ShantanuT01/DACTYL-Pretraining huggingface dataset:
We characterise the homogeneous and isotropic gauge invariant and quasifree states for free Dirac quantum fields on Robertson-Walker spacetimes in any even dimension. Using this characterisation, we construct adiabatic vacuum states of order $n$ corresponding to some Cauchy surface. We then show that any two such states (of sufficiently high order) are locally quasi-equivalent. We propose a microlocal version of the Hadamard condition for spinor fields on arbitrary spacetimes, which is shown to entail the usual short distance behaviour of the twopoint function. The polarisation set of these twopoint functions is determined from the Dencker connection of the spinorial Klein-Gordon operator which we show to equal the (pull-back) of the spin connection. Finally it is demonstrated that adiabatic states of infinite order are Hadamard, and that those of order $n$ correspond, in some sense, to a truncated Hadamard series and will therefore allow for a point splitting renormalisation of the expected stress-energy tensor.
We discuss the quantum phases of hard-core bosons on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions, as realizable with polar molecules trapped in optical lattices. In the limit of small tunneling, we find evidence for a devil's staircase, where solid phases appear at all rational fillings of the underlying lattice. For finite tunneling, we establish the existence of extended regions of parameters where the groundstate is a supersolid, obtained by doping the solids either with particles or vacancies. Here the solid-superfluid quantum melting transition consists of two consecutive second-order transitions, with a supersolid as the intermediate phase. The effects of finite temperature and confining potentials relevant to experiments are discussed.
The properties that govern the production and escape of hydrogen ionizing photons (Lyman continuum, LyC; with energies >13.6 eV) in star-forming galaxies are still poorly understood, but they are key to identifying and characterizing the sources that reionized the Universe. Here we empirically explore the relationship between the hardness of ionizing radiation and the LyC leakage in a large sample of low-$z$ star-forming galaxies from the recent Hubble Space Telescope Low-$z$ Lyman Continuum Survey. Using Sloan Digital Sky Survey stacks and deep XShooter observations, we investigate the hardness of the ionizing spectra ($Q_{\rm He^+}/Q_{\rm H}$) between 54.4 eV (He$^{+}$) and 13.6 eV (H) from the optical recombination lines HeII 4686A and H$\beta$ 4861A for galaxies with LyC escape fractions spanning a wide range, $f_{\rm esc} \rm (LyC) \simeq 0 - 90\%$. We find that the observed intensity of HeII/H$\beta$ is primarily driven by variations in the metallicity, but is not correlated with LyC leakage. Both very strong ($<f_{\rm esc} \rm (LyC)> \simeq 0.5$) and nonleakers ($ < f_{\rm esc} \rm (LyC) > \simeq 0$) present similar observed intensities of HeII/H$\beta$ at comparable metallicity, between $\simeq 0.01$ and $\simeq 0.02$ for $12 + \log({\rm O/H}) > 8.0$ and $<8.0$, respectively. Our results demonstrate that $Q_{\rm He^+}/Q_{\rm H}$ does not correlate with $f_{\rm esc} \rm (LyC)$, which implies that strong LyC emitters do not show harder ionizing spectra than nonleakers at similar metallicity.
We present VLA HI imaging of four LSB galaxies which were thought to strongly deviate from the TF relation based on Arecibo single-dish observations. We do not detect three of the four targeted LSB galaxies in HI down to a 4-sigma limit of 0.08Jy km/s. We find that two of the four of these LSBs have bright galaxies which have contaminated the Arecibo signal. A further examination of the Arecibo sample shows that five out of the six galaxies that were found to deviate from TF have nearby bright galaxies and we conclude that possibly all but one of the non-TF galaxies are contaminated by HI from nearby galaxies. The sixth galaxy was not detected by us. A new observation by Arecibo did not confirm the earlier detection. The integrated profiles of the bright galaxies are consistent with the Arecibo results both in velocity range and amplitude, which indicates that most of the extreme deviators from the TF relation must have been affected by bright companions in this earlier HI survey. A more recent determination of the sidelobe structure of the Arecibo beam supports our conclusion and shows that the degree of sidelobe contamination was much larger than could have been initially predicted. Hence, we have corrected the results found in O'Neil et al. (2000) and have reconstructed the TF relation. These new observations then show a) a reconstructed TF relation that has relatively large scatter at all values of rotational velocity (possibly indicating the true range in disk galaxy properties) and b) the presence of at least some red, gas poor, LSB disks that indeed may be in an advanced evolutionary state as the faded remnants of their former high surface brightness actively star forming state.
