ShantanuT01/DACTYL-Pretraining huggingface dataset:
A self-consistent projection operator method for single-particle excitations is developed. It describes the nonlocal correlations on the basis of a projection technique to the retarded Green function and the off-diagonal effective medium. The theory takes into account long-range intersite correlations making use of an incremental cluster expansion in the medium. A generalized self-consistent coherent potential is derived. It yields the momentum-dependent excitation spectra with high resolution. Numerical studies for the Hubbard model on a simple cubic lattice at half filling show that the theory is applicable in a wide range of Coulomb interaction strength. In particular, it is found that the long-range antiferromagnetic correlations in the strong interaction regime cause shadow bands in the low-energy region and sub-peaks of the Mott-Hubbard bands.
We analyze the effects of different forms of the sound-velocity function cs(T) on the hydrodynamic evolution of matter formed in the central region of relativistic heavy-ion collisions. At high temperatures (above the critical temperature Tc) the sound velocity is calculated from the recent lattice simulations of QCD, while in the low temperature region it is obtained from the hadron gas model. In the intermediate region we use different interpolations characterized by the values of the sound velocity at the local maximum (at T = 0.4 Tc) and local minimum (at T = Tc). In all considered cases the temperature dependent sound velocity functions yield the entropy density, which is consistent with the lattice QCD simulations at high temperature. Our calculations show that the presence of a distinct minimum of the sound velocity leads to a very long (about 20 fm/c) evolution time of the system, which is not compatible with the recent estimates based on the HBT interferometry. Hence, we conclude that the hydrodynamic description is favored in the case where the cross-over phase transition renders the smooth sound velocity function with a possible shallow minimum at Tc.
We estimated the galactic model parameters for a set of 20 intermediate-latitude fields with galactic longitudes 0<l<100 and 160<l<240, included in the currently available Data Release 6 (DR6) of SDSS, to explore their possible variation with galactic longitude. The local space densities of the thick disc and halo are almost the same for all fields, <(n_{2}/n_{1})>=6.52% and <(n_{3}/n_{1})>=0.35%, respectively, a result different than the one cited for high-latitude fields. The thin disc's scaleheight is 325 pc in the galactic centre changes to 369 pc in the third quadrant, which confirms the existence of disc flare, whereas the thick disc scaleheight is as large as 952 pc at galactic longitude l=20 and 10% lower at l=160, which confirms the existence of the disc long bar in the direction l=27. Finally, the variation of the axis ratio of the halo with galactic longitude is almost flat, <(c/a)>=0.56, except a slight minimum and a small maximum in the second and third quadrants, respectively, indicating an effect of the long bar which seems plausible for a shallow halo. We estimated the metallicities of unevolved G-type stars and discussed the metallicity gradient for different vertical distances. The metallicity gradient is d[M/H]/dz=-0.30 dex kpc$^{-1}$ for short distances, confirming the formation of this region of the Galaxy by dissipational collapse. However, its change is steeper in the transition regions of different galactic components. The metallicity gradient is almost zero for inner halo (5<z<10 kpc), indicating a formation of merger or accretion of numerous fragments such as dwarf galaxies.
In this paper we present an approach to study arithmetical properties of global function fields by working with Artin L-functions. In particular we recall and then extend a criteria of two function fields to be arithmetically equivalent in terms of Artin L-functions of representations associated to the common normal closure of those fields. We provide few examples of such non-isomorphic fields and also discuss an algorithm to construct many such examples by using torsion points on elliptic curves. Finally, we will show how to apply our results in order to distinguish two global fields by a finite list of Artin L-functions.
We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule.
Adsorption of CO$_2$ on a semiconductor surface is a prerequisite for its photocatalytic reduction. Owing to superior photocorrosion resistance, nontoxicity and suitable band edge positions, TiO$_2$ is considered to be the most efficient photocatalyst for facilitating redox reactions. However, due to the absence of adequate understanding of the mechanism of adsorption, the CO$_2$ conversion efficiency on TiO$_2$ surfaces has not been maximized. While anatase TiO$_2$ (101) is the most stable facet, the (001) surface is more reactive and it has been experimentally shown that the stability can be reversed and a larger percentage (up to ~ 89%) of the (001) facet can be synthesized in the presence fluorine ions. Therefore, through density functional calculations we have investigated the CO$_2$ adsorption on TiO$_2$ (001) surface. We have developed a three-state quantum-mechanical model that explains the mechanism of chemisorption, leading to the formation of a tridentate carbonate complex. The electronic structure analysis reveals that the CO$_2$-TiO$_2$ interaction at the surface is uniaxial and long ranged, which gives rise to anisotropy in binding energy (BE). It negates the widely perceived one-to-one correspondence between coverage and BE and infers that the spatial distribution of CO$_2$ primarily determines the BE. A conceptual experiment is devised where the CO$_2$ concentration and flow direction can be controlled to tune the BE within a large window of ~1.5 eV. The experiment also reveals that a maximum of 50% coverage can be achieved for chemisorption. In the presence of water, the activated carbonate complex forms a bicarbonate complex by overcoming a potential barrier of ~0.9 eV.
