ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a novel approach to long-range correlations beyond dynamical mean-field theory through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Neel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte-Carlo (QMC) results. An illustration of how the approach captures and allows to distinguish short- and long-range correlations is given.
A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy and show that it obeys the stress strain relation of linear elasticity. Dislocations in a two dimensional hexagonal lattice are shown to be composite topological defects in the amplitude expansion of the phase field, with topological charges given by the Burgers vector. This allows us to introduce a formal relation between dislocation velocity and the evolution of the coarse grained envelopes of the phase field. Standard dissipative dynamics of the phase field crystal model is shown to determine the velocity of the dislocations. When the amplitude equation is valid, we derive the Peach-Koehler force on a dislocation, and compute the associated defect mobility. A numerical integration of the phase field crystal equations in two dimensions is used to compute the motion of a dislocation dipole, and good agreement is found with the theoretical predictions.
We study the fluctuations of standard thin accretion disks by linear analysis of the time-dependent energy equation together with the vertical hydrostatic equilibrium and the equation of state. We show that some of the simulation results in Hirose et al. (2009b), such as the time delay, the relationship of power spectra, and the correlation between magnetic energy and radiation energy, can be well understood by our analytic results.
We present B, V, R, and H alpha photometry of 8 clusters in the Small Magellanic Cloud, 5 in the Large Magellanic Cloud, and 3 Galactic clusters, and use 2 color diagrams (2-CDs) to identify candidate Be star populations in these clusters. We find evidence that the Be phenomenon is enhanced in low metallicity environments, based on the observed fractional early-type candidate Be star content of clusters of age 10-25 Myr. Numerous candidate Be stars of spectral types B0 to B5 were identified in clusters of age 5-8 Myr, challenging the suggestion of Fabregat & Torrejon (2000) that classical Be stars should only be found in clusters at least 10 Myr old. These results suggest that a significant number of B-type stars must emerge onto the zero-age-main-sequence as rapid rotators. We also detect an enhancement in the fractional content of early-type candidate Be stars in clusters of age 10-25 Myr, suggesting that the Be phenomenon does become more prevalent with evolutionary age. We briefly discuss the mechanisms which might contribute to such an evolutionary effect. A discussion of the limitations of utilizing the 2-CD technique to investigate the role evolutionary age and/or metallicity play in the development of the Be phenomenon is offered, and we provide evidence that other B-type objects of very different nature, such as candidate Herbig Ae/Be stars may contaminate the claimed detections of ``Be stars'' via 2-CDs.
In this paper we prove an observability inequality for a degenerate transport equation. First we introduce a local in time Carleman estimate for the degenerate equation, then we apply it to obtain a global in time observability inequality by using also an energy estimate.
High-dispersion spectra centered on the Li 6708 A line have been obtained for 70 potential members of the open cluster NGC 3680, with an emphasis on stars in the turnoff region. A measurable Li abundance has been derived for 53 stars, 39 of which have radial velocities and proper motions consistent with cluster membership. After being transferred to common temperature and abundance scales, previous Li estimates have been combined to generate a sample of 49 members, 40 of which bracket the cluster Li-dip. Spectroscopic elemental analysis of 8 giants and 5 turnoff stars produces [Fe/H] = -0.17 +/- 0.07 (sd) and -0.07 +/- 0.02 (sd), respectively. We also report measurements of Ca, Si and Ni which are consistent with scaled-solar ratios within the errors. Adopting [Fe/H] = -0.08 (Sect. 3.6), Y^2 isochrone comparisons lead to an age of 1.75 +/- 0.10 Gyr and an apparent modulus of (m-M) = 10.30 +/- 0.15 for the cluster, placing the center of the Li-dip at 1.35 +/- 0.03 solar masses. Among the giants, 5 of 9 cluster members are now known to have measurable Li with A(Li) near 1.0. A combined sample of dwarfs in the Hyades and Praesepe is used to delineate the Li-dip profile at 0.7 Gyr and [Fe/H] = +0.15, establishing its center at 1.42 +/- 0.02 solar masses and noting the possible existence of secondary dip on its red boundary. When evolved to the typical age of the clusters NGC 752, IC 4651 and NGC 3680, the Hyades/Praesepe Li-dip profile reproduces the observed morphology of the combined Li-dip within the CMD's of the intermediate-age clusters while implying a metallicity dependence for the central mass of the Li-dip given by Mass = (1.38 +/-0.04) + (0.4 +/- 0.2)[Fe/H]. The implications of the similarity of the Li-dichotomy among giants in NGC 752 and IC 4651 and the disagreement with the pattern among NGC 3680 giants are discussed.
We explain a generalization of the K. Saito higher residue pairing for local system of $p$-adic isocrystals.
