ShantanuT01/DACTYL-Pretraining huggingface dataset:
The field-theoretical approach is reviewed. Perturbations in general relativity as well as in an arbitrary $D$-dimensional metric theory are studied on a background, which is a solution (arbitrary) of the theory. Lagrangian for perturbations is defined, and field equations for perturbations are derived from the variational principle. These equations are exact and equivalent to the equations in the standard formulation, but can be approximate also. The field-theoretical description is invariant under gauge (inner) transformations, which can be presented both in exact and approximate forms. Following the usual field-theoretical prescription, conserved quantities for perturbations are constructed. Conserved currents are expressed through divergences of superpotentials -- antisymmetric tensor densities. This form allows to relate a necessity to consider local properties of perturbations with a theoretical representation of the quasi-local nature of conserved quantities in metric theories. Applications of the formalism in general relativity are discussed. Generalized formulae for an arbitrary metric $D$-dimensional theory are tested in the Einstein-Gauss-Bonnet gravity.
Where do quasars reside? Are quasars located in environments similar to those of typical L* galaxies, and, if not, how do they differ? An answer to this question will help shed light on the triggering process of quasar activity. We use the Sloan Digital Sky Survey to study the environment of quasars and compare it directly with the environment of galaxies. We find that quasars (M_i < -22, z < 0.4) are located in higher local overdensity regions than are typical L* galaxies. The enhanced environment around quasars is a local phenomenon; the overdensity relative to that around L* galaxies is strongest within 100 kpc of the quasars. In this region, the overdensity is a factor of 1.4 larger than around L* galaxies. The overdensity declines monotonically with scale to nearly unity at ~1 Mpc, where quasars inhabit environments comparable to those of L* galaxies. The small-scale density enhancement depends on quasar luminosity, but only at the brightest end: the most luminous quasars reside in higher local overdensity regions than do fainter quasars. The mean overdensity around the brightest quasars (M_i < -23.3) is nearly three times larger than around L* galaxies while the density around dimmer quasars (M_i = -22.0 to -23.3) is ~1.4 times that of L* galaxies. By ~0.5 Mpc, the dependence on quasar luminosity is no longer significant. The overdensity on all scales is independent of redshift to z = 0.4. The results suggest a picture in which quasars typically reside in L* galaxies, but have a local excess of neighbors within ~0.1 - 0.5 Mpc; this local density excess likely contributes to the triggering of quasar activity through mergers and other interactions.
We investigate the observational signatures of three models of the early Universe in the $B$-mode polarization of the Cosmic Microwave Background (CMB) radiation. In addition to the standard single field inflationary model, we also consider the constraints obtainable on the loop quantum cosmology model (from Loop Quantum Gravity) and on cosmic strings, expected to be copiously produced during the latter stages of Brane inflation. We first examine the observational features of the three models, and then use current $B$-mode polarization data from the BICEP and QUaD experiments to constrain their parameters. We also examine the detectability of the primordial $B$-mode signal predicted by these models and forecast the parameter constraints achievable with future CMB polarization experiments. We find that: (a) these three models of the early Universe predict different features in the CMB B-mode polarization power spectrum, which are potentially distinguishable from the CMB experiments; (b) since $B$-mode polarization measurements are mostly unaffected by parameter degeneracies, they provide the cleanest probe of these early Universe models; (c) using the BICEP and QUaD data we obtain the following parameter constraints: $r=0.02^{+0.31}_{-0.26}$ ($1\sigma$ for the tensor-to-scalar ratio in the single field inflationary model); $m < 1.36\times 10^{-8} \text{M}_{\text{pl}}$ and $k_{*} < 2.43 \times 10^{-4} \text{Mpc}^{-1}$ ($1\sigma$ for the mass and scale parameters in the loop quantum cosmology model); and $G\mu < 5.77 \times 10^{-7}$ ($1\sigma$ for the cosmic string tension); (d) future CMB observations (both satellite missions and forthcoming sub-orbital experiments) will provide much more rigorous tests of these early Universe models.