We construct the retarded Green function and the Hadamard function in the Lorentzian (d+1)-dimensional anti-de Sitter spacetime for the Poincar\'e coordinate by performing the mode integration directly. We explore the structure of singularities for the position-space Feynman propagator derived from them. The boundary scaling limits of the bulk Feynman propagator yield the bulk-boundary propagator and the boundary conformal correlation function with an extra factor.
In this paper, we move from a "proof of concept" to challenging predictions in a flavour model emerging from a single fermion family in six dimensions (6-D) with the two extra dimensions compactified on a sphere. The most striking predictions (beyond the basic ingredients already demonstrated for a realistic quark mass pattern) are for the neutrino sector. Not only can 4-D Majorana masses be generated from 6-D (where no Majorana spinors exist), but Majorana masses are naturally associated to large mixing. The model favours inverted hierarchy and a quasi-Dirac partial suppression of neutrinoless double beta decay.
We show that the "cold" Hubble flow observed for galaxies around the Milky Way does not represent a problem in cosmology but is due to the particular geometry and dynamics of our local wall. The behavior of the perturbed Hubble flow around the Milky Way is the result of two main factors: at small scales (R < 1 Mpc) the inflow is dominated by the gravitational influence of the Milky Way. At large scales (R > 1 Mpc) the out flow reflects the expansion of our local wall which "cools down" the peculiar velocities. This is an intrinsic property of walls and is independent of cosmology. We find the dispersion of the local Hubble flow (1 < R < 3 Mpc) around simulated "Milky Way" haloes located at the centre of low-density cosmological walls to be {\sigma}_H ~ 30 km/s, in excellent agreement with observations. The expansion of our local wall is also reflected in the value of the measured local Hubble constant. For "Milky Way" haloes inside walls, we find super-Hubble flows with h_local \simeq 0.77 - 1.13. The radius of equilibrium (R_0) depends not only on the mass of the central halo and the Hubble expansion but also on the dynamics given by the local LSS geometry. The super-Hubble flow inside our local wall has the effect of reducing the radius at which the local expansion balances the gravitational influence of the Milky Way. By ignoring the dynamical effect of the local wall, the mass of the Milky Way estimated from R_0 can be underestimated by as much as ~ 30%.
We study the minimisation of a cost functional which measures the misfit on the boundary of a domain between a component of the solution to a certain parametric elliptic PDE system and a prediction of the values of this solution. We pose this problem as a PDE-constrained minimisation problem for a supremal cost functional in ${\mathrm{L}}^\infty$, where except for the PDE constraint there is also a unilateral constraint on the parameter. We utilise approximation by PDE-constrained minimisation problems in ${\mathrm{L}}^p$ as $p\to\infty$ and the generalised Kuhn-Tucker theory to derive the relevant variational inequalities in ${\mathrm{L}}^p$ and ${\mathrm{L}}^\infty$. These results are motivated by the mathematical modelling of the novel bio-medical imaging method of Fluorescent Optical Tomography.
A N-sized inertial classical Heisenberg ferromagnet, which consists in a modification of the well-known standard model, where the spins are replaced by classical rotators, is studied in the limit of infinite-range interactions. The usual canonical-ensemble mean-field solution of the inertial classical $n$-vector ferromagnet (for which $n=3$ recovers the particular Heisenberg model considered herein) is briefly reviewed, showing the well-known second-order phase transition. This Heisenberg model is studied numerically within the microcanonical ensemble, through molecular dynamics.
