$-forms and all the $n$-forms of a fiber are holomorphically liftable to $\mathcal{X}$. Moreover we show that generic Torelli holds for such a family $\pi\colon \mathcal{X}\to B$ if, in addition to the above hypothesis, we assume that the fibers are minimal and their minimal model is unique. There are counterexamples to the above statements if the canonical image is contained inside quadrics of rank $\leq 2n+3$. We also solve the infinitesimal Torelli problem for an $n$-dimensional variety $X$ of general type with irregularity $\geq n+1$ and such that its cotangent sheaf is generated and the canonical map is a rational map whose image is not contained in a quadric of rank less or equal to $2n+3$.
We present the exact solution of the 1D Dirac equation for the inverse-square-root potential $1/\sqrt{x}$ for several configurations of vector, pseudo-scalar and scalar fields. Each fundamental solution of the problem can be written as an irreducible linear combination of two Hermite functions of a scaled and shifted argument. We derive the exact equations for bound-state energy eigenvalues and construct accurate approximations for the energy spectrum.
We investigate the thermal and electronic collective fluctuations that contribute to the finite-temperature adsorption properties of flexible adsorbates on surfaces on the example of the molecular switch azobenzene C$_{12}$H$_{10}$N$_{2}$ on the Ag(111) surface. Using first-principles molecular dynamics simulations we obtain the free energy of adsorption that accurately accounts for entropic contributions, whereas the inclusion of many-body dispersion interactions accounts for the electronic correlations that govern the adsorbate binding. We find the adsorbate properties to be strongly entropy-driven, as can be judged by a kinetic molecular desorption prefactor of 10$^{24}$ s$^{-1}$ that largely exceeds previously reported estimates. We relate this effect to sizable fluctuations across structural and electronic observables. Comparison of our calculations to temperature-programmed desorption measurements demonstrates that finite-temperature effects play a dominant role for flexible molecules in contact with polarizable surfaces, and that recently developed first-principles methods offer an optimal tool to reveal novel collective behavior in such complex systems.
In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results using second order modulus of continuity, Peetres K-functional Lipschitz class.
We establish the extent to which photons and dileptons are penetrating probes of hot hadronic matter by computing mean free paths. Absorption is indeed negligible for real photons as mean free paths are roughly tenths of \AAngstr\"oms. However, vector dominance effects, which provide rich structure in virtual photon mass spectra, introduce nonnegligible reabsorption and rehadronization resulting in mean free paths of the order of tens of femtometers. Consequences are illustrated by considering the net dilepton yield near the rho peak via thermal \pi\pi annihilation from a short-lived hadronic fireball. Results suggest that disappearance of the rho in heavy-ion collisions can be due in part to reabsorption/rehadronization rather than solely due to collective effects.
We study the extension of a result of Loxton (1972) on representation of algebraic integers as sums of roots of unity to Kummer extensions.
We present an analysis of super-giant molecular complexes (SGMCs) in the overlap region of the Antennae galaxy merger, based on ALMA CO(3-2) interferometry and VLT/SINFONI imaging spectroscopy of H2 1-0 S(1) at angular resolutions of 0.9" and 0.7", respectively. All but one SGMC have multiple velocity components offset from each other by up to 150 km/s. H2 line emission is found in all SGMCs and the kinematics of H2 and CO are well matched. H2/CO line ratios vary by up to a factor of 10 among SGMCs and different velocity components of the same SGMCs. We also identify the CO counterpart of a bright, compact source of near-IR H2 line emission, which shows no Brgamma, and was first identified with SINFONI. This source has the highest H2/CO line ratio, and coincides with the steepest CO velocity gradient of the entire overlap region. With a size of 50 pc and a virial mass of a few 10^7 Msun it is perhaps a pre-cluster cloud that has not yet formed significant numbers of massive stars. We present observational evidence that the H2 emission is powered by shocks, and demonstrate how the H2 1-0 S(1) and the CO(3-2) lines can be used as tracers of energy dissipation and gas mass, respectively. The variations in the H2/CO line ratio may indicate that the SGMCs are dissipating their turbulent kinetic energy at different rates. The compact source could represent a short (~ 1 Myr) evolutionary stage in the early formation of super-star clusters.
As indicated by the observed X-ray flares, a great amount of energy could be intermediately released from the postburst central engine of gamma-ray bursts (GRBs). As a natural consequence, the GRB external shock could be energized over and over. With such a multiple energy injection model, we explore the unique X-ray afterglow light curve of GRB 050712, which exists four apparent shallow decay plateaus. Together with three early X-ray flares, the central engine of GRB 050712 is supposed to release energy at least seven times after the burst. Furthermore we find that the energy released during four plateaus are all on the same order of magnitude, but the luminosity decreases with time significantly. These results may provide some interesting implications for the GRB central engine.
We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny.
In this article the current knowledge of the group of lambda Bootis stars is reviewed. These metal poor objects are quite outstanding compared to other chemically peculiar stars of the upper main sequence. Up to now no theory has been developed which is able to explain the majority of observational results. This article is mainly focused on the work which needs to be done in the future in order to clarify the lambda Bootis phenomenon.
The properties of single-crystal SrTiO$_{3}$ substrates and homoepitaxial SrTiO$_{3}$ films grown by pulsed laser deposition have been compared, in order to understand the loss of interfacial conductivity when more than a critical thickness of nominally homoepitaxial SrTiO$_{3}$ is inserted between a LaAlO$_{3}$ film and a SrTiO$_{3}$ substrate. In particular, the chemical composition and the structure of homoepitaxial SrTiO$_{3}$ investigated by low-energy ion-scattering and surface x-ray diffraction, show that for insulating heterointerfaces, a Sr-excess is present between the LaAlO$_{3}$ and homoepitaxial SrTiO$_{3}$. Furthermore, an increase in the out-of-plane lattice constant is observed in LaAlO$_{3}$, indicating that the conductivity both with and without insertion of SrTiO$_{3}$ thin film originates from a Zener breakdown associated with the polar catastrophe. When more than a critical thickness of homoepitaxial SrTiO$_{3}$ is inserted between LaAlO$_3$ and SrTiO$_3$, the electrons transferred by the electronic reconstruction are trapped by the formation of a Sr-rich secondary phase and Sr-vacancies. The migration of Sr towards the surface of homoepitaxial STO and accompanying loss of interfacial conductivity can be delayed by reducing the Sr-content in the PLD target.