We study the two-point cross-correlation function between two populations of galaxies: for instance a bright population and a faint population. We show that this cross-correlation is asymmetric under the exchange of the line-of-sight coordinate of the galaxies, i.e. that the correlation is different if the bright galaxy is in front of, or behind, the faint galaxy. We give an intuitive, quasi-Newtonian derivation of all the effects that contribute to such an asymmetry in large-scale structure: gravitational redshift, Doppler shift, lensing, light-cone, evolution and Alcock-Paczynski effects - interestingly, the gravitational redshift term is exactly canceled by some of the others, assuming geodesic motion. Most of these effects are captured by previous calculations of general relativistic corrections to the observed galaxy density fluctuation; the asymmetry arises from terms that are suppressed by the ratio H/k - H is the Hubble constant and k is the wavenumber - which are more readily observable than the terms suppressed by (H/k)^2. Some of the contributions to the asymmetry, however, arise from terms that are generally considered 'Newtonian' - the lensing and evolution - and thus represent a contaminant in the search for general relativistic corrections. We propose methods to disentangle these different contributions. A simple method reduces the contamination to a level of < 10% for redshifts z<1. We also clarify the relation to recent work on measuring gravitational redshifts by stacking clusters.
We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension $d\geq 3$ and find two critical curves intersecting at one same point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the problem admits a global weak solution obtained by the limits of strong solutions to an approximated system. Based on the second moment of solutions, initial data are constructed to make sure blow up occurs in finite time below these curves (i.e. critical and supercritical cases). In addition, the existence or non-existence of minimizers of free energy functional is discussed on the critical curves and the solutions exist globally in time if the size of initial data is small. We also investigate the crossing point between the critical lines in which a refined criteria in terms of the masses is given again to distinguish the dichotomy between global existence and blow up. We also show that the blow ups is simultaneous for both species.
The spectral properties of itinerant 2D systems with (nearly) ferromagnetic ground state are studied within the spin-fermion and the classical s-d exchange models. While the former model describes the effect of collective magnetic excitations on the electronic properties, the latter one considers the effect of local moments. We use the equation of motion approach combined with the 1/M and 1/z expansions (M is the number of spin components, z is the coordination number) to investigate spectral functions. In both the models the spectrum splitting occurs at low temperatures T in the renormalized classical regime due to strong magnetic fluctuations. For the interaction J between electronic and magnetic degrees of freedom comparable to the bandwidth (the intermediate-coupling regime) the 1/z expansion predicts full splitting of electronic spectrum below some temperature T_s. At the same time, the spectrum remains only partly split in the 1/M expansion with the quasiparticle structure which becomes fully coherent at low T.
We report the magnetic properties of Mg$_{0.2}$Co$_{0.2}$Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$O, a high-entropy oxide with rocksalt structure, and the influence of substitutions on these properties. From the magnetic susceptibility and neutron diffraction measurements, we found that this compound exhibits long-range magnetic order below 120 K despite the substantial structuraldisorder. The other rocksalt-type high-entropy oxides with various chemical substitutions were found to host either an antiferromagnetic order or spin-glass state depending on the amount of magnetic ions. The presence of magnetic order for such a disordered material potentially provide a route to explore novel magnetic properties and functions.
Using series expansions around the dimer limit, we show that the ground state of the Heisenberg Antiferromagnet on the Kagome Lattice appears to be a Valence Bond Crystal (VBC) with a 36-site unit cell, and an energy per site of $E/J=-0.433\pm0.001$. It is a honeycomb lattice of `perfect hexagons' as discussed by Nikolic and Senthil. The energy difference between the ground state and other ordered states with the maximum number of `perfect hexagons', such as a stripe-ordered state, is of order $0.001 J$. The energy of the 36-site system with periodic boundary conditions is further lowered by an amount of $0.005\pm 0.001 J$, consistent with Exact Diagonalization. Every unit cell of the VBC has two singlet states whose degeneracy is not lifted to $6th$ order in the expansion. We estimate this energy difference to be smaller than $0.001 J$. Two leading orders of perturbation theory find the lowest-energy triplet excitations to be dispersionless and confined to the `perfect hexagons'.