We study the anticipative backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H greater than 1/2. The stochastic integral used throughout the paper is the divergence operator type integral. We obtain the existence and uniqueness of solutions to these equations. A comparison theorem for this type of anticipative BSDEs is also established.
We present non-LTE oxygen abundances for a sample of B stars in the Orion association. The abundance calculations included non-LTE line formation and used fully blanketed non-LTE model atmospheres. The stellar parameters were the same as adopted in the previous study by Cunha & Lambert (1994). We find that the young Orion stars in this sample of 10 stars are described by a single oxygen abundance with an average value of A(O)=8.78 and a small dispersion of +/- 0.05 dex, which is of the order of the uncertainties in the analysis. This average oxygen abundance compares well with the average oxygen abundance obtained previously in Cunha & Lambert (1994): A(O) = 8.72 +/- 0.13 although this earlier study, based upon non-blanketed model atmospheres in LTE, displayed larger scatter. Small scatter of chemical abundances in Orion B stars had also been found in our previous studies for neon and argon; all based on the same effective temperature scale. The derived oxygen abundance distribution for the Orion association compares well with other results for the oxygen abundance in the solar neighborhood.
In this paper, we investigate some properties of the associated sequence of Daehee and Changhee polynomials. Finally, we give some interesting identities of associated sequence involving some special polynomials.
We compare the N=1 F-theory compactification of Donagi, Grassi and Witten with modular superpotential - and some closely related models - to dual heterotic models. We read of the F-theory spectrum from the cohomology of the fourfold and discuss on the heterotic side the gauge bundle moduli sector (including the spectral surface) and the necessary fivebranes. Then we consider the N=1 superpotential and show how a heterotic superpotential matching the F-theory computation is built up by worldsheet instantons. Finally we discuss how the original modular superpotential should be corrected by an additional modular correction factor, which on the F-theory side matches nicely with a `curve counting function' for the del Pezzo surface. On the heterotic side we derive the same factor demanding correct T-duality transformation properties of the superpotential.
'Normal' galaxies observed at z>6, when the Universe was <1 billion years old, thus far show no evidence of the cold dust that accompanies star formation in the local Universe, where the dust-to-gas mass ratio is 1%. A prototypical example is 'Himiko' (z=6.6), which a mere 840 Myr after the Big Bang is forming stars at a rate of 30-100 Msun/yr, yielding a mass assembly time M^{star}/SFR 150x10^6 yr. Himiko is estimated to have a low fraction (2-3% of the Solar value) of elements heavier than helium (metallicity), and although its gas mass cannot be asserted at this time its dust-to-stellar mass ratio is constrained to be <0.05%. The local galaxy I Zw 18, with a metallicity 4% solar and forming stars less rapidly than Himiko but still vigorously for its mass (M^{star}/SFR 1.6x10^9 yr), is also very dust deficient and perhaps one of the best analogues of primitive galaxies accessible to detailed study. Here we report observations of dust emission from I Zw 18 from which we determine its dust mass to be 450-1800 Msun, yielding a dust-to-stellar mass ratio \approx 10^{-6}-10^{-5} and a dust-to-gas mass ratio 3.2-13x10^{-6}. If I Zw 18 is a reasonable analog of Himiko, then Himiko's dust mass is \approx 50,000 Msun, a factor of 100 below the current upper limit. These numbers are considerably uncertain, but if most high-z galaxies are more like Himiko than like the quasar host SDSS J114816.64+525150.3, then the prospects for detecting the gas and dust in them are much poorer than hitherto anticipated.
Various processes have been proposed previously to study a0(980)-f0(980) mixing through f0(980)->a0(980) transition. Here we investigate in detail the difference between a0(980)->f0(980) and f0(980)->a0(980) transitions. It is found that the a0(980)->f0(980) transition can provide additional constrains to the parameters of a0(980) and f0(980) mesons. Proposal is made to study a0(980)-f0(980) mixing from chi_{c1}->pi^0 a0(980) -> pi^0 f0(980) reaction at the upgraded Beijing electron positron collider with the BESIII detector.
