ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a generalized Greenberger-Horne-Zeilinger (GHZ) theorem, which involves more than two local measurement settings for some parties, and cannot be reduced to one with less settings. Our results hold for an odd number of parties. We use a set of observables, which are incompatible but share a common eigenstate, here a GHZ state. Such observables are called concurrent. The idea is illustrated with an example of a three-qutrit system and then generalized to systems of higher dimensions, and more parties. The GHZ paradoxes can lead to, e.g., secret sharing protocols.
We present expressions for the energy, linear momentum and angular momentum carried away from an isolated system by gravitational radiation based on spin-weighted spherical harmonics decomposition of the Weyl scalar $\Psi_4$. We also show that the expressions derived are equivalent to the common expressions obtained when using a framework based on perturbations of a Schwazschild background. The main idea is to collect together all the different expressions in a uniform and consistent way. The formulae presented here are directly applicable to the calculation of the radiated energy, linear momentum and angular momentum starting from the gravitational waveforms which are typically extracted from numerical simulations.
In a recent paper [Phys. Rev. E \textbf{92}, 012123 (2015)] a modified $d$-dimensional $\Phi^4$ model was investigated which differs from the standard one in that the $\Phi^4$ term was replaced by a nonlocal one with a potential $u(\bm{x}-\bm{x}')$ that depends on a parameter $\sigma$ and decays exponentially as $|\bm{x}-\bm{x}'|\to\infty$ on a scale $|m|^{-1}<\infty$. The authors claim the upper critical dimension of this model to be $d_\sigma=4+2\sigma$. Performing a one-loop calculation they arrive at expansions in powers of $\epsilon_\sigma=d_\sigma-d$ for critical exponents such as $\eta$ and related ones to $O(\epsilon_\sigma)$ whose $O(\epsilon_\sigma)$ coefficients depend on $\sigma$ and the ratio $w=m^2/\Lambda^2$, where $\Lambda$ is the UV cutoff. We show that these claims are unfounded and based on misjudgments and an ill-conceived renormalization group calculation.
We develop a method to characterize topological phase transitions for strongly correlated Hamiltonians defined on two-dimensional lattices based on the many-body Berry curvature. Our goal is to identify a class of quantum critical points between topologically nontrivial phases with fractionally quantized Hall (FQH) conductivity and topologically trivial gapped phases through the discontinuities of the many-body Berry curvature in the so-called flux Brillouin zone (fBZ), the latter being defined by imposing all possible twisted boundary conditions. For this purpose, we study the finite-size signatures of several quantum phase transitions between fractional Chern insulators and charge-ordered phases for two-dimensional lattices by evaluating the many-body Berry curvature numerically using exact diagonalization. We observe degeneracy points (nodes) of many-body energy levels at high-symmetry points in the fBZ, accompanied by diverging Berry curvature. We find a correspondence between the number and order of these nodal points, and the change of the topological invariants of the many-body ground states across the transition, in close analogy with Weyl nodes in non-interacting band structures. This motivates us to apply a scaling procedure, originally developed for non-interacting systems, for the Berry curvature at the nodal points. This procedure offers a useful tool for the classification of topological phase transitions in interacting systems harboring FQH-like topological order.
We solve Schwinger-Dyson (SD) equation for the color superconducting (CS) gap in nonlocal gauge which justifies the ladder approximation in subleading order calculation. The gap prefactor increases about 1.6 times to the leading order gap determined in Landau gauge.
This paper is concerned with a reaction-diffusion single species model with harvesting on $n$-dimensional isotropically growing domain. The model on growing domain is derived and the corresponding comparison principle is proved. The asymptotic behavior of the solution to the problem is obtained by using the method of upper and lower solutions. The results show that the growth of domain takes a positive effect on the asymptotic stability of positive steady state solution while it takes a negative effect on the asymptotic stability of the trivial solution, but the effect of the harvesting rate is opposite. The analytical findings are validated with the numerical simulations.
