ShantanuT01/DACTYL-Pretraining huggingface dataset:
The study of asymptotic properties of solutions to differential equations has a long and arduous history, with the most significant advances having been made in the development of quantum mechanics. A very powerful method of analysis is that of Phase Integrals, described by Heading. Key to this analysis are the Stokes constants and the rules for analytic continuation of an asymptotic solution through the complex plane. These constants are easily determined for isolated singular points, by analytically continuing around them and, in the case of analytic functions, requiring the asymptotic solution to be single valued. However, most interesting problems of mathematical physics involve several singular points. By examination of analytically tractable problems and more complex bound state problems involving multiple singular points, we show that the method of Phase Integrals can greatly improve the determination of bound state energies over the simple WKB values. We also find from these examples that in the limit of large separation the Stokes constant for a first order singular point approaches the isolated singular point value.
Motivated by recent experimental and theoretical progress on the Er2Ti2O7 pyrochlore XY antiferromagnet, we study the problem of quantum order-by-disorder in pyrochlore XY systems. We consider the most general nearest-neighbor pseudo spin-1/2 Hamiltonian for such a system characterized by anisotropic spin-spin couplings J_e = [J_\pm, J_{\pm\pm}, J_{z\pm}, J_{zz}] and construct zero-temperature phase diagrams. Combining symmetry arguments and spin-wave calculations, we show that the ground state phase boundaries between the two candidate ground states of the \Gamma_5 irreducible representation, the \psi_2 and \psi_3 (basis) states, are rather accurately determined by a cubic equation in J_{\pm}J_{\pm\pm})/J_{z\pm}^2. Depending on the value of J_{zz}, there can be one or three phase boundaries that separate alternating regions of \psi_2 and \psi_3 states. In particular, we find for sufficiently small J_{zz}/J_{\pm} a narrow \psi_2 sliver sandwiched between two \psi_3 regions in the J_{\pm\pm}/J_\pm vs J_{z\pm}/J_\pm phase diagram. Our results further illustrate the very large potential sensitivity of the ground state of XY pyrochlore systems to minute changes in their spin Hamiltonian. Using the experimentally determined J_3 and g-tensor values for Er2Ti2O7, we show that the heretofore neglected long-range 1/r^3 magnetostatic dipole-dipole interactions do not change the conclusion that Er2Ti2O7 has a \psi_2 ground state induced via a quantum order-by-disorder mechanism. We propose that the CdDy2Se4 chalcogenide spinel, in which the Dy^{3+} ions form a pyrochlore lattice and may be XY-like, could prove interesting to investigate.
In this short note we give a refinement of Brascamp-Lieb in the style of Houdre-Kagan extension for Poincare inequality in one dimension. This is inspired by works of Helffer and Ledoux.
Rescattering effects in coherent eta photoproduction on the deuteron are studied in the region of the S_11(1535) resonance. For the elementary reaction mechanism on the nucleon, an effective isobar model with inclusion of resonances and Born terms is used. The resonance parameters are fixed by considering pion photoproduction only. For the coherent eta production on the deuteron we have considered the impulse approximation taking into account the P_11(1440), D_13(1520), and S_11(1535) resonances, rescattering, and meson exchange currents. For the rescattering mechanism a coupled channel model including the dominant S_11(1535) resonance is used.
The relativity of Global Positioning System (GPS) pseudorange measurements is explored within the geometrical optics approximation in the curved space-time near Earth. A space-time grid for navigation is created by the discontinuities introduced in the electromagnetic field amplitude by the P-code broadcast by the GPS satellites. We compute the world function of space-time near Earth, and we use it to define a scalar phase function that describes the space-time grid. We use this scalar phase function to define the measured pseudorange, which turns out to be a two-point space-time scalar under generalized coordinate transformations. Though the measured pseudorange is an invariant, it depends on the world lines of the receiver and satellite. While two colocated receivers measure two different pseudoranges to the same satellite, they obtain correct position and time, independent of their velocity. We relate the measured pseudorange to the geometry of space-time and find corrections to the conventional model of pseudorange that are on the order of the gravitational radius of the Earth.
