ShantanuT01/DACTYL-Pretraining huggingface dataset:
An eikonal expansion is developed in order to provide systematic corrections to the eikonal approximation through order 1/k^2, where k is the wave number. The expansion is applied to wave functions for the Klein-Gordon equation and for the Dirac equation with a Coulomb potential. Convergence is rapid at energies above about 250 MeV. Analytical results for the eikonal wave functions are obtained for a simple analytical form of the Coulomb potential of a nucleus. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. Focusing factors are shown to arise from the corrections to the eikonal approximation. A precise form of the effective-momentum approximation is developed by use of a momentum shift that depends on the electron's energy loss.
A general description of the Vi\`ete coefficients of the gaussian period polynomials is given, in terms of certain symmetric representations of the subgroups and the corresponding quotient groups of the multiplicative group \mathbf{F}_{p}^{*} of a finite prime field of characteristics p, an odd prime number. The known values of these coefficients are recovered by this technique and further results of general nature are presented.
The Yang-Mills theory associated with the restricted Lorentz group is revisited as a candidate for a theory of gravity. This is a natural idea because the principle of equivalence of gravitation and inertia suggests to introduce locally inertial coordinate systems with the gauge freedom of Lorentz transformations. Compared to previous implementations of the idea, we use a generalized expression for the vector potential of the gauge theory in terms of the metric, which involves a coupling constant. One can verify that, in the limit of small coupling constant, all the classical predictions of general relativity are reproduced. For the resulting higher-order field equations, the nature of the singularity associated with black holes changes. The proposed theory is based on a dimensionless action for coupling the Yang-Mills field to matter.
Children, sitting in a circle, each have a nonnegative number of candies in front of them. A whistle is blown and each child with more than one candy passes one candy to the left and one to the right. The sharing process is repeated until a fixed state is attained, or the system enters a periodic cycle. This paper treats the case where the total number of candies equals the number of children. For a given initial distribution of candies, a necessary and sufficient condition is given for the system to ultimately attain the equitable distribution in which each child has one candy.
We write down an anisotropic solution for a flat 5+1 dimensional Universe in Gauss-Bonnet gravity. In the model under investigation this solution replaces the generalized Kasner solution near a cosmological singularity.
Monte Carlo simulations applied to the Spin-Fermion model for cuprates show the existence of antiferromagnetic spin domains and charge stripes upon doping. The stripes are partially filled, with a filling of approximately 1/2 hole per site, and they separate spin domains with a $\pi$ phase shift among them. The stripes observed run either along the x or y axes and they are separated by a large energy barrier. No special boundary conditions or external fields are needed to stabilize these structures at low temperatures. When magnetic incommensurate peaks are observed at momentum $\pi(1,1-\delta)$ and symmetrical points, charge incommensurate peaks appear at $(0,2 \delta)$ and symmetrical points, as experimentally observed. The strong charge fluctuations responsible for the formation of the stripes also induce a pseudogap in the density of states.
The immense interest in carbon nanomaterials continues to stimulate intense research activities aimed to realize carbon nanowires, since linear chains of carbon atoms are expected to display novel and technologically relevant optical, electrical and mechanical properties. Although various allotropes of carbon (e.g., diamond, nanotubes, graphene, etc.) are among the best known materials, it remains challenging to stabilize carbon in the one-dimensional form because of the difficulty to suitably saturate the dangling bonds of carbon. Here, we show through first-principles calculations that ordered polymeric carbon chains can be stabilized in solid Li$_2$C$_2$ under moderate pressure. This pressure-induced phase (above 5 GPa) consists of parallel arrays of twofold zigzag carbon chains embedded in lithium cages, which display a metallic character due to the formation of partially occupied carbon lone-pair states in \emph{sp}$^2$-like hybrids. It is found that this phase remains the most favorable one in a wide range of pressure. At extreme pressure (larger the 215 GPa) a structural and electronic phase transition towards an insulating single-bonded threefold-coordinated carbon network is predicted.