We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the Dirichlet-to-Neumann map. We exploit the integration by parts formula for Riemann-Liouville and Caputo derivatives to derive the Runge approximation property for our space-time fractional operator based on the unique continuation property of the fractional Laplacian. This enables us to extend early unique determination results for space-fractional but time-local operators to the space-time fractional case.
Under the generalized Lindel\"of Hypothesis in the t- and q-aspects, we bound exponential sums with coefficients of Dirichlet series belonging to a certain class. We use these estimates to establish a conditional result on squares of Hecke eigenvalues at Piatetski-Shapiro primes.
Zigzag edges of the honeycomb structure of graphene exhibit magnetic polarization making them attractive as building blocks for spintronic devices. Here, we show that devices with zigzag edged triangular antidots perform essential spintronic functionalities, such as spatial spin-splitting or spin filtering of unpolarized incoming currents. Near-perfect performance can be obtained with optimized structures. The device performance is robust against substantial disorder. The gate-voltage dependence of transverse resistance is qualitatively different for spin-polarized and spin-unpolarized devices, and can be used as a diagnostic tool. Importantly, the suggested devices are feasible within current technologies.
Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have achieved only limited success in the classification of images that undergo geometric transformations. In this work we present a novel Transformation Invariant Graph-based Network (TIGraNet), which learns graph-based features that are inherently invariant to isometric transformations such as rotation and translation of input images. In particular, images are represented as signals on graphs, which permits to replace classical convolution and pooling layers in deep networks with graph spectral convolution and dynamic graph pooling layers that together contribute to invariance to isometric transformation. Our experiments show high performance on rotated and translated images from the test set compared to classical architectures that are very sensitive to transformations in the data. The inherent invariance properties of our framework provide key advantages, such as increased resiliency to data variability and sustained performance with limited training sets. Our code is available online.
A supersymmetric extension of the dynamical symmetry group $Sp^{B}(12,R)$ of the Interacting Vector Boson Model (IVBM), to the orthosymplectic group $OSp(2\Omega/12,R)$ is developed in order to incorporate fermion degrees of freedom into the nuclear dynamics and to encompass the treatment of odd mass nuclei. The bosonic sector of the supergroup is used to describe the complex collective spectra of the neighboring even-even nuclei and is considered as a core structure of the odd nucleus. The fermionic sector is represented by the fermion spin group $SO^{F}(2\Omega)\supset SU^{F}(2)$.   The so obtained, new exactly solvable limiting case is applied for the description of the nuclear collective spectra of odd mass nuclei. The theoretical predictions for different collective bands in three odd mass nuclei, namely $^{157}Gd$, $^{173}Yb$ and $^{163}Dy$ from rare earth region are compared with the experiment. The $B(E2)$ transition probabilities for the $^{157}Gd$ and $^{163}Dy$ between the states of the ground band are also studied. The important role of the symplectic structure of the model for the proper reproduction of the $B(E2)$ behavior is revealed. The obtained results reveal the applicability of the models extension.
We have analysed here the role of the geometric phase in dynamical mechanism of quantum phase transition in the transverse Ising model. We have investigated the system when it is driven at a fixed rate characterized by a quench time $\tau_q$ across the critical point from a paramagnetic to ferromagnetic phase. Our argument is based on the fact that the spin fluctuation occurring during the critical slowing down causes random fluctuation in the ground state geometric phase at the critical regime. The correlation function of the random geometric phase determines the excitation probability of the quasiparticles, which are excited during the transition from the inital paramagnetic to the ferromagnetic phase. This helps us to evaluate the number density of the kinks formed during the transition, which is found to scale as $\tau_q^{-\frac{1}{2}}$. In addition, we have also estimated the spin-spin correlation at criticality.
New charged vector bosons $W'$ decaying into gauge boson pairs $WZ$ are predicted in many scenarios of new physics, including models with an extended gauge sector (EGM). Due to the large variety of models (other unification groups, models with Supersymmetry, Little Higgs Models, Extra Dimensions) the more general EGM approach is here considered. For what concerns $W'$-production, these models are parametrised by two parameters, the $W^\prime$ mass $M_{W^\prime}$ and the $W$-$W^\prime$ mixing parameter $\xi$. The diboson $WZ$ production allows to place stringent constraints on this mixing angle and the $W'$ mass, which we determine and present for the first time by using data from $pp$ collisions at $\sqrt{s}=13$ TeV recorded by the ATLAS detector at the CERN LHC, with integrated luminosity of 36.1 fb$^{-1}$. By comparing the experimental limits to the theoretical predictions for the total cross section of $W'$ resonant production and its subsequent decay into $WZ$ pairs, we show that the derived constraints on the mixing angle for the benchmark model are rather small, between $10^{-4}$ and $10^{-3}$, i.e., greatly improved with respect to those derived from the global analysis of electroweak data which yield $\xi\sim 10^{-2}$. We combine the limits derived from $WZ$ production data with those obtained from the $W'\to e\nu$ process in order to significantly extend the exclusion region in the $M_{W'}$-$\xi$ parameter plane and obtain the most stringent exclusion limits to date. We present the combined allowed parameter space for the EGM $W'$ boson after incorporating indirect constraints from low energy electroweak data, direct search constraints from Tevatron and from the LHC Run I with 7 and 8 TeV as well as at Run II with 13 TeV data.
