ShantanuT01/DACTYL-Pretraining huggingface dataset:
One dimensional spin-1/2 $XXZ$ model in a transverse magnetic field is studied. It is shown that the field induces the gap in the spectrum of the model with easy-plain anisotropy. Using conformal invariance the field dependence of the gap at small fields is found. The ground state phase diagram is obtained. It contains four phases with different types of the long range order (LRO) and a disordered one. These phases are separated by critical lines, where the gap and the long range order vanish. Using scaling estimations and a mean-field approach as well as numerical calculations in the vicinity of all critical lines we found the critical exponents of the gap and the LRO. It is shown that transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.
In this paper, we establish the following two identities involