ShantanuT01/DACTYL-Pretraining huggingface dataset:
We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, O, we consider the anomalous dimensions, gamma(n,l), of the double-trace operators of the form O (del^2)^n (del)^l O. Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of |gamma(n,l)|<4. Non-renormalizable AdS interactions lead to violations of the bound at large values of n. We also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. We show that the presence of the heavy field "unitarizes" the growth in the anomalous dimensions, and leads to a resonance-like behavior in gamma(n,l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, we demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum of anomalous dimensions in d-dimensional CFTs and flat-space S-matrix elements in d+1 dimensions. We comment on the emergence of flat-space locality from the CFT perspective.
We forecast constraints on primordial non-Gaussianity (PNG) and bias parameters from measurements of galaxy power spectrum and bispectrum in future radio continuum and optical surveys. In the galaxy bispectrum, we consider a comprehensive list of effects, including the bias expansion for non-Gaussian initial conditions up to second order, redshift space distortions, redshift uncertainties and theoretical errors. These effects are all combined in a single PNG forecast for the first time. Moreover, we improve the bispectrum modelling over previous forecasts, by accounting for trispectrum contributions. All effects have an impact on final predicted bounds, which varies with the type of survey. We find that the bispectrum can lead to improvements up to a factor $\sim 5$ over bounds based on the power spectrum alone, leading to significantly better constraints for local-type PNG, with respect to current limits from \textit{Planck}. Future radio and photometric surveys could obtain a measurement error of $\sigma(f_{\mathrm{NL}}^{\mathrm{loc}}) \approx 0.2$. In the case of equilateral PNG, galaxy bispectrum can improve upon present bounds only if significant improvements in the redshift determinations of future, large volume, photometric or radio surveys could be achieved. For orthogonal non-Gaussianity, expected constraints are generally comparable to current ones.
We study the dynamical properties of a driven-dissipative Bose-Hubbard model in the strongly interacting regime through a quantum trajectory approach with a cluster-Gutzwiller Ansatz for the wave function. This allows us to take classical and quantum correlations into account. By studying the dynamical hysteresis surface that arises by sweeping through the coherent driving strength we show that the phase diagram for this system is in qualitative correspondence with the Gutzwiller mean-field result. However, quantitative differences are present and the inclusion of classical and quantum correlations causes a significant shift of the critical parameters. Additionally, we show that approximation techniques relying on a unimodal distribution such as the mean field and $1/z$ expansion drastically underestimate the particle number fluctuations. Finally, we show that a proposed mapping of the driven-dissipative many-body Bose-Hubbard model onto a single driven-dissipative Kerr model is not accurate for parameters in the hysteresis regime.
We investigate effects of doping on formation energy and concentration of oxygen vacancies at a metal oxide surface, using MgO (100) as an example. Our approach employs density-functional theory, where the performance of the exchange-correlation functional is carefully analyzed, and the functional is chosen according to a fundamental condition on DFT ionization energies. The approach is further validated by CCSD(T) calculations for embedded clusters. We demonstrate that the concentration of oxygen vacancies at a doped oxide surface is largely determined by formation of a macroscopically extended space charge region.
Bondal and Kapranov describe how to assign to a full exceptional collection on a variety X a DG category C such that the bounded derived category of coherent sheaves on X is equivalent to the bounded derived category of C. In this paper we show that the category C has finite dimensional spaces of morphisms. We describe how it behaves under mutations and present an algorithm allowing to calculate it for full exceptional collections with vanishing Ext^k groups for k > 1. Finally, we use it to describe an example of a non-commutative deformation of certain rational surfaces.
Recently, Huang gave a very elegant proof of the Sensitivity Conjecture by proving that hypercube graphs have the following property: every induced subgraph on a set of more than half its vertices has maximum degree at least $\sqrt{d}$, where $d$ is the valency of the hypercube. This was generalised by Alon and Zheng who proved that every Cayley graph on an elementary abelian $2$-group has the same property. Very recently, Potechin and Tsang proved an analogous results for Cayley graphs on abelian groups. They also conjectured that all Cayley graphs have the analogous property. We disprove this conjecture by constructing various counterexamples, including an infinite family of Cayley graphs of unbounded valency which admit an induced subgraph of maximum valency $1$ on a set of more than half its vertices.
We study an isothermal system of semi-degenerate self-gravitating fermions in general relativity. Such systems present mass density solutions with a central degenerate core, a plateau and a tail which follows a power law behaviour $r^{-2}$. The different solutions are governed by the free parameters of the model: the degeneracy and temperature parameters at the center, and the particle mass $m$. We then analyze in detail the free parameter space for a fixed $m$ in the keV regime, by studying the one-parameter sequences of equilibrium configurations up to the critical point, which is represented by the maximum in a central density ($\rho_0$) Vs. core mass ($M_c$) diagram. We show that for fully degenerate cores, the known expression for the critical core mass $M_c^{cr}\propto m_{pl}^3/m^2$ is obtained, while instead for low degenerate cores, the critical core mass increases showing the temperature effects in a non linear way. The main result of this work is that when applying this theory to model the distribution of dark matter in galaxies from the very center up to the outer halos, we do not find any critical core-halo configuration of self-gravitating fermions, which be able to explain the super massive dark object in their centers together with an outer halo simultaneously.