The Hubbard model is the simplest model of interacting fermions on a lattice and is of similar importance to correlated electron physics as the Ising model is to statistical mechanics or the fruit fly to biomedical science. Despite its simplicity, the model exhibits an incredible wealth of phases, phase transitions, and exotic correlation phenomena. While analytical methods have provided a qualitative description of the model in certain limits, numerical tools have shown impressive progress in achieving quantitative accurate results over the last years. This article gives an introduction to the model, motivates common questions, and illustrates the progress that has been achieved over the last years in revealing various aspects of the correlation physics of the model.
Presently the quarkonium spectrum, written in terms of the quark MSbar-mass, is known at O(alpha_s^3 m) accuracy. We point out that in order to achieve O(alpha_s^4 m) accuracy it is sufficient to calculate further (I) the O(alpha_s^4 m) relation between the MSbar-mass and the pole-mass, and (II) the binding energy at O(alpha_s^5 m) in the large-beta_0 approximation. We calculate the latter correction analytically for the 1S-state and study its phenomenological implications.
The spin Hall effect for polaritons (SHEP) in a transition metal dichalcogenides (TMDC) monolayer embedded in a microcavity is predicted. We demonstrate that two counterpropagating laser beams incident on a TMDC monolayer can deflect a superfluid polariton flow due to the generation the effective gauge vector and scalar potentials. The components of polariton conductivity tensor for both non-interacting polaritons without Bose-Einstein condensation (BEC)and for weakly-interacting Bose gas of polaritons in the presence of BEC and superfluidity are obtained. It is shown that the polariton flows in the same valley are splitting: the superfluid components of the \textit{A} and \textit{B} polariton flows propagate in opposite directions along the counterpropagating beams, while the normal components of the flows slightly deflect in opposite directions and propagate almost perpendicularly to the beams. The possible experimental observation of SHEP in a microcavity is proposed.
We study the total cross section for photo production of open charm hadrons near threshold using a hadronic Lagrangian. Both two-body final states involving $\Lambda_c$ and a charmed meson as well as three-body final states involving nucleon and a charm-anticharm meson pair are included. With appropriate cut-off parameters in the form factors at interaction vertices, the model gives a total cross section that is consistent with the measured data at center-of-mass energy of 6 GeV. The result is compared with the prediction from the leading-order perturbative QCD.
The Lorentzian Hamiltonian constraint is solved for isotropic loop quantum cosmology coupled to a massless scalar field. As in the Euclidean case, the discreteness of quantum geometry removes the classical singularity from the quantum Friedmann models. In spite of the absence of the classical singularity, a modified DeWitt initial condition is incompatible with a late-time smooth behavior. Further, the smooth behavior is recovered only for positive or negatives times but not both. An important feature, which is shared with the Euclidean case, is a minimal initial energy of the order of the Planck energy required for the system to evolve dynamically. By forming wave packets of the matter field an explicit evolution in terms of an internal time is obtained.
We investigate the two-dimensional kpc-scale structure of the extinction in a representative sample of local ULIRGs using the Halpha/Hbeta line ratio.We use optical integral field spectroscopy obtained with the INTEGRAL instrument at the William Herschel Telescope. Complementary optical and near-IR high angular resolution HST images have also been used. The extinction exhibits a very complex and patchy structure in ULIRGs on kpc scales, from basically transparent regions to others deeply embedded in dust (Av~0.0 to Av~8.0 mag). Nuclear extinction covers a broad range in Av from 0.6 to 6 mag, 69% of the nuclei having Av>2.0 mag. Extinction in the external regions is substantially lower than in the nuclei with 64% of the ULIRGs in the sample having median Av of less than 2 mag for the entire galaxy. While post-coalescence nuclei tend to cluster around Av values of 2 to 3 mag, pre-coalescence nuclei appear more homogeneously distributed over the entire 0.4 mag <Av< 7.7 mag range. For the average extinction (Av~2.0 derived for the ULIRGs of the sample, the ratio of the de-reddened to observed SFR values is 6. The extinction-corrected, Halpha-based SFR ranges from 10 to 300 Msun/yr. For only 28% of the cases the de-reddened SFR is <20 Msun/yr, whereas for the observed SFR this percentage increases to 72%. The IR-based SFR is always higher than the optical-based one, with differences ranging from about 2 to up to 30. The nuclear observed SFR has an average contribution to the total one of 16% for the entire sample. Once corrected for extinction, the average value becomes 31%. Because of mostly extinction effects, the optical (I-band) half-light radius in the sample galaxies is on average a factor 2.3 larger than the corresponding near-IR (H-band) value.
Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the acceptance of his approach to quantum mechanics over de Broglie's had no reasonable foundation. But Bohr's interpretation changed little from the time of its first appearance, and stood independent of any philosophical presuppositions. The principle of complementarity is itself best read as a conjecture of unusually wide scope, on the nature and future course of explanations in the sciences (and not only the physical sciences). If it must be judged a failure today, it is not because of any internal inconsistency.
We review the experimental and theoretical status of the standard electroweak theory, and its fundamental parameters. We obtain the global best fit result for the Standard Model Higgs boson of M_H = 107^{+67}_{-45} GeV, and find the 95% upper limit of 255 GeV. Parameters describing physics beyond the Standard Model are discussed as well. Particular emphasis is given to implications for supersymmetric extensions of the Standard Model.
Let $X$ be an integral projective scheme satisfying the condition $S_3$ of Serre and $H^1({\mathcal O}_X(n)) = 0$ for all $n \in {\mathbb Z}$. We generalize Rao's theorem by showing that biliaison equivalence classes of codimension two subschemes without embedded components are in one-to-one correspondence with pseudo-isomorphism classes of coherent sheaves on $X$ satisfying certain depth conditions.   We give a new proof and generalization of Strano's strengthening of the Lazarsfeld--Rao property, showing that if a codimension two subscheme is not minimal in its biliaison class, then it admits a strictly descending elementary biliaison.   For a three-dimensional arithmetically Gorenstein scheme $X$, we show that biliaison equivalence classes of curves are in one-to-one correspondence with triples $(M,P,\alpha)$, up to shift, where $M$ is the Rao module, $P$ is a maximal Cohen--Macaulay module on the homogeneous coordinate ring of $X$, and $\alpha: P^{\vee} \to M^* \to 0$ is a surjective map of the duals.
Evolution of an anisotropic universe described by a Bianchi type I (BI) model in presence of nonlinear spinor field has been studied by us recently in a series of papers. On offer the Bianchi models, those are both inhomogeneous and anisotropic. Within the scope of Bianchi type VI (BVI) model the self-consistent system of nonlinear spinor and gravitational fields are considered. The role of inhomogeneity in the evolution of spinor and gravitational field is studied.
For a morphism $f:\P^N \to \P^N$, the points whose forward orbit by $f$ is finite are called preperiodic points for $f$. This article presents an algorithm to effectively determine all the rational preperiodic points for $f$ defined over a given number field $K$. This algorithm is implemented in the open-source software Sage for $\Q$. Additionally, the notion of a dynatomic zero-cycle is generalized to preperiodic points. Along with examining their basic properties, these generalized dynatomic cycles are shown to be effective.
We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes $W^r_p([0,1]^d)$ and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Novak on integration of functions from H\"older classes.
We investigate the evolution of initially metal-free, low-mass Red Giant stars through the He core flash at the tip of the Red Giant Branch. The low entropy barrier between the helium- and hydrogen-rich layers enables a penetration of the helium flash driven convective zone into the inner tail of the extinguishing H-burning shell. As a consequence, protons are mixed into high-temperature regions triggering a H-burning runaway. The subsequent dredge-up of matter processed by He and H burning enriches the stellar surface with large amounts of helium, carbon and nitrogen. Extending previous results by Hollowell et al. (1990) and Fujimoto et al. (2000), who claimed that the H-burning runaway is an intrinsic property of extremely metal-poor low-mass stars, we found that its occurrence depends on additional parameters like the initial composition and the treatment of various physical processes.   We perform some comparisons between predicted surface chemical abundances and observational measurements for extremely metal-deficient stars. As in previous investigations, our results disclose that although the described scenario provides a good qualitative agreement with observations, considerable discrepancies still remain. They may be due to a more complex evolutionary path of `real' stars, and/or some shortcomings in current evolutionary models.   In addition, we analyze the evolutionary properties after the He core flash, during both the central and shell He-burning phases, allowing us to deduce some interesting differences between models whose Red Giant Branch progenitor has experienced the H-flash and canonical models. In particular, the Asymptotic Giant Branch evolution of extremely metal-deficient stars and the occurrence of thermal pulses are strongly affected by the previous RGB evolution.
We reconsider the Mott transition problem in the presence of long range Coulomb interactions. Using an extended DMFT, that sums an important class of diagrams absent in ordinary DMFT, we show that in the presence of Coulomb the Mott transition in two and three dimensions is discontinuous as envisioned by Mott.