Evidences of a discrete symmetry behind the pattern of lepton mixing are analyzed. The program of "symmetry building" is outlined. Generic features and problems of realization of this program in consistent gauge models are formulated. The key issues include the flavor symmetry breaking, connection of mixing and masses, {\it ad hoc} prescription of flavor charges, "missing" representations, existence of new particles, possible accidental character of the TBM mixing. Various ways are considered to extend the leptonic symmetries to the quark sector and to reconcile them with Grand Unification. In this connection the quark-lepton complementarity could be a viable alternative to TBM. Observational consequences of the symmetries and future experimental tests of their existence are discussed.
The baryon spectra are discussed in the context of the $1/N_c$ expansion approach, with emphasis on mixed symmetric states. The contributions of the spin dependent terms as a function of the excitation energy are shown explicitly. At large energies these contributions are expected to vanish.
We describe the target selection algorithm for the low latitude disk portion of the LAMOST Pilot Survey, which aims to test systems in preparation for the LAMOST spectroscopic survey. We use the PPMXL (Roeser et al. 2010) astrometric catalog, which provides positions, proper motions, B/R/I magnitudes (mostly) from USNO-B (Monet et al. 2003) and J/H/Ks from The Two Micron All Sky Survey (2MASS, see Skrutskie et al. 2006) as well. We chose 8 plates along the Galactic plane, in the region $0^\circ<\alpha<67^\circ$ and $42^\circ<\delta<59^\circ$, that cover 22 known open clusters with a range of ages. Adjacent plates may have small overlapping. Each plate covers an area $2.5^\circ$ in radius,with central star (for Shack-Hartmann guider) brighter than $\sim8^{\rm th}$ magnitude. For each plate, we create an input catalog in the magnitude range $11.3<Imag<16.3$ and $Bmag$ available from PPMXL. The stars are selected to satisfy the requirements of the fiber positioning system and have a uniform distribution in the $I$ vs. $B-I$ color-magnitude diagram. Our final input catalog consists of 12,000 objects on each of 8 plates that are observable during the winter observing season in Xinglong Station of the National Astronomical Observatory of China.
The marked interplay between the crystalline, electronic, and magnetic structure of atomically thin magnets has been regarded as the key feature for designing next-generation magneto-optoelectronic devices. In this respect, a detailed understanding of the microscopic interactions underlying the magnetic responses of these crystals is of primary importance. Here, we combine model Hamiltonians with multi-reference configuration interaction wavefunctions to accurately determine the strength of the spin couplings in the prototypical single-layer magnet CrI$_3$. Our calculations identify the (ferromagnetic) Heisenberg exchange interaction $J = -1.44$ meV as the dominant term, being the inter-site magnetic anisotropies substantially {weaker}. We also find that single-layer CrI$_3$ features an out-of-plane easy axis ensuing from a single-ion anisotropy $A = -0.10$ meV, and predict $g$-tensor in-plane components $g_{xx} = g_{yy} = 1.90$ and out-of-plane component $g_{zz} = 1.92$. In addition, we assess the performance of a dozen widely used density functionals against our accurate correlated wavefunctions {calculations} and available experimental data, thereby establishing reference results for future first-principles investigations. Overall, our findings offer a firm theoretical ground to experimental observations.