The expression of gravitational time advancement (negative time delay) for particles with non-zero mass in Schwarzschild geometry has been obtained. The influences of the gravitational field that describes the observed rotation curves of spiral galaxies and that of dark energy (in the form of cosmological constant) on time advancement of particles have also been studied. The present findings suggest that in presence of dark matter gravitational field the time advancement may take place irrespective of gravitational field of the observer, unlike the case of pure Schwarzschild geometry where gravitational time advancement takes place only when the observer is situated at stronger gravitational field compare to the gravitational field encountered by the particle during its journey. When applied to the well known case of SN 1987a, it is found that the net time delay of a photon/gravitational wave is much smaller than quoted in the literature. In the presence of dark matter field, the photon and neutrinos from SN 1987a should have been suffered gravitational time advancement rather than the delay.
The current fleet of space-based solar observatories offers us a wealth of opportunities to study solar flares over a range of wavelengths. Significant advances in our understanding of flare physics often come from coordinated observations between multiple instruments. Consequently, considerable efforts have been, and continue to be made to coordinate observations among instruments (e.g. through the Max Millennium Program of Solar Flare Research). However, there has been no study to date that quantifies how many flares have been observed by combinations of various instruments. Here we describe a technique that retrospectively searches archival databases for flares jointly observed by RHESSI, SDO/EVE (MEGS-A and -B), Hinode/(EIS, SOT, and XRT), and IRIS. Out of the 6953 flares of GOES magnitude C1 or greater that we consider over the 6.5 years after the launch of SDO, 40 have been observed by six or more instruments simultaneously. Using each instrument's individual rate of success in observing flares, we show that the numbers of flares co-observed by three or more instruments are higher than the number expected under the assumption that the instruments operated independently of one another. In particular, the number of flares observed by larger numbers of instruments is much higher than expected. Our study illustrates that these missions often acted in cooperation, or at least had aligned goals. We also provide details on an interactive widget now available in SSWIDL that allows a user to search for flaring events that have been observed by a chosen set of instruments. This provides access to a broader range of events in order to answer specific science questions. The difficulty in scheduling coordinated observations for solar-flare research is discussed with respect to instruments projected to begin operations during Solar Cycle 25, such as DKIST, Solar Orbiter, and Parker Solar Probe.
Dipole excitations in neutron-rich nuclei below the neutron threshold are investigated. The method is based on Hartree-Fock-Bogoliubov (HFB) and Quasiparticle-Phonon Model (QPM) theory. Of our special interest are the properties of the low-lying 1- Pygmy Resonance and the two-phonon quadrupole-octupole 1- states in Sn-isotopes including exploratory investigations for the experimentally unknown mass regions. In particular we investigate the evolution of the dipole strength function with the neutron excess. The use of HFB mean-field potentials and s.p. energies is found to provide a reliable extrapolation into the region off stability.
We develop algorithms, implemented in Maple, that study the number of vertices with a particular number of children in a random ordered tree where all vertices must have a number of children in some finite set. By calculating the mixed moments of two such numbers, the package gives strong experimental evidence numbers are pairwise asymptotically normal.
The existence and the location of the critical end point (CEP) between the crossover and the first order part of the chiral phase transition in the phase diagram of the strongly interacting matter is a heavily studied area of recent particle physics. The baryon number fluctuations and related quantities such as kurtosis and other susceptibility ratios, that are assumed to be good signatures of CEP, are calculated in an (axial)vector meson extended $(2 + 1)$ flavor Polyakov linear sigma model (EL$\sigma$M) at zero and finite $\mu_B$ . It is compared with the results of lattice as well as other effective model calculations. Divergence of the kurtosis is found at the critical end point.
A finite simple connected graph $G$ with maximum degree $k$ is $k$-critical if it has chromatic index $\chi'(G)=k+1$ and $\chi'(G-e)=k$ for every edge $e\in E(G)$. Bej and the first author raised the question whether every $k$-critical graph has an even factor. We prove that every $k$-critical graph with at most $2k-6$ vertices of degree 2 has an even factor.
Let $K$ be an imaginary quadratic number field and let $L(s,\xi_{\ell})$ denote the Hecke $L$-function to an angular character $\xi_{\ell}$ with frequency $\ell$. We detect values of $\log |L(\tfrac12,\xi_{\ell})|$ with size at least $(\sqrt{2} + o_K(1))(\log X / \log \log X)^{1/2}$ along each dyadic range $X \leqslant \ell \leqslant 2X$. This result relies on the resonance method, which is applied for the first time to this family of $L$-functions, where the classification and extraction of diagonal terms depends on the geometry of the complex embedding of $K$.