Ultrathin freestanding membranes with a pronounced metal-insulator transition (MIT) provides huge potential in future flexible electronic applications as well as a unique aspect of the study of lattice-electron interplay. However, the reduction of the thickness to an ultrathin region (a few nm) is typically detrimental to the MIT in epitaxial films, and even catastrophic for their freestanding form. Here, we report an enhanced MIT in VO2-based freestanding membranes, with a lateral size up to millimetres and VO2 thickness down to 5 nm. The VO2-membranes were detached by dissolving a Sr3Al2O6 sacrificial layer between the VO2 thin film and c-Al2O3(0001) substrate, allowing a transfer onto arbitrary surfaces. Furthermore, the MIT in the VO2-membrane was greatly enhanced by inserting an intermediate Al2O3 buffer layer. In comparison to the best available ultrathin VO2-membranes, the enhancement of MIT is over 400% at 5 nm VO2 thickness and more than one order of magnitude for VO2 above 10 nm. Our study widens the spectrum of functionality in ultrathin and large-scale membranes, and enables the potential integration of MIT into flexible electronics and photonics.
Materials exhibiting reversible resistive switching in electrical fields are highly demanded for functional elements in oxide electronics. In particular, multilevel switching effects allow for advanced applications like neuromorphic circuits. Here we report on a structurally driven switching mechanism involving the so-called `dead layers' of perovskite manganite surfaces. Forming a tunnel barrier whose thickness can be changed in monolayer steps by electrical fields, the switching effect exhibits well-defined and robust resistive states.
The pseudofermion functional renormalization group (pf-FRG) has been put forward as a semi-analytical scheme that, for a given microscopic spin model, allows to discriminate whether the low-temperature states exhibit magnetic ordering or a tendency towards the formation of quantum spin liquids. However, the precise nature of the putative spin liquid ground state has remained hard to infer from the original (single-site) pf-FRG scheme. Here we introduce a cluster pf-FRG approach, which allows for a more stringent connection between a microscopic spin model and its low-temperature spin liquid ground states. In particular, it allows to calculate spatially structured fermion bilinear expectation values on spatial clusters, which are formed by splitting the original lattice into several sublattices, thereby allowing for the positive identification of a family of bilinear spin liquid states. As an application of this cluster pf-FRG approach, we consider the $J_1$-$J_2$ SU($N$)-Heisenberg model on a square lattice, which is a paradigmatic example for a frustrated quantum magnet exhibiting quantum spin liquid behavior for intermediate coupling strengths. In the well-established large-$N$ limit of this model, we show that our approach correctly captures the emergence of the $\pi$-flux spin liquid state at low temperatures. For small $N$, where the precise nature of the ground state remains controversial, we focus on the widely studied case of $N=2$, for which we determine the low-temperature phase diagram near the strongly-frustrated regime after implementing the fermion number constraint by the flowing Popov-Fedotov method. Our results suggest that the $J_1$-$J_2$-Heisenberg model does not support the formation of a fermion bilinear spin liquid state.
A number of planetary nebulae show binary central stars and significant abundance discrepancies between values estimated from colisionally excited lines when compared to the same abundances estimated from recombination lines. One approach to investigate this yet unsolved problem is using spatially resolved images of emission lines in an attempt to detect a possibly distinct metal rich component in the nebula. In this work we present results of spatially resolved bundance analysis of NGC 6778 based on data gathered from VLT VIMOS-IFU. We discuss the spatial variations found as well as possible limitations of the method in answering questions about abundance variations.
Random walk is one of the most classical and well-studied model in probability theory. For two correlated random walks on lattice, every step of the random walks has only two states, moving in the same direction or moving in the opposite direction. This paper presents a decomposition method to study the dependency structure of the two correlated random walks. By applying change-of-time technique used in continuous time martingales (see for example [1] for more details), the random walks are decomposed into the composition of two independent random walks $X$ and $Y$ with change-of-time $T$, where $X$ and $Y$ model the common movements and the counter movements of the correlated random walks respectively. Moreover, we give a sufficient and necessary condition for mutual independence of $X$, $Y$ and $T$.
In this survey article, we give an introduction to two methods of proof in random matrix theory: The method of moments and the Stieltjes transform method. We thoroughly develop these methods and apply them to show both the semicircle law and the Marchenko-Pastur law for random matrices with independent entries. The material is presented in a pedagogical manner and is suitable for anyone who has followed a course in measure-theoretic probability theory.