We generalize results of Alladi, Dawsey, and Sweeting and Woo for Chebotarev densities to general densities of sets of primes. We show that if $K$ is a number field and $S$ is any set of prime ideals with natural density $\delta(S)$ within the primes, then \[ -\lim_{X \to \infty}\sum_{\substack{2 \le \operatorname{N}(\mathfrak{a})\le X\\ \mathfrak{a} \in D(K,S)}}\frac{\mu(\mathfrak{a})}{\operatorname{N}(\mathfrak{a})} = \delta(S), \] where $\mu(\mathfrak{a})$ is the generalized M\"obius function and $D(K,S)$ is the set of integral ideals $ \mathfrak{a} \subseteq \mathcal{O}_K$ with unique prime divisor of minimal norm lying in $S$. Our result can be applied to give formulas for densities of various sets of prime numbers, including those lying in a Sato-Tate interval of a fixed elliptic curve, and those in Beatty sequences such as $\lfloor\pi n\rfloor$.
Size-dependent quantization of energy spectrum of conducting electrons in solids leads to oscillating dependence of electronic properties on corresponding dimension(s). In conventional metals with typical energy Fermi EF~1 eV and the charge carrier's effective masses m* of the order of free electron mass m0, the quantum size phenomena provide noticeable impact only at nanometer scales. Here we experimentally demonstrate that in single-crystalline semimetal bismuth nanostructures the electronic conductivity non-monotonously decreases with reduction of the effective diameter. In samples grown along the particular crystallographic orientation the electronic conductivity abruptly increases at scales of about 50 nm due to metal-to-insulator transition mediated by the quantum confinement effect. The experimental findings are in reasonable agreement with theory predictions. The quantum-size phenomena should be taken into consideration to optimize operation of the next generation of ultra-small quantum nanoelectronic circuits.
Measurements of the temperature and density structure of the solar corona provide critical constraints on theories of coronal heating. Unfortunately, the complexity of the solar atmosphere, observational uncertainties, and the limitations of current atomic calculations, particularly those for Fe, all conspire to make this task very difficult. A critical assessment of plasma diagnostics in the corona is essential to making progress on the coronal heating problem. In this paper we present an analysis of temperature and density measurements above the limb in the quiet corona using new observations from the EUV Imaging Spectrometer (EIS) on \textit{Hinode}. By comparing the Si and Fe emission observed with EIS we are able to identify emission lines that yield consistent emission measure distributions. With these data we find that the distribution of temperatures in the quiet corona above the limb is strongly peaked near 1 MK, consistent with previous studies. We also find, however, that there is a tail in the emission measure distribution that extends to higher temperatures. EIS density measurements from several density sensitive line ratios are found to be generally consistent with each other and with previous measurements in the quiet corona. Our analysis, however, also indicates that a significant fraction of the weaker emission lines observed in the EIS wavelength ranges cannot be understood with current atomic data.
We describe three presentations relating to the X-ray pulsar GX 1+4 at a workshop on magnetic fields and accretion at the Astrophysical Theory Centre, Australian National University on 1998, November 12-13. Optical and X-ray spectroscopy indicate that GX 1+4 is seen through a cloud of gravitationaly bound matter. We discuss an unstable negative feedback mechanism (originally proposed by Kotani et al, 1999), based on X-ray heating of this matter which controls the accretion rate when the source is in a low X-ray luminosity state. A deep minimum lasting ~6 hours occurred during observations with the RXTE satellite over 1996, July 19-21. The shape of the X-ray pulses changed remarkably from before to after the minimum. These changes may be related to the transition from neutron star spin-down to spin-up which occurred at about the same time. Smoothed particle hydrodynamic simulations of the effect of adding matter with opposite angular momentum to an existing disc, show that it is possible for a number of concentric rings with alternating senses of rotation to co-exist in a disc. This could provide an explanation for the step-like changes in Pdot which are observed in GX 1+4. Changes at the inner boundary of the disc occur at the same timescale as that imposed at the outer boundary. Reversals of material torque on the neutron star occur at a minimum in L_X.