Recent observations have shown that compact nuclear star clusters (NSCs) are present in up to 80% of galaxies. However, detailed studies of their dynamical and chemical properties are confined mainly to spiral galaxy hosts, where they are more easily observed. In this paper we present our study of the NSC in FCC 277, a nucleated elliptical galaxy in the Fornax cluster. We use a combination of adaptive optics assisted near-infrared integral field spectroscopy, Hubble Space Telescope imaging, and literature long slit data. We show that while the NSC does not appear to rotate within our detection limit of ~6 km/s, rotation is detected at larger radii, where the isophotes appear to be disky, suggesting the presence of a nuclear disk. We also observe a distinct central velocity dispersion drop that is indicative of a dynamically cold rotating sub-system. Following the results of orbit-based dynamical modelling, co-rotating as well as counter-rotating stellar orbits are simultaneously needed to reproduce the observed kinematics. We find evidence for varying stellar populations, with the NSC and nuclear disk hosting younger and more metal rich stars than the main body of the galaxy. We argue that gas dissipation and some level of merging have likely played an important role in the formation of the nucleus of this intermediate-mass galaxy. This is in contrast to NSCs in low-mass early- type galaxies, which may have been formed primarily through the infall of star clusters.
This is a rework of our old file, which has been left unpublished since September 1994, on an explicit spectral decomposition of the fourth power moment of the Riemann zeta-function against a weight which is the square of a Dirichlet polynomial. At this occasion we add an explicit treatment of generalized Kloosterman sums associated with arbitrary Hecke congruence subgroups (Section 15), which might have an independent interest. At the end (Section 36) of our discussion, we set out a few problems on the distribution of eigenvalues of the hyperbolic Laplacian, which appear to us to be related to the nature of the sixth power moment of the Riemann zeta-function. The contents of this work were presented in a worshop at RIMS Kyoto University on October 18, 2007.   In this second version, some corrections are made in the part on generalized Kloosterman sums, and in Addendum a mention is made concerning a recent work by C.P. Hughes and M.P. Young (0709.2345).
State-of-the-art rest-frame UV and FIR photometric and spectroscopic observations are now pushing the redshift frontiers of galaxy formation studies up to $z\sim9-11$ and beyond. Recent HST observations unveiled the presence of a star-forming galaxy exhibiting the Lyman break at $\lambda_{\rm obs}=1.47\pm0.01$ $\mu$m, i.e., a $z=11.09^{+0.08}_{-0.12}$ galaxy with a stellar mass of $\sim10^9 M_\odot$, demonstrating that galaxy build-up was well underway early in the epoch of reionization (EoR) at $z>10$. Targeted spectroscopy of a lensed Lyman break galaxy uncovers the earliest metals known to date up to $z=9.1096\pm0.0006$ by detecting the bright [OIII] 88~$\mu$m nebular line, indicating the onset of star formation 250 million years after the Big Bang, i.e., corresponding to a redshift of $z\sim15$. These latest findings lead us to a number of key questions: How and when metal enrichment happened in the EoR? What was the nature of the earliest-epoch star-forming galaxies at $z=10-15$? What was the spatial distribution of such galaxies, and what was the relation to the putative large-scale ionization bubbles during the EoR? What were the dark-halo masses of such earliest-epoch star-forming galaxies? To address all these questions, we need to uncover a statistically large number of $z=10-15$ galaxies in the pre-reionization era. Here we argue two possible pathways: (1) a wide-area, sensitive blind spectroscopic survey of [OIII] 88 $\mu$m line-emitting galaxies at submillimeter wavelengths, and (2) an ultra-wide-area, high-cadence photometric survey of transient sources at radio-to-(sub)millimeter wavelengths, together with the immediate follow-up spectroscopy with an ultra-wide-band spectrograph, to catch the pop-III $\gamma$-ray bursts.
We propose a novel stochastic method to generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time $t_{f}$ under a given potential $U(x)$. These paths are sampled with a probability given by the overdamped Langevin dynamics. We show that these paths can be exactly generated by a local Stochastic Partial Differential Equation (SPDE). This equation cannot be solved in general. We present several approximations that are valid either in the low temperature regime or in the presence of barrier crossing. We show that this method warrants the generation of statistically independent transition paths. It is computationally very efficient. We illustrate the method on the two dimensional Mueller potential as well as on the Mexican hat potential.