We consider the transformation of multi-partite states in the single copy setting under positive-partial-transpose-preserving operations (PPT-operations) and obtain both qualitative and quantitative results. Firstly, for some pure state transformations that are impossible under local operations and classical communication (LOCC), we demonstrate that they become possible with a surprisingly large success probability under PPT-operations. Furthermore, we clarify the convertibility of arbitrary multipartite pure states under PPT-operations, and show that a drastic simplification in the classification of pure state entanglement occurs when the set of operations is switched from LOCC to PPT-operations. Indeed, the infinitely many types of LOCC-incomparable entanglement are reduced to only one type under the action of PPT-operations. This is a clear manifestation of the increased power afforded by the use of PPT-bound entanglement. In addition, we further enlarge the set of operations to clarify the effect of another type of bound entanglement, multipartite unlockable bound entanglement, and show that a further simplification occurs. As compared to pure states a more complicated situation emerges in the mixed state settings. While single copy distillation becomes possible under PPT-operations for some mixed states it remains impossible for other mixed states.
The half-Heusler alloy NiMnSb is one of the local-moment ferromagnets with unique properties for future applications. Band structure calculations predict exclusively majority bands at the Fermi level, thus indicating {100%} spin polarization there. As one thinks about applications and the design of functional materials, the influence of chemical disorder in these materials must be considered. The magnetization, spin polarization, and electronic structure are expected to be sensitive to structural and stoichiometric changes. In this contribution, we report on an investigation of the spin-dependent electronic structure of NiMnSb. We studied the influence of chemical disorder on the unoccupied electronic density of states by use of the ab-initio Coherent Potential Approximation method. The theoretical analysis is discussed along with corresponding spin-resolved Appearance Potential Spectroscopy measurements. Our theoretical approach describes the spectra as the fully-relativistic self-convolution of the matrix-element weighted, orbitally resolved density of states.
We show that for any metric probability space $(M,d,\mu)$ with a subgaussian constant $\sigma^2(\mu)$ and any set $A \subset M$ we have $\sigma^2(\mu_A) \leq c \log\left(e/\mu(A)\right)\,\sigma^2(\mu)$, where $\mu_A$ is a restriction of $\mu$ to the set $A$ and $c$ is a universal constant. As a consequence we deduce concentration inequalities for non-Lipschitz functions.
Wolf-Rayet (WR) stars are the evolutionary phases of very massive stars prior to the final supernova explosion stage. These stars lose substantial mass during WN and WC stages. The mass losses are associated with diverse elemental and isotopic signatures that represent distinct stellar evolutionary processes. The WR strong winds can host environments for condensation of dust grains with diverse compositions. The condensation of dust in the outflows of the massive stars is supported by several observations. The present work is an attempt to develop a theoretical framework of thermodynamics associated with the condensation of dust grains in the winds of WN and WC phases. A novel numerical code has been developed for dust condensation. Apart from the equilibrium dust condensation calculations, we have attempted, perhaps for the first time, a set of non-equilibrium scenarios for dust condensation in various WR stages. These scenarios differ in terms of the magnitude of the non-equilibrium state, defined in terms of a simulation non-equilibrium parameter. Here, we attempt to understand the sensitivity of the simulation non-equilibrium parameter on the condensation sequence of dust grains. In general, we found that mostly C (graphite), TiC, SiC, AlN, CaS and Fe-metal are condensed in WR winds. The extent of non-equilibrium influences the relative proportions of earliest dust condensate compared to the condensates formed at later stages subsequent to the cooling of the gas. The results indicate that dust grains condensed in the WC phase may substantially contribute carbon-rich dust grains to the interstellar medium.
We measure the projected cross-correlation between low redshift (z < 0.5) far-IR selected galaxies in the SDP field of the Herschel-ATLAS (H-ATLAS) survey and optically selected galaxies from the Galaxy and Mass Assembly (GAMA) redshift survey. In order to obtain robust correlation functions, we restrict the analysis to a subset of 969 out of 6900 H-ATLAS galaxies, which have reliable optical counterparts with r<19.4 mag and well-determined spectroscopic redshifts. The overlap region between the two surveys is 12.6 sq. deg; the matched sample has a median redshift of z ~ 0.2. The cross-correlation of GAMA and H-ATLAS galaxies within this region can be fitted by a power law, with correlation length r_0 ~ 4.63 +/- 0.51 Mpc. Comparing with the corresponding auto-correlation function of GAMA galaxies within the SDP field yields a relative bias (averaged over 2-8 Mpc) of H-ATLAS and GAMA galaxies of b_H/b_G ~ 0.6. Combined with clustering measurements from previous optical studies, this indicates that most of the low redshift H-ATLAS sources are hosted by halos with masses comparable to that of the Milky Way. The correlation function appears to depend on the 250 um luminosity, L_250, with bright (median luminosity \nu L_250 ~ 1.6 x 10^10 L_sun) objects being somewhat more strongly clustered than faint (\nu L_250 ~ 4.0 x 10^9 L_sun) objects. This implies that galaxies with higher dust-obscured star formation rates are hosted by more massive halos.