We consider the connected component of the partial duplication model for a random graph, a model which was introduced by Bhan, Galas and Dewey as a model for gene expression networks. The most rigorous results are due to Hermann and Pfaffelhuber, who show a phase transition between a subcritical case where in the limit almost all vertices are isolated and a supercritical case where the proportion of the vertices which are connected is bounded away from zero.   We study the connected component in the subcritical case, and show that, when the duplication parameter $p<e^{-1}$, the degree distribution of the connected component has a limit, which we can describe in terms of the stationary distribution of a certain Markov chain and which follows an approximately power law tail, with the power law index predicted by Ispolatov, Krapivsky and Yuryev. Our methods involve analysing the quasi-stationary distribution of a certain continuous time Markov chain associated with the evolution of the graph.
There are at least two formation scenarios consistent with the first gravitational-wave observations of binary black hole mergers. In field models, black hole binaries are formed from stellar binaries that may undergo common envelope evolution. In dynamic models, black hole binaries are formed through capture events in globular clusters. Both classes of models are subject to significant theoretical uncertainties. Nonetheless, the conventional wisdom holds that the distribution of spin orientations of dynamically merging black holes is nearly isotropic while field-model black holes prefer to spin in alignment with the orbital angular momentum. We present a framework in which observations of black hole mergers can be used to measure ensemble properties of black hole spin such as the typical black hole spin misalignment. We show how to obtain constraints on population hyperparameters using minimal assumptions so that the results are not strongly dependent on the uncertain physics of formation models. These data-driven constraints will facilitate tests of theoretical models and help determine the formation history of binary black holes using information encoded in their observed spins. We demonstrate that the ensemble properties of binary detections can be used to search for and characterize the properties of two distinct populations of black hole mergers.
Charge-independence breaking due to the pion-mass difference in the (chiral) two-pion-exchange nucleon-nucleon force is investigated. A general argument based on symmetries is presented that relates the charge-symmetric part of that force to the proton-proton case. The static potential linear in that mass difference is worked out as an explicit example by means of Feynman diagrams, and this confirms the general argument.
We suggest definition of effective interaction intensity for soft hadron collisions and discuss its energy dependence in the preasymptotic region. Practical importance of this quantity consists in separation of rising interaction radius from effective interaction intensity increase both contributing to the total cross--section growth. It would be helpful for understanding the origin of this growth at the accelerator energies. The essential feature is that the effective interaction intensity is an experimentally measurable quantity.
We demonstrate an algorithm that reconstructs the number of walkers in an unknown graph from observations of their returns to a fixed point.
(Abridged) We have obtained spectra of 135 HII regions located in the inner and extended disks of the spiral galaxies NGC 1512 and NGC 3621, spanning the range of galactocentric distances 0.2-2 x R25 (from 2-3 kpc to 18-25 kpc). We find that the excitation properties of nebulae in the outer (R>R25) disks are similar to those of the inner disks, but on average younger HII regions tend to be selected in the bright inner disks. Reddening by dust is not negligible in the outer disks, and subject to significant large-scale spatial variations. For both galaxies the radial abundance gradient flattens to a constant value outside of the isophotal radius. The outer disk O/H abundance ratio is highly homogeneous, with a scatter of only ~0.06 dex. Based on the excitation and chemical (N/O ratio) analysis we find no compelling evidence for variations in the upper initial mass function of the ionizing clusters of extended disks. The O/H abundance in the outer disks of the target galaxies corresponds to 35% of the solar value (or higher, depending on the metallicity diagnostic). This conflicts with the notion that metallicities in extended disks of spiral galaxies are necessarily low. The observed metal enrichment cannot be produced with the current level of star formation. We discuss the possibility that metal transport mechanisms from the inner disks lead to metal pollution of the outer disks. Gas accretion from the intergalactic medium, enriched by outflows, offers an alternative solution.