We study the timelike geodesic congruences in the generalized Ellis-Bronnikov spacetime (4D-GEB) and in recently proposed 5D model where a 4D-GEB is embedded in a warped geometry (5D-WGEB) and conduct a comparative study. Analytical expressions of ESR variables (for 4D geometries) are found which reveal the role of the wormhole parameter. In more general 4D and 5D scenarios geodesic equation, geodesic deviation equation and Raychaudhury equations are solved numerically. The evolution of cross-sectional area of the congruences of timelike geodesics (orthogonal to the geodesic flow lines) projected on 2D-surfaces yield an interesting perspective and shows the effects of the wormhole parameter and growing/decaying warp factors. Presence of warping factor triggers rotation or accretion even in the absence of initial congruence rotation. Presence of rotation in the congruence is also found to be playing a crucial role which we discuss in detail.
It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we show that this is not unique to this model, but happens also to the Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos. We focus on two indicators of chaos, the correlation hole, which is a dynamical tool, and the distribution of off-diagonal elements of local observables, which is used in the eigenstate thermalization hypothesis. Both methods avoid spectrum unfolding and can detect chaos even when the eigenvalues are not separated by symmetry sectors.
We investigate the adsorption of a Ni monolayer on the $\beta$-SiC(001) surface by means of highly precise first-principles all-electron FLAPW calculations.   Total energy calculations for the Si- and C-terminated surfaces reveal high Ni-SiC adsorption energies, with respect to other metals, confirmining the strong reactivity and the stability of the transition metal/SiC interface. These high binding energies, about 7.3-7.4 eV, are shown to be related to strong $p$-$d$ hybridization, common to both surface terminations and different adsorption sites and despite the large mismatch, can stabilize overlayer growth. A detailed analysis of the bonding mechanism, hybridization of the surface states, charge transfer and surface core level shifts reveals the strong covalent character of the bonding. After a proper accounting of the Madelung term, the core level shift is shown to follow the charge transfer trend.
The astrophysical S-factor for proton-proton fusion, S_11(E), is obtained with the nuclear matrix element analytically calculated in pionless effective field theory. To the third order, the zero-energy result S_11(0) and the first energy derivative S'_11(0) are found to be (3.99 \pm 0.14)* 10^-25 MeV b and S_11(0)*(11.3 \pm 0.1) MeV^-1, respectively; both consistent with the current adopted values. The second energy derivative is also calculated for the first time, and the result S"_11(0) = S_11(0)*(170 \pm 2) MeV^-2 contributes at the level of 0.5% to the fusion rate at the solar center, which is smaller than 1% as previously estimated.
The ANTARES deep sea neutrino telescope has been taking data continuously since its completion in 2008. With its excellent view of the Galactic plane and good angular resolution the telescope can constrain the origin of the diffuse astrophysical neutrino flux reported by IceCube. Assuming various spectral indices for the energy spectrum of neutrino emitters, the Southern sky and in particular central regions of our Galaxy have been studied searching for point-like objects, for extended regions of emission, and for signal from transient objects selected through multi-messenger observations. For the first time, cascade events are used for these searches.   ANTARES has also provided results on searches for hypothetical particles (such as magnetic monopoles and nuclearites in the cosmic radiation), and multi-messenger studies of the sky in combination with various detectors. Of particular note are the searches for dark matter: the limits obtained for the spin-dependent WIMP-nucleon cross section surpassing those of current direct-detection experiments.
Flexible magnetic devices, i.e., magnetic devices fabricated on flexible substrates, are very attractive in application of detecting magnetic field in arbitrary surface, non-contact actuators, and microwave devices due to the stretchable, biocompatible, light-weight, portable, and low cost properties. Flexible magnetic films are essential for the realization of various functionalities of flexible magnetic devices. To give a comprehensive understanding for flexible magnetic films and related devices, we have reviewed recent advances in the studies of flexible magnetic films including fabrication methods, magnetic and transport properties of flexible magnetic films, and their applications in magnetic sensors, actuators, and microwave devices. Three typical methods were introduced to prepare the flexible magnetic films. Stretching or bending the flexible magnetic films offers a good way to apply mechanical strain on magnetic films, so that magnetic anisotropy, exchanged bias, coercivity, and magnetoresistance can be effectively manipulated. Finally, a series of examples were shown to demonstrate the great potential of flexible magnetic films for future applications.
Most hadronic event generators which can be used for simulating hadronic and nuclear collisions up to the highest energies are quite similar in their construction and in the underlying theoretical concepts. At energies, where data from accelerator and collider experiments are available the models agree rather well with each other and with the most important features of the data. As soon as we compare the extrapolations of the models at higher energy we find in spite of the similarities in the underlying theoretical concepts quite often striking differences between the predictions of the models.