In recent years, considerable progress has been made in the research area of Question Answering (QA) on document images. Current QA approaches from the Document Image Analysis community are mainly focusing on machine-printed documents and perform rather limited on handwriting. This is mainly due to the reduced recognition performance on handwritten documents. To tackle this problem, we propose a recognition-free QA approach, especially designed for handwritten document image collections. We present a robust document retrieval method, as well as two QA models. Our approaches outperform the state-of-the-art recognition-free models on the challenging BenthamQA and HW-SQuAD datasets.
An approximate method to quantify the mass dependence of the number of two-nucleon (2N) short-range correlations (SRC) in nuclei is suggested. The proposed method relies on the concept of the "local nuclear character" of the SRC. We quantify the SRC and its mass dependence by computing the number of independent-particle model (IPM) nucleon pairs in a zero relative orbital momentum state. We find that the relative probability per nucleon for 2N SRC follows a power law as a function of the mass number $A$. The predictions are connected to measurements which provide access to the mass dependence of SRC. First, the ratio of the inclusive inelastic electron scattering cross sections of nuclei to $^{2}$H at large values of the Bjorken variable. Second, the EMC effect, for which we find a linear relationship between its magnitude and the predicted number of SRC-prone pairs.
In this work, we extend the concept of the double of an ideal defined in \cite{G2}, to the context of modules. We also obtain the genericity of the infinitesimal Lipschitz condition A for an enlarged class of analytic spaces.
An integer $k$ is called regular (mod $n$) if there exists an integer $x$ such that $k^2x\equiv k$ (mod $n$). This holds true if and only if $k$ possesses a weak order (mod $n$), i.e., there is an integer $m\ge 1$ such that $k^{m+1} \equiv k$ (mod $n$). Let $\varrho(n)$ denote the number of regular integers (mod $n$) in the set $\{1,2,\ldots,n\}$. This is an analogue of Euler's $\phi$ function. We introduce the multidimensional generalization of $\varrho$, which is the analogue of Jordan's function. We establish identities for the power sums of regular integers (mod $n$) and for some other finite sums and products over regular integers (mod $n$), involving the Bernoulli polynomials, the Gamma function and the cyclotomic polynomials, among others. We also deduce an analogue of Menon's identity and investigate the maximal orders of certain related functions.
Far infrared cooling lines are ubiquitous features in the spectra of star forming galaxies. Surveys of redshifted fine-structure lines provide a promising new tool to study structure formation and galactic evolution at redshifts including the epoch of reionization as well as the peak of star formation. Unlike neutral hydrogen surveys, where the 21 cm line is the only bright line, surveys of red-shifted fine-structure lines suffer from confusion generated by line broadening, spectral overlap of different lines, and the crowding of sources with redshift. We use simulations to investigate the resulting spectral confusion and derive observing parameters to minimize these effects in pencil-beam surveys of red-shifted far-IR line emission. We generate simulated spectra of the 17 brightest far-IR lines in galaxies, covering the 150 to 1300 micron wavelength region corresponding to redshifts 0 < z < 7, and develop a simple iterative algorithm that successfully identifies the 158 micron [CII] line and other lines. Although the [CII] line is a principal coolant for the interstellar medium, the assumption that the brightest observed lines in a given line of sight are always [CII] lines is a poor approximation to the simulated spectra once other lines are included. Blind line identification requires detection of fainter companion lines from the same host galaxies, driving survey sensitivity requirements. The observations require moderate spectral resolution 700 < R < 4000 with angular resolution between 20 arcsec and 10 armin, sufficiently narrow to minimize confusion yet sufficiently large to include a statistically meaningful number of sources.
We investigate Knight shift and nuclear spin relaxation rate in a charge ordered state of the one-dimensional extended Hubbard model with a quarter filled band by using RPA around the mean-field solution. It is shown that both quantities show splitting below the critical temperature of the charge order, as is experimentally observed. The relationship between the mount of the splitting in the both quantities and the charge disproportionation rate is discussed.
We present the first application to real data from the BOSS DR12 dataset of the Extractor procedure to determine the acoustic scale imprinted on Baryonic Acoustic Oscillations (BAO). We show that, being largely insensitive to the broadband shape of the Power Spectrum, this procedure requires a lower number of nuisance parameters than those used by the BOSS collaboration, For non-reconstructed data our analysis improves the accuracy on the acoustic scale by about 20 %, while for reconstructed ones we get essentially the same level of accuracy as the BOSS analysis.