The development of a robust light source that emits one photon at a time is an outstanding challenge in quantum science and technology. Here, at the transition from many to single photon optical communication systems, fully quantum mechanical effects may be utilized to achieve new capabilities, most notably perfectly secure communication via quantum cryptography. Practical implementations place stringent requirements on the device properties, including stable photon generation, room temperature operation, and efficient extraction of many photons. Single photon light emitting devices based on fluorescent dye molecules, quantum dots, and carbon nanotube material systems have all been explored, but none have simultaneously demonstrated all criteria. Here, we describe the design, fabrication, and characterization of a bright source of single photons consisting of an individual Nitrogen-vacancy color center (NV center) in a diamond nanowire operating in ambient conditions. The nanowire plays a positive role in increasing the number of single photons collected from the NV center by an order of magnitude over devices based on bulk diamond crystals, and allows operation at an order of magnitude lower power levels. This result enables a new class of nanostructured diamond devices for room temperature photonic and quantum information processing applications, and will also impact fields as diverse as biological and chemical sensing, opto-mechanics, and scanning-probe microscopy.
For the recent four years we have been studying feedback heating in cooling flow (CF) clusters by AGN activity that inflate bubbles by jets; this short contribution to a meeting summarizes our main results. To achieve our results we had to self-consistently inflate the bubbles with jets, rather than inject them artificially. Our main results are as follows   (1) Feedback mechanisms that are based on Bondi accretion fail. Instead, the accretion to the central super-massive black hole (SMBH) is in the form of cold dense blobs that fall-in from an extended region. (2) Slow massive wide (SMW) jets, or rapidly precessing jets, can inflate bubbles similar to those observed in CF clusters. (3) Contrary to some claims in the literature, the inflated bubbles are stable for a relatively long time, becoming unstable only at later times. (4) A single bubble inflation episode excites multiple sound waves and shocks. These can then heat the intracluster medium (ICM). (5) Mixing of the bubble material to the ICM is efficient, and can serve as a main heating channel. (6) The heating processes work in all directions, and can explain the heating of the ICM in CF in clusters and in galaxies.
The phenomenological symplectic model with a Davidson potential is used to construct rotational states for a rare-earth nucleus with microscopic wave functions. The energy levels and E2 transitions obatined are in remarkably close agreement (to within a few percent) with those of the rotor model with vibrational shape fluctuations that are adiabatically decoupled from the rotational degrees of freedom. An analysis of the states in terms of their SU(3) content shows that SU(3) is a very poor dynamical symmetry but an excellent quasi-dynamical symmetry for the model. It is argued that such quasi-dynamical symmetry can be expected for any Hamiltonian that reproduces the observed low-energy properties of a well-deformed nucleus, whenever the latter are well-described by the nuclear rotor model.
Today, Type Ia supernovae are essential tools for cosmology, and recognized as major contributors to the chemical evolution of galaxies. The construction of detailed supernova progenitor models, however, was so far prevented by various physical and numerical difficulties in simulating binary systems with an accreting white dwarf component, e.g., unstable helium shell burning which may cause significant expansion and mass loss. Here, we present the first binary evolution calculation which models both stellar components and the binary interaction simultaneously, and where the white dwarf mass grows up to the Chandrasekhar limit by mass accretion. Our model starts with a 1.6 Msun helium star and a 1.0 Msun CO white dwarf in a 0.124 day orbit. Thermally unstable mass transfer starts when the CO core of the helium star reaches 0.53 Msun, with mass transfer rates of 1...8 times 10^{-6} Msun/yr. The white dwarf burns the accreted helium steadily until the white dwarf mass has reached ~ 1.3 Msun and weak thermal pulses follow until carbon ignites in the center when the white dwarf reaches 1.37 Msun. Although the supernova production rate through this channel is not well known, and this channel can not be the only one as its progenitor life time is rather short (~ 10^7 - 10^8 yr), our results indicate that helium star plus white dwarf systems form a reliable route for producing Type Ia supernovae.
A light bridge is a prominent structure commonly observed within a sunspot. Its presence usually triggers a wealth of dynamics in a sunspot, and has a lasting impact on sunspot evolution. However, the fundamental structure of light bridges is still not well understood. In this study, we used the high-resolution spectropolarimetry data obtained by the Solar Optical Telescope onboard the Hinode satellite to analyze the magnetic and thermal structure of a light bridge at \AR. We also combined the high-cadence $1700\unit{\AA}$ channel data provided by the Atmospheric Imaging Assembly onboard the Solar Dynamic Observatory to study the dynamics on this bridge. We found that a pair of blue and red Doppler shift patches at two ends of this bridge, this pattern appears to be the convective motion directed by the horizontal component of the magnetic field aligned with the spine of this bridge. Paired upward and downward motions implies that the light bridge could have a two-legged or undulate magnetic field. Significant four minute oscillations in the emission intensity of the $1700\unit{\AA}$ bandpass were detected at two ends, which had overlap with the paired blue and red shift patches. The oscillatory signals at the light bridge and the penumbra were highly correlated with each other. Although they are separated in space at the photosphere, the periodicity seems to have a common origin from the underneath. Therefore, we infer that the light bridge and penumbra could share a common magnetic source and become fragmented at the photosphere by magneto-convection.
We present a scenario where the stability of dark matter and the phenomenology of neutrinos are related by the breaking of a flavour symmetry. We propose two models based on this idea for which we have obtained interesting neutrino and dark matter phenomenology.
We studied the dynamics of all prominence tornadoes detected by the Solar Dynamics Observatory/Atmospheric Imaging Assembly from 2011 January 01 to December 31. In total, 361 events were identified during the whole year, but only 166 tornadoes were traced until the end of their lifetime. Out of 166 tornadoes, 80 (48%) triggered CMEs in hosting prominences, 83 (50%) caused failed coronal mass ejections (CMEs) or strong internal motion in the prominences, and only 3 (2%) finished their lifetimes without any observed activity. Therefore, almost all prominence tornadoes lead to the destabilization of their hosting prominences and half of them trigger CMEs. Consequently, prominence tornadoes may be used as precursors for CMEs and hence for space weather predictions.
We constrain the rest-UV size-luminosity relation for star-forming galaxies at z~4 and z~6, 7, and 8 identified behind clusters from the Hubble Frontier Fields (HFF) program. The size-luminosity relation is key to deriving accurate luminosity functions (LF) for faint galaxies. Making use of the latest lensing models and full data set for these clusters, lensing-corrected sizes and luminosities are derived for 68 z~4, 184 z~6, 93 z~7, and 53 z~8 galaxies. We show that size measurements can be reliably measured up to linear magnifications of 30x, where the lensing models are well calibrated. The sizes we measure span a >1-dex range, from <50 pc to >~500 pc. Uncertainties are based on both the formal fit errors and systematic differences between the public lensing models. These uncertainties range from ~20 pc for the smallest sources to 50 pc for the largest. Using a forward-modeling procedure to model the impact of incompleteness and magnification uncertainties, we characterize the size-luminosity relation at both z~4 and z~6-8. We find that the source sizes of star-forming galaxies at z~4 and z~6-8 scale with luminosity L as L^{0.54\pm0.08} and L^{0.40+/-0.04}, respectively, such that lower luminosity (>~-18 mag) galaxies are smaller than expected from extrapolating the size-luminosity relation at high luminosities (<~-18 mag). The new evidence for a steeper size-luminosity relation (3 sigma) adds to earlier evidence for small sizes based on the prevalence of highly magnified galaxies in high shear regions, theoretical arguments against upturns in the LFs, and other independent determinations of the size-luminosity relation from the HFF clusters.
Quasinormal modes of Dirac field in the background of a non-Schwarzschild black holes in theories with higher curvature corrections are investigated in this paper. With the help of the semi-analytic WKB approximation and further using of Pad\'e approximants as prescribed in [1] we consider quasinormal modes of a test massless Dirac field in the Einstein-dilaton-Gauss-Bonnet (EdGB) and Einstein-Weyl (EW) theories. Even though the effective potential for one of the chiralities has a negative gap we show that the Dirac field is stable in both theories. We find the dependence of the modes on the new dimensionless parameter $p$ (related to the coupling constant in each theory) for different values of the angular parameter $\ell$ and show that the frequencies tend to linear dependence on $p$. The allowed deviations of qausinormal modes from their Schwarzschild limit are one order larger for the Einstein-Weyl theory than for the Einstein-dilaton-Gauss-Bonnet one, achieving the order of tens of percents. In addition, we test the Hod conjecture which suggests the upper bound for the imaginary part of the frequency of the longest lived quasinormal modes by the Hawking temperature multiplied by a factor. We show that in both non-Schwarzschild metrics the Dirac field obeys the above conjecture for the whole range of black-hole parameters.
When an explicit expression for a probability distribution function $F(x)$ can not be found, asymptotic properties of the tail probability function $\bar{F}(x)=1-F(x)$ are very valuable, since they provide approximations or bounds for system performance, and approaches for computing probability distribution. In this paper, we study tail asymptotic properties for the number of the customers in the $M/G/1$ retrial queueing system. For queueing systems, studies on asymptotic tails have mainly concentrated on the first order asymptotic behavior. To best our knowledge, there is no second order tail asymptotic analysis for retrial queueing models with heavy-tailed service time. Second order asymptotic expansions provide the refined asymptotic results from the first order approximation, and are often more difficult to obtain as expected. The main contribution of this paper is the second order asymptotic analysis for the $M/G/1$ retrial queue.
Motivated by lubrication problems, we consider a micropolar uid ow in a 2D domain with a rough and free boundary. We assume that the thickness and the roughness are both of order 0 < " << 1. We prove the existence and uniqueness of a solution of this problem for any value of " and we establish some a priori estimates. Then we use the two-scale convergence technique to derive the limit problem when " tends to zero. Moreover we show that the limit velocity and micro-rotation elds are uniquely determined via auxiliary well-posed problems and the limit pressure is given as the unique solution of a Reynolds equation.
Monopoles in topologically massive gauge theories in 2+1 dimensions with a Chern-Simon mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang-Mills-Higgs model with an additional Chern-Simon mass term in the action. Pisarski argued that there is a monopole solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern-Simon term strength and for several fixed values of Higgs field strength.
Nanoscale CoFeB amorphous films have been synthesized on GaAs(100) and studied with X-ray magnetic circular dichroism (XMCD) and transmission electron microscopy (TEM). We have found that the ratios of the orbital to spin magnetic moments of both the Co and Fe in the ultrathin amorphous film have been enhanced by more than 300% compared with those of the bulk crystalline Co and Fe, and in specifically, a large orbital moment of 0.56*10^-6 B from the Co atoms has been observed and at the same time the spin moment of the Co atoms remains comparable to that of the bulk hcp Co. The results indicate that the large uniaxial magnetic anisotropy (UMA) observed in the ultrathin CoFeB film on GaAs(100) is related to the enhanced spin-orbital coupling of the Co atoms in the CoFeB. This work offers experimental evidences of the correlation between the UMA and the elementary specific spin and orbital moments in the CoFeB amorphous film on the GaAs(100) substrate, which is significant for spintronics applications.
We investigate surface brightness profiles (SBPs) of dwarf galaxies in field, group, and cluster environments. With deep $BVI$ images from the Korea Microlensing Telescope Network Supernova Program, SBPs of 38 dwarfs in the NGC 2784 group are fitted by a single exponential or double exponential model. We find that 53% of the dwarfs are fitted with single exponential profiles ("Type I"), while 47% of the dwarfs show double exponential profiles. 37% of all dwarfs have smaller sizes of the outer part than inner part ("Type II"), while 10% have a larger sized outer than inner part ("Type III"). We compare these results with those in the field and in the Virgo cluster, where SBP types of 102 field dwarfs are compiled from a previous study and SBP types of 375 cluster dwarfs are measured using SDSS $r$-band images. As a result, the distributions of SBP types are different in three environments. Common SBP types of the field, the NGC 2784 group, and the Virgo cluster are Type II, Type I and II, and Type I and III profiles, respectively. After comparing sizes of dwarfs in different environments, we suggest that since sizes of some dwarfs are changed due to the environmental effects, SBP types are able to be transformed and the distributions of SBP types in three environments are different. We discuss possible environmental mechanisms on the transformation of SBP types.