We study the Taylor expansion around the point $x=1$ of a classical modular form, the Jacobi theta constant $\theta_3$. This leads naturally to a new sequence $(d(n))_{n=0}^\infty=1,1,-1,51,849,-26199,\ldots$ of integers, which arise as the Taylor coefficients in the expansion of a related "centered" version of $\theta_3$. We prove several results about the numbers $d(n)$ and conjecture that they satisfy the congruence $d(n)\equiv (-1)^{n-1}\ (\textrm{mod }5)$ and other similar congruence relations.
We report the engineering of the polar magnetooptical (MO) Kerr effect in perpendicularly magnetized L10-MnAl epitaxial films with remarkably tuned magnetization, strain, and structural disorder by varying substrate temperature (Ts) during molecular-beam epitaxy growth. The Kerr rotation was enhanced by a factor of up to 5 with Ts increasing from 150 to 350 oC as a direct consequence of the improvement of the magnetization. A similar remarkable tuning effect was also observed on the Kerr ellipticity and the magnitude of the complex Kerr angle, while the phase of the complex Kerr angle appears to be independent of the magnetization. The combination of the good semiconductor compatibility, the moderate coercivity of 0.3-8.2 kOe, the tunable polar MO Kerr effect of up to ~0.034o, and giant spin procession frequencies of up to ~180 GHz makes L10-MnAl films a very interesting MO material. Our results give insights on both the microscopic mechanisms of the MO Kerr effect in L10-MnAl alloys and their scientific and technological application potential in the emerging spintronics and ultrafast MO modulators.
Predictions from the RQMD model are systematically compared to recently published charged hadron distributions of AGS Experiment 802 for central Si+Au collisions at 14.6$A$ GeV/$c$, taking into account both the experimental trigger condition and acceptance. The main features of the data, including K$^+$ production, can be understood quantitatively to better than 20\% within the framework of the model, although several discrepancies are found, most importantly for the proton spectra.
In the framework of the kt-factorization approach, the production and polarization of prompt J/Psi mesons in pp collisions at the LHC energy 7 TeV is studied. Both the direct production mechanism as well as feed-down contributions from chic1, chic2 and psi' decays are taken into account. Our consideration is based on the color singlet model supplemented with the off-shell matrix elements for the corresponding partonic subprocesses. The unintegrated gluon densities in a proton are determined using the CCFM evolution equation as well the Kimber-Martin-Ryskin prescription. We compare our numerical predictions with the first experimental data taken by the CMS, ATLAS and LHCb collaborations. The estimation of all polarization parameters which determine J/Psi spin density matrix is performed.
Scanning nanofocus X-ray diffraction (nXRD) performed at a synchrotron is used for the first time to simultaneously probe the morphology and the structural properties of spin-coated CH3NH3PbI3 (MAPI) perovskite films for photovoltaic devices. MAPI films are spin-coated on a Si/SiO2/PEDOT:PSS substrate held at different temperatures during the deposition in order to tune the perovskite film coverage, and then investigated by nXRD, scanning electron microscopy (SEM) and grazing incidence wide angle X-ray scatter-ing (GI-WAXS). The advantages of nXRD over SEM and GI-WAXS are dis-cussed. A method to visualize, selectively isolate, and structurally charac-terize single perovskite grains buried within a complex, polycrystalline film is developed. The results of nXRD measurements are correlated with solar cell device measurements, and it is shown that spin-coating the perovskite precursor solution at elevated temperatures leads to improved surface coverage and enhanced solar cell performance.