Balance equations are derived from Enskog's kinetic equation for a two-dimensional system of hard disks using Grad's moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional fluids. The set of independent hydrodynamic fields in the present formulations are: density, velocity, temperature {\em and also}--following Grad's original idea--the symmetric and traceless pressure tensor $p_{ij}$ and the heat flux vector $\mathbf q^{k}$. An approximation scheme similar in spirit to one made by Grad in his original work is made. Once the hydrodynamics is derived it is used to discuss the nature of a simple one-dimensional heat conduction problem. It is shown that, not too far from equilibrium, the nonequilibrium pressure in this case only depends on the density, temperature and heat flux vector.
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
Vertically thickened bars, observed in the form of boxy/peanut (B/P) bulges, are found in the majority of massive barred disc galaxies in the local Universe, including our own. B/P bulges indicate that their host bars have suffered violent bending instabilities driven by anisotropic velocity distributions. We investigate for the first time how the frequency of B/P bulges in barred galaxies evolves from $z = 1$ to $z\approx 0$, using a large sample of non-edge-on galaxies with masses $M_{\star} > 10^{10}\:M_{\odot}$, selected from the HST COSMOS survey. We find the observed fraction increases from $0^{+3.6}_{-0.0}\%$ at $z = 1$ to $37.8^{+5.4}_{-5.1}\%$ at $z = 0.2$. We account for problems identifying B/P bulges in galaxies with low inclinations and unfavourable bar orientations, and due to redshift-dependent observational biases with the help of a sample from the Sloan Digital Sky Survey, matched in resolution, rest-frame band, signal-to-noise ratio and stellar mass and analysed in the same fashion. From this, we estimate that the true fraction of barred galaxies with B/P bulges increases from $\sim 10\%$ at $z \approx 1$ to $\sim 70\%$ at $z = 0$. In agreement with previous results for nearby galaxies, we find a strong dependence of the presence of a B/P bulge on galaxy stellar mass. This trend is observed in both local and high-redshift galaxies, indicating that it is an important indicator of vertical instabilities across a large fraction of the age of the Universe. We propose that galaxy formation processes regulate the thickness of galaxy discs, which in turn affect which galaxies experience violent bending instabilities of the bar.
Using the conformal invariance of the $SL(2,R)\otimes SO(1,1)^{d-2}/SO(1,1)$ coset models we calculate the conformally exact metric and dilaton, to all orders in the $1/k$ expansion. We consider both vector and axial gauging. We find that these cosets represent two different space--time geometries: ($2d$ black hole)$\otimes \IR^{d-2}$ for the vector gauging and ($3d$ black string)$\otimes \IR^{d-3}$ for the axial one. In particular for $d=3$ and for the axial gauging one obtains the exact metric and dilaton of the charged black string model introduced by Horne and Horowitz. If the value of $k$ is finite we find two curvature singularities which degenerate to one in the semi--classical $k\to \infty$ limit. We also calculate the reflection and transmission coefficients for the scattering of a tachyon wave and using the Bogoliubov transformation we find the Hawking temperature.
We explore the collective density oscillations of a collection of charged massive Dirac particles, in one, two and three dimensions and their one dimensional superlattice. We calculate the long wavelength limit of the dynamical polarization function analytically, and use the random phase approximation to obtain the plasmon dispersion. The density dependence of the long wavelength plasmon frequency in massive Dirac systems is found to be different compared to systems with parabolic, and gapless Dirac dispersion. We also calculate the long wavelength plasmon dispersion of a 1d metamaterial made from 1d and 2d massive Dirac plasma. Our analytical results will be useful for exploring the use of massive Dirac materials as electrostatically tunable plasmonic metamaterials and can be experimentally verified by infrared spectroscopy as in the case of graphene [L. Ju. et. al., Nat. Nanotechnol. 6, 630 (2011)].