Let $N=pq$ be a product of two distinct primes. There is an isogeny $J_0(N)^{\rm new}\to J^N$ defined over $\mathbf{Q}$ between the new quotient of $J_0(N)$ and the Jacobian of the Shimura curve attached to the indefinite quaternion algebra of discriminant $N$. In the case when $p=2,3,5,7,13$, Ogg made predictions about the kernels of these isogenies. We show that Ogg's conjecture is not true in general. Afterwards, we propose a strategy for proving results toward Ogg's conjecture in certain situations. Finally, we discuss this strategy in detail for $N=5\cdot 13$.
We report on the growth of stoichiometric Sr$_2$IrO$_4$ single crystals, which allow us to unveil their intrinsic magnetic properties. The effect of different growth conditions has been investigated for crystals grown by the flux method. We find that the magnetic response depends very sensitively on the details of the growth conditions. We assess the defect concentration based on magnetization, X-ray diffraction, Raman scattering, and optical conductivity measurements. We find that samples with a low concentration of electronically active defects show much reduced in-gap spectral weight in the optical conductivity and a pronounced two-magnon peak in the Raman scattering spectrum. A prolonged exposure at high temperature during the growth leads to higher defect concentration likely due to creation of oxygen vacancies. We further demonstrate a systematic intergrowth of Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$ phases by varying the growth temperature. Our results thus emphasize that revealing the intrinsic magnetic properties of Sr$_2$IrO$_4$ and related materials requires a scrupulous control of the crystal growth process.
This paper is devoted to the study of eigenvalue region of the doubly stochastic matrices which are also permutative, that is, each row of such a matrix is a permutation of any other row. We call these matrices as permutative doubly stochastic (PDS) matrices. A method is proposed to obtain symbolic representation of all PDS matrices of order $n$ by finding equivalence classes of permutationally similar symbolic PDS matrices. This is a hard problem in general as it boils down to finding all Latin squares of order $n.$ However, explicit symbolic representation of matrices in these classes are determined in this paper when $n=2, 3, 4.$ It is shown that eigenvalue regions are same for doubly stochastic matrices and PDS matrices when $n=2, 3.$ It is also established that this is no longer true for $n=4,$ and two line segments are determined which belong to the eigenvalue region of doubly stochastic matrices but not in the eigenvalue region of PDS matrices. Thus a conjecture is developed for the boundary of the eigenvalue region of PDS matrices of order $4.$ Finally, inclusion theorems for eigenvalue region of PDS matrices are proved when $n\geq 2.$
Torsional Alfven waves are likely excited with bursts in rotating magnetars. These waves are probably propagated through corotating atmospheres toward a vacuum exterior. We have studied the physical effects of the azimuthal wave number and the characteristic height of the plasma medium on wave transmission. In this work, explicit calculations were carried out based on the three-layered cylindrical model. We found that the coupling strength between the internal shear and the external Alfven modes is drastically enhanced, when resonance occurs in the corotating plasma cavity. The spatial structure of the electromagnetic fields in the resonance cavity is also investigated when Alfven waves exhibit resonance.
The one-qubit teleportation protocol is reexamined when it is executed in the presence of various decohering environments. The results revealed that this quantum protocol is more robust under the influence of dephaisng environment than those under the influence of dissipative or noisy environment. The environment may deprive the quantum advantage of teleportation over purely classical communication in a finite or infinite lifetime, which is dependent on the type of environment. Also we found that except entanglement, the purity of the entangled state resource is also crucial in determine the quality of the teleported state.