The Newman-Janis Ansatz was used first to obtain the stationary Kerr metric from the static Schwarzschild metric. Many works have been devoted to investigate the physical significance of this Ansatz, but no definite answer has been given so far. We show that this Ansatz can be applied in general to conformastatic vacuum metrics, and leads to stationary generalizations which, however, do not preserve the conformal symmetry. We investigate also the particular case when the seed solution is given by the Schwarzschild spacetime and show that the resulting rotating configuration does not correspond to a vacuum solution, even in the limiting case of slow rotation. In fact, it describes in general a relativistic fluid with anisotropic pressure and heat flux. This implies that the Newman-Janis Ansatz strongly depends on the choice of representation for the seed solution. We interpret this result as as a further indication of its applicability limitations.
We have systematically studied the mechanical stability of all noble metal carbides with the rock-salt structure by calculating their elastic constants within the density function theory scheme. It was found that only four carbides (RuC, PdC, AgC and PtC) are mechanically stable. In particular, we have shown that RuC, PdC, and PtC have very high bulk modulus, which has been remarkably observed by the most recent experiment for the case of PtC. From the calculated density of states, we can conclude that these compounds are metallic, like the conventional group IV and group V transition metal carbides.
We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is allowed.
A tight Heffter array H(m,n) is an m x n matrix with nonzero entries from Z_{2mn+1} such that i) the sum of the elements in each row and each column is 0, and ii) no element from {x,-x\ appears twice. We prove that H(m,n) exist if and only if both m and n are at least 3. If all entries are integers of magnitude at most mn satisfying every row and column sum is 0 over the integers and also satisfying ii) we call H an integer Heffter array. We show integer Heffter arrays exist if and only if mn \equiv 0,3 (mod 4). Finally, an integer Heffter array is shiftable if each row and column contains an the same number of positive and negative integers. We show that shiftable integer arrays exists exactly when both $m,n$ are even.   This research report contains all of the details of the proofs. It is meant to accompany the journal version of this paper.
We report on large exciton tuning in WSe$_2$ monolayers via substrate induced non-degenerate doping. We observe a redshift of $\sim$62 meV for the $A$ exciton together with a 1-2 orders of magnitude photoluminescence (PL) quenching when the monolayer WSe$_2$ is brought in contact with highly oriented pyrolytic graphite (HOPG) compared to the dielectric substrates such as hBN and SiO$_2$. As the evidence of doping from HOPG to WSe$_2$, a drastic increase of the trion emission intensity was observed. Using a systematic PL and Kelvin probe force microscopy (KPFM) investigation on WSe$_2$/HOPG, WSe$_2$/hBN, and WSe$_2$/graphene, we conclude that this unique excitonic behavior is induced by electron doping from the substrate. Our results propose a simple yet efficient way for exciton tuning in monolayer WSe$_2$, which plays a central role in the fundamental understanding and further device development.
Electronic structure of NiS_{2-x}Se_x system has been investigated for various compositions (x) using x-ray photoemission spectroscopy. An analysis of the core level as well as the valence band spectra of NiS_2 in conjunction with many-body cluster calculations provides a quantitative description of the electronic structure of this compound. With increasing Se content, the on-site Coulomb correlation strength (U) does not change, while the band width W of the system increases, driving the system from a covalent insulating state to a pd-metallic state.
Partial multivariate Bell polynomials have been defined by E.T. Bell in 1934. These polynomials have numerous applications in Combinatorics, Analysis, Algebra, Probabilities, etc. Many of the formulae on Bell polynomials involve combinatorial objects (set partitions, set partitions in lists, permutations, etc.). So it seems natural to investigate analogous formulae in some combinatorial Hopf algebras with bases indexed by these objects. The algebra of symmetric functions is the most famous example of a combinatorial Hopf algebra. In a first time, we show that most of the results on Bell polynomials can be written in terms of symmetric functions and transformations of alphabets. Then, we show that these results are clearer when stated in other Hopf algebras (this means that the combinatorial objects appear explicitly in the formulae). We investigate also the connexion with the Fa{\`a} di Bruno Hopf algebra and the Lagrange-B{\"u}rmann formula.
We exhibit infinite families of planar graphs with real chromatic roots arbitrarily close to 4, thus resolving a long-standing conjecture in the affirmative.