In the present paper, we establish the uniqueness and nondegeneracy of positive energy solutions to the Kirchhoff equation \begin{eqnarray*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)\Delta u+u=|u|^{p-1}u & & \text{in }\mathbb{R}^{3}, \end{eqnarray*} where $a,b>0$, $1<p<5$ are constants. Then, as applications, we derive the existence and local uniqueness of solutions to the perturbed Kirchhoff problem   \begin{eqnarray*} -\left(\epsilon^2a+\epsilon b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)\Delta u+V(x)u=|u|^{p-1}u & & \text{in }\mathbb{R}^{3} \end{eqnarray*} for $\epsilon>0$ sufficiently small, under some mild assumptions on the potential function $V:\mathbb{R}^3\to \mathbb{R}$. The existence result is obtained by applying the Lyapunov-Schmidt reduction method. It seems to be the first time to study singularly perturbed Kirchhoff problems by reduction method, as all the previous results were obtained by various variational methods. Another advantage of this approach is that it gives a unified proof to the perturbation problem for all $p\in (1,5)$, which is quite different from using variational methods in the literature. The local uniqueness result is totally new. It is obtained by using a type of local Pohozaev identity, which is developed quite recently by Deng, Lin and Yan in their work "On the prescribed scalar curvature problem in $\mathbb{R}^N$, local uniqueness and periodicity." (see J. Math. Pures Appl. (9) {\bf 104}(2015), 1013-1044).
Chromium substituted cobalt ferrite with grain size less than the single domain (approx. 70 nm) has been prepared by the sol-gel method. XRD analysis reveals that the samples crystallize to cubic symmetry with spacegroup number 227. Two transition temperatures (TD (approx. 450 K) and TM (approx. 600 K) have been observed from the impedance verses temperature measurement. TD increases with the increase in frequency due to dipole response to the frequency. TM is comparable with the para-ferrimagnetic transition temperature of cobalt ferrite, which is independent of frequency. This result is well supported by the temperature dependent DC conductivity measurement. The modified Debye relaxation could be explained the impedance spectra of CoFe2-xCrxO4. The grain and grain boundary effect on impedance spectroscopy has been observed from Cole-Cole analysis. The ac conductivity follows Arrhenius behavior at different frequencies. All the samples exhibit the negative temperature coefficient of resistance behavior which reveals the semiconducting behavior of the material. The Mott VRH model could explain the DC electrical conductivity. Both ac impedance and DC resistivity are well co-related each other to explain the electron transport properties in Cr substituted cobalt ferrite. The electrical transport properties could be explained by the electron hopping between different metal ions via oxygen in the material.
We study percolation properties of the upper invariant measure of the contact process on $\mathbb{Z}^d$. Our main result is a sharp percolation phase transition with exponentially small clusters throughout the subcritical regime and a mean-field lower bound for the infinite cluster density in the supercritical regime. This generalizes and simplifies an earlier result of Van den Berg [Ann. App. Prob., 2011], who proved a sharp percolation phase transition on $\mathbb{Z}^2$. Our proof relies on the OSSS inequality for Boolean functions and is inspired by a series of papers by Duminil-Copin, Raoufi and Tassion in which they prove similar sharpness results for a variety of models.
Ultrahigh energy protons and nuclei from extragalactic cosmic ray sources initiate intergalactic electromagnetic cascades, resulting in observable fluxes of $\gamma$-rays in the GeV-TeV energy domain. The total spectrum of such cascade $\gamma$-rays of hadronic nature is significantly harder than the one usually expected from blazars. The spectra of some sources known as "extreme TeV blazars" could be well-described by this "intergalactic hadronic cascade model" (IHCM). We calculate the shape of the observable point-like spectrum, as well as the observable angular distibution of $\gamma$-rays, for the first time taking into account the effect of primary proton deflection in filaments and galaxy clusters of the extragalactic magnetic field assuming the model of Dolag et al. (2005). We present estimates of the width of the observable $\gamma$-ray angular distribution derived from simple geometrical considerations. We also employ a hybrid code to compute the observable spectral and angular distributions of $\gamma$-rays. The observable point-like spectrum at multi-TeV energies is much softer than the one averaged over all values of the observable angle. The presence of a high-energy cutoff in the observable spectra of extreme TeV blazars in the framework of the IHCM could significantly facilitate future searches of new physics processes that enhance the apparent $\gamma$-ray transparency of the Universe (for instance, $\gamma \rightarrow ALP$ oscillations). The width of the observable angular distribution is greater than or comparable to the extent of the point spread function of next-generation $\gamma$-ray telescopes.