In this paper, we present a unifying approach to the general theory of abelian Stark conjectures. To do so we define natural notions of `zeta element', of `Weil-\'etale cohomology complexes' and of `integral Selmer groups' for the multiplicative group $\mathbb{G}_m$ over finite abelian extensions of number fields. We then conjecture a precise connection between zeta elements and Weil-\'etale cohomology complexes, we show this conjecture is equivalent to a special case of the equivariant Tamagawa number conjecture and we give an unconditional proof of the analogous statement for global function fields. We also show that the conjecture entails much detailed information about the arithmetic properties of generalized Stark elements including a new family of integral congruence relations between Rubin-Stark elements (that refines recent conjectures of Mazur and Rubin and of the third author) and explicit formulas in terms of these elements for the higher Fitting ideals of the integral Selmer groups of $\mathbb{G}_m$, thereby obtaining a clear and very general approach to the theory of abelian Stark conjectures. As first applications of this approach, we derive, amongst other things, a proof of (a refinement of) a conjecture of Darmon concerning cyclotomic units, a proof of (a refinement of) Gross's `Conjecture for Tori' in the case that the base field is $\mathbb{Q}$, a proof of new cases of the equivariant Tamagawa number conjecture in situations in which the relevant $p$-adic $L$-functions have trivial zeroes, explicit conjectural formulas for both annihilating elements and, in certain cases, the higher Fitting ideals (and hence explicit structures) of ideal class groups, a reinterpretation of the $p$-adic Gross-Stark Conjecture in terms of the properties of zeta elements and a strong refinement of many previous results (of several authors) concerning abelian Stark conjectures.
Let u, v be two harmonic functions in the disk of radius two which have exactly the same set Z of zeros. We observe that the gradient of \log |u/v| is bounded in the unit disk by a constant which depends on Z only. In case Z is empty this goes back to Li-Yau's gradient estimate for positive harmonic functions. The general boundary Harnack principle gives H\"older estimates on \log |u/v|.
The recent discovery and analysis of a classical Cepheid in the well detached, double-lined, eclipsing binary OGLE-LMC-CEP0227, has provided the first determination of the dynamical mass of a classical Cepheid variable to an unprecedented 1% accuracy. We show here that modern stellar evolution models widely employed to study Galactic and extragalactic stellar systems, are able to match simultaneously mass and radius (and effective temperature) of the two components with a single value for the age of the system, without any specific fine-tuning. Our conclusion is that there is no discrepancy between dynamical and evolutionary masses for the Cepheid star in this system, contrary to previous claims of an overestimate of the Cepheid mass by stellar evolution theory.
This article studies the global well-posedness for a class of defocusing, generalized sixth-order Boussinesq equations, extending a previous result obtained by Wang and Esfahani for the case when the nonlinear term is cubic.
We consider a Josephson junction formed by a quantum dot connected to two bulk superconductors in presence of Coulomb interaction and coupling to both an electromagnetic environment and a finite density of electronic quasi-particles. In the limit of large superconducting gap we obtain a Born-Markov description of the system dynamics. We calculate the current-phase relation and we find that the experimentally unavoidable presence of quasi-particles can dramatically modify the 0-pi standard transition picture. We show that photon-assisted quasi-particles absorption allows the dynamic switching from the 0- to the pi-state and vice-versa, washing out the 0-pi transition predicted by purely thermodynamic arguments.
Ultrafast two-color pump-probe measurements, involving coherent acoustic phonon (CAP) waves, have provided information simultaneously on the mechanical properties and on the electronic structure of ferromagnetic GaMnAs. The elastic constant C11 of Ga1-xMnxAs (0.03<x<0.07) are observed to be systematically smaller than those of GaAs. Both C11 and Vs of GaMnAs are found to increase with temperature (78 K<T<295 K), again in contrast to the opposite behavior in GaAs. In addition, the fundamental bandgap (at E0 critical point) of Ga1-xMnxAs is found to shift slightly to higher energies with Mn concentration.
A mechanism that produces conical dispersion relations is presented. A Kronig Penney one dimensional array with two different strengths delta function potentials gives rise to both the gap closure and the dispersion relation observed in graphene and other materials. The Schr\''odinger eigenvalue problem is locally invariant under the infinite dimensional Virasoro algebra near conical dispersion points in reciprocal space, thus suggesting a possible relation to string theory.