In this article we discuss a scheme of teleportation of atomic states. The experimental realization proposed makes use of cavity Quatum Electrodynamics involving the interaction of Rydberg atoms with a micromaser cavity prepared in a coherent state. We start presenting a scheme to prepare atomic Bell states via the interaction of atoms with a cavity. In our scheme the cavity and some atoms play the role of auxiliary systems used to achieve the teleportation.
We present deep imaging in the {\em U} band covering an area of 630 arcmin$^{2}$ centered on the southern field of the Great Observatories Origins Deep Survey (GOODS). The data were obtained with the VIMOS instrument at the ESO Very Large Telescope. The final images reach a magnitude limit $U_{lim} \approx 29.8$ (AB, 1$\sigma$, in a 1\arcsec radius aperture), and have good image quality, with full width at half maximum $\approx 0.8\arcsec$. They are significantly deeper than previous U--band images available for the GOODS fields, and better match the sensitivity of other multi--wavelength GOODS photometry. The deeper U--band data yield significantly improved photometric redshifts, especially in key redshift ranges such as $2<z<4$, and deeper color--selected galaxy samples, e.g., Lyman--break galaxies at $z\approx 3$. We also present the coaddition of archival ESO VIMOS R band data, with $R_{lim} \approx 29$ (AB, 1$\sigma$, 1\arcsec radius aperture), and image quality $\approx 0.75 \arcsec$. We discuss the strategies for the observations and data reduction, and present the first results from the analysis of the coadded images.
We propose a N=2 twisted superspace formalism with a central charge in four dimensions by introducing a Dirac-K\"ahler twist. Using this formalism, we construct a twisted hypermultiplet action and find an explicit form of fermionic scalar, vector and tensor transformations. We construct a off-shell Donaldson-Witten theory coupled to the twisted hypermultiplet. We show that this action possesses N=4 twisted supersymmetry at on-shell level. It turns out that four-dimensional Dirac-K\"ahler twist is equivalent to the Marcus's twist.
It has been shown that the dynamics of dwarf Irregular (dIrr) galaxies are dominated by dark matter. It is also observed that these galaxies have low star formation rates and metallicities, and no gamma-ray emission at ultra very high energies is expected. Because of their distance, dark matter content and vast number, dIrr galaxies are good targets to perform indirect dark matter searches by ground-based and wide field of view gamma-ray experiments, like HAWC. We analyzed data at the position of 31 dIrr galaxies within the HAWC field-of-view and no significant excess was found. Here, we present the individual and combined limits on the annihilation cross-section and decay lifetime of weakly interacting massive particles with a mass between 1 and 100 TeV.
We give an algorithm to enumerate all primitive abundant numbers (briefly, PANs) with a fixed $\Omega$ (the number of prime factors counted with their multiplicity), and explicitly find all PANs up to $\Omega=6$, count all PANs and square-free PANs up to $\Omega=7$ and count all odd PANs and odd square-free PANs up to $\Omega=8$. We find primitive weird numbers (briefly, PWNs) with up to 16 prime factors, improving the previous results of [Amato-Hasler-Melfi-Parton] where PWNs with up to 6 prime factors have been given. The largest PWN we find has 14712 digits: as far as we know, this is the largest example existing, the previous one being 5328 digits long [Melfi]. We find hundreds of PWNs with exactly one square odd prime factor: as far as we know, only five were known before. We find all PWNs with at least one odd prime factor with multiplicity greater than one and $\Omega = 7$ and prove that there are none with $\Omega < 7$. Regarding PWNs with a cubic (or higher) odd prime factor, we prove that there are none with $\Omega\le 7$, and we did not find any with larger $\Omega$. Finally, we find several PWNs with 2 square odd prime factors, and one with 3 square odd prime factors. These are the first such examples.
Excited negative parity hyperon masses are calculated in a chiral bag model in which the pion and the kaon fields are treated as perturbations. We also calculate the hadronic widths of $\lama$ and $\lamb$ as well as the coupling constants of the lightest $I=0$ excited hyperon to the meson-baryon channels, and discuss how the dispersive effects of the hadronic meson-baryon decay channels affect the excited hyperon masses. Meson cloud corrections to the electromagnetic decay widths of the two lightest excited hyperons into ground states $\lamz$ and $\sigz$ are calculated within the same model and are found to be small. Our results strengthen the argument that predictions of these hyperon radiative decay widths provide an excellent test for various quark models of hadrons.