We report on the fabrication and characterization of single crystal field-effect transistors (FETs) based on diphenylbenzo diselenophene (DPh-BDSe). These organic field-effect transistors (OFETs) function as p-channel accumulation-mode devices. At room temperature, for the best devices, the threshold voltage is less than -7V and charge carrier mobility is nearly gate bias independent, ranging from 1cm2/Vs to 1.5 cm2/Vs depending on the source-drain bias. Mobility is increased slightly by cooling below room temperature and decreases below 280 K.
The behavior of the mesons and diquarks is studied at finite temperatures, chemical potentials and densities, notably when the color superconductivity is taken into account. The Nambu and Jona-Lasinio model complemented by a Polyakov loop (PNJL description) has been adapted in order to model these composite particles in this regime. This paper focuses on the scalar and pseudo-scalar mesons and diquarks, in a three-flavor and three-color description, with the isospin symmetry and at null strangeness. A finality of this work is to underline the modifications carried out by the color superconducting regime on the used equations and on the obtained results. It has been observed that the two-flavor color-superconducting (2SC) phase affects the masses of the mesons and diquarks in a non-negligible way. This observation is particularly true at high densities and low temperatures for the pions, $\eta$ and the diquarks [ud] whose color is rg. This reveals that the inclusion of the color superconductivity is relevant to describe the mesons and diquarks near the first order chiral phase transition.
A sizeable difference in the differential production cross section of top and antitop quarks, respectively, is predicted for hadronically produced heavy quarks. It is of order $\alpha_s$ and arises from the interference between charge odd and even amplitudes respectively. For the TEVATRON it amounts up to 15\% for the differential distribution in suitable chosen kinematical regions. The resulting integrated forward-backward asymmetry of 4--5\% could be measured in the next round of experiments. At the LHC the asymmetry can be studied by selecting appropriately chosen kinematical regions. Furthermore, a slight preference at LHC for centrally produced antitop is predicted, with top quarks more abundant at large positive and negative rapidities.
Much of our understanding of dark matter halos comes from the assumption that the mass-to-light ratio (M/L) of spiral disks is constant. The best way to test this hypothesis is to measure the disk surface mass density directly via the kinematics of old disk stars. To this end, we have used planetary nebulae (PNe) as test particles and have measured the vertical velocity dispersion (sigma_z) throughout the disks of five nearby, low-inclination spiral galaxies: IC 342, M74 (NGC 628), M83 (NGC 5236), M94 (NGC 4736), and M101 (NGC 5457). By using HI to map galactic rotation and the epicyclic approximation to extract sigma_z from the line-of-sight dispersion, we find that, with the lone exception of M101, our disks do have a constant M/L out to ~3 optical scale lengths. However, once outside this radius, sigma_z stops declining and becomes flat with radius. Possible explanations for this behavior include an increase in the disk mass-to-light ratio, an increase in the importance of the thick disk, and heating of the thin disk by halo substructure. We also find that the disks of early type spirals have higher values of M/L and are closer to maximal than the disks of later-type spirals, and that the unseen inner halos of these systems are better fit by pseudo-isothermal laws than by NFW models.
We consider a two dimensional skip-free reflecting random walk on a nonnegative integer quadrant. We are interested in the tail asymptotics of its stationary distribution, provided its existence is assumed. We derive exact tail asymptotics for the stationary probabilities on the coordinate axis. This refines the asymptotic results in the literature, and completely solves the tail asymptotic problem on the stationary marginal distributions in the coordinate and diagonal directions. For this, we use the so-called analytic function method in such a way that either generating functions or moment generating functions are suitably chosen. The results are exemplified by a two node network with simultaneous arrivals.
We numerically estimate the divergence of several two-vertex diagrams that contribute to the radiative corrections for the Lorentzian EPRL spin foam propagator. We compute the amplitudes as functions of a homogeneous cutoff over the bulk quantum numbers, fixed boundary data, and different Immirzi parameters, and find that for a class of two-vertex diagrams, those with fewer than six internal faces are convergent. The calculations are done with the numerical framework sl2cfoam-next.