Recently, the concept of rotational mixing has been challenged by some authors (e.g. Hunter et al. 2008). We show that the excess N/H is a multivariate function f(M, age, v, sin i, multiplicity,Z). To find a correlation of a multivariate function with some parameter, it is evidently necessary to limit as much as possible the range of the other involved parameters. When this is done, the concept of rotational mixing is supported by the observations. We also show that the sample data are not free from several biases. A fraction of about 20% of the stars may escape to the relation as a result of binary evolution.
Let $0<\lambda\leq1$, $\lambda\notin\left\{\frac24, \frac27, \frac2{10}, \frac2{13}, \ldots\right\}$, be a real and $p$ a prime number, with $[p,p+\lambda p]$ containing at least two primes. Denote by $f_\lambda(p)$ the largest integer which cannot be written as a sum of primes from $[p,p+\lambda p]$. Then \[f_\lambda(p)\sim\left\lfloor2+\frac2\lambda\right\rfloor\cdot p\text{, as }p\text{ goes to infinity.}\]   Further a question of Wilf about the 'Money-Changing Problem' has a positive answer for all semigroups of multiplicity $p$ containing the primes from $[p,2p]$. In particular, this holds for the semigroup generated by all primes not less than $p$. The latter special case was already shown in a previous paper.
This article presents the theory of focal locus applied to the hypersurfaces in the projective space which are (finitely) covered by linear spaces and such that the tangent space is constant along these spaces.
Studying CMEs in coronagraph data can be challenging due to their diffuse structure and transient nature, and user-specific biases may be introduced through visual inspection of the images. The large amount of data available from the SOHO, STEREO, and future coronagraph missions, also makes manual cataloguing of CMEs tedious, and so a robust method of detection and analysis is required. This has led to the development of automated CME detection and cata- loguing packages such as CACTus, SEEDS and ARTEMIS. Here we present the development of a new CORIMP (coronal image processing) CME detection and tracking technique that overcomes many of the drawbacks of current catalogues. It works by first employing the dynamic CME separation technique outlined in a companion paper, and then characterising CME structure via a multiscale edge-detection algorithm. The detections are chained through time to determine the CME kinematics and morphological changes as it propagates across the plane-of-sky. The effectiveness of the method is demonstrated by its application to a selection of SOHO/LASCO and STEREO/SECCHI images, as well as to synthetic coronagraph images created from a model corona with a variety of CMEs. The algorithms described in this article are being applied to the whole LASCO and SECCHI datasets, and a catalogue of results will soon be available to the public.
Samarium hexaboride (SmB6) has been presumed to show a topological Kondo insulating state consisting of fully occupied quasiparticle bands in the concept of a Fermi liquid. This gap emerging below a small coherence temperature is the ultimate sign of coherence for a many-body system, which in addition induces a non-trivial topology. Here, we demonstrate that just one energy scale governs the gap formation in SmB6, which supports the Fermi liquid description. The temperature dependence of the gap formation in the mixed valence regime is captured within the dynamical mean field (DMFT) approximation to the periodic Anderson model (PAM). The scaling property of the model with the topological coherence temperature provides a strong connection to the photoemission spectra of SmB6. Our results suggest a simple way to compare a model study and an experiment result for heavy fermion insulators.
PSR J2032+4127 is a gamma-ray and radio-emitting pulsar which has been regarded as a young luminous isolated neutron star. However, its recent spin-down rate has extraordinarily increased by a factor of two. We present evidence that this is due to its motion as a member of a highly-eccentric binary system with a 15-solar-mass Be star, MT91~213. Timing observations show that, not only are the positions of the two stars coincident within 0.4 arcsec, but timing models of binary motion of the pulsar fit the data much better than a model of a young isolated pulsar. MT91~213, and hence the pulsar, lie in the Cyg~OB2 stellar association, which is at a distance of only 1.4-1.7 kpc. The pulsar is currently on the near side of, and accelerating towards, the Be star, with an orbital period of 20-30 years. The next periastron is well-constrained to occur in early 2018, providing an opportunity to observe enhanced high-energy emission as seen in other Be-star binary systems.
We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of local unitary operations. We study basic properties of multipartite invariant states: separability criteria and multi-PPT conditions.