A detailed multi-wavelength study of the properties of the triple-peaked AGN Mrk\,622 showing different aspects of the nuclear emission region is presented. Radio, near- and mid-infrared, optical and X-ray data has been considered for the analysis. In the optical, the WHAN diagnostic diagrams show that the three nuclear peaks are strong active galactic nuclei since the EW of $H{\alpha}$ is $>$\,6 \AA\, and $\log$ [NII]$\lambda$6584/H$\alpha$\, ratio is $>$\,-0.4. Optical variability of both the continuum flux and intensity of the narrow emission lines is detected in a time-span of 13 years. The size of the narrow line region is found to be 2.7\,pc, with a light-crossing time of 8.7\,y. Analysis done to an archival Hubble Space Telescope image at 1055.2\,nm shows that the host galaxy has a 3.6\,kpc inner bar with PA\,=\,74$^\circ$, faint spiral arms and a pseudobulge, evolving through secular processes. High resolution mid-infrared images obtained with the \textit{Gran Telescopio Canarias (GTC)} and the instrument \textit{CanariCam} show that the nuclear emission at 11.6 $\mu$m is not spatially resolved. Very Large Array archival observations at 10\,GHz reveal a core source with a total flux density of 1.47\,$\pm$\,0.03\,mJy. The spectral index of the core between 8 and 12\,GHz is -0.5\,$\pm$\,0.2, characteristic of AGN. The core deconvolves into a source with dimensions of 82\,$\pm$\,13\,mas\,$\,\times\,$\,41\,$\pm$\,20\,mas, and a PA\,=\,70\,$\pm$\,18\,deg; which suggests that the core is elongated or that it is constituted by multiple components distributed along a $\sim$65$^\circ$ axis.
An intriguing new duality between planar MHV gluon amplitudes and light-like Wilson loops in N=4 super Yang-Mills is investigated. We extend previous checks of the duality by performing a two-loop calculation of the rectangular and pentagonal Wilson loop. Furthermore, we derive an all-order broken conformal Ward identity for the Wilson loops and analyse its consequences. Starting from six points, the Ward identity allows for an arbitrary function of conformal invariants to appear in the expression for the Wilson loop. We compute this function at six points and two loops and discuss its implications for the corresponding gluon amplitude. It is found that the duality disagrees with a conjecture for the gluon amplitudes by Bern et al. A recent calculation by Bern et al indeed shows that the latter conjecture breaks down at six gluons and at two loops. By doing a numerical comparison with their results we find that the duality between gluon amplitudes and Wilson loops is preserved. This review is based on the author's PhD thesis and includes developments until May 2008.
We have used a model of magnetic accretion to investigate the rotational equilibria of magnetic cataclysmic variables (mCVs). The results of our numerical simulations demonstrate that there is a range of parameter space in the P_spin / P_orb versus mu_1 plane at which rotational equilibrium occurs. This has allowed us to calculate the theoretical histogram describing the distribution of magnetic CVs as a function of P_spin / P_orb. We show that this agrees with the observed distribution assuming that the number of systems as a function of white dwarf magnetic moment is distributed approximately according to N(mu_1) d mu_1 proportional to 1/mu_1 d mu_1. The rotational equilibria also allow us to infer approximate values for the magnetic moments of all known intermediate polars. We predict that intermediate polars with mu_1 > 5 x 10^33 G cm^3 and P_orb > 3h will evolve into polars, whilst those with mu_1 < 5 x 10^33 G cm^3 and P_orb > 3h will either evolve into low field strength polars which are (presumably) unobservable, and possibly EUV emitters, or, if their fields are buried by high accretion rates, evolve into conventional polars once their magnetic fields re-surface when the mass accretion rate reduces. We speculate that EX Hya-like systems may have low magnetic field strength secondaries and so avoid synchronisation. Finally we note that the equilibria we have investigated correspond to a variety of different types of accretion flow, including disc-like accretion at small P_spin / P_orb values, stream-like accretion at intermediate P_spin / P_orb values, and accretion fed from a ring at the outer edge of the white dwarf Roche lobe at higher P_spin / P_orb values.