The question if a Mott insulator and a band insulator are fundamentally different has been the matter of intensive research recently. Here we consider a simple model which allows by tuning one parameter to go continously from a Mott insulator to band insulator. The model consists of two Hubbard systems connected by single particle hopping. The Hubbard Hamiltonian is solved by the Dynamical Mean-Field theory using Quantum Monte Carlo to solve the resulting quantum impurity problem. The quasiparticle spectral function is calculated. Here we focus on the optical conductivity and in particular on the Drude weight which can be experimentally measured. From our calculation we conclude that there is a continous crossover from the band insulator to the Mott insulator phase at finite temperature.
This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localization, and that the optimal strategy for reducing a three-qubit GHZ state to a two-qubit one via local measurements and classical communications in the amplitude-damping case is different from that in the noise-free case. We also show that the idea of entanglement localization could be utilized to improve the quality of bipartite entanglement distributing through amplitude-damping channels. These findings might shed a new light on entanglement manipulations and transformations.
We investigate the connection between local structure and dynamical heterogeneity in supercooled liquids. Through the study of four different models we show that the correlation between a particle's mobility and the degree of local order in nearby regions is highly system dependent. Our results suggest that the correlation between local structure and dynamics is weak or absent in systems that conform well to the mean-field picture of glassy dynamics and strong in those that deviate from this paradigm. Finally, we investigate the role of order-agnostic point-to-set correlations and reveal that they provide similar information content to local structure measures, at least in the system where local order is most pronounced.
In this paper, we define the notion of graph trace kernels as a generalization of trace kernels. We associate a microlocal Lefschetz class with a graph trace kernel and prove that this class is functorial with respect to the composition of kernels. We apply graph trace kernels to the microlocal Lefschetz fixed point formula for constructible sheaves.
We report on observations of four southern Anomalous X-ray Pulsars, (1RXS J170849.0-400910, 1E 1048.1-5937, 1E 1841-045 and AX J1845-0258), obtained at 1.4 GHz using the Parkes radio telescope. Radio pulsations from these sources have been searched (i) by directly folding the time series at a number of trial periods centered on the value of the spin rate obtained from the X-ray observations; (ii) by performing a blind search; (iii) using a code sensitive to single dedispersed pulses, in the aim to detect signals similar to those of the recently discovered Rotating RAdio Transients. No evidence for radio pulsations with an upper limit of ~0.1 mJy for any of the four targets has been found. The blind search led to the serendipitous discovery of two new pulsars, rotating with a spin period of about 0.7 s and of 92 ms respectively, and to the further detection of 18 known pulsars, two of which were also detected in the single-pulse search.
In the present paper we consider the problem of constructing all the projective rooted spanning trees of a given graph. We propose an algorithm based on reducing this problem to the problem of constructing all the maximal independent sets of a certain derived graph. We also offer an algorithm for step-by-step growing the spanning trees that sifts, at each step, any sub-trees non-extendable to projective spanning trees. The proposed algorithms were applied for analyzing the possible variants of the syntactic subordination of nouns through prepositions .
Customary two-dimensional flux transport models for the evolution of the magnetic field at the solar surface do not account for the radial structure and the volume diffusion of the magnetic field. When considering the long-term evolution of magnetic flux, this omission can lead to an unrealistic long-term memory of the system and to the suppression of polar field reversals. In order to avoid such effects, we propose an extension of the flux transport model by a linear decay term derived consistently on the basis of the eigenmodes of the diffusion operator in a spherical shell. A decay rate for each eigenmode of the system is determined and applied to the corresponding surface part of the mode evolved in the flux transport model. The value of the volume diffusivity associated with this decay term can be estimated to be in the range 50--100 km^2/s by considering the reversals of the polar fields in comparison of flux transport simulations with observations. We show that the decay term prohibits a secular drift of the polar field in the case of cycles of varying strength, like those exhibited by the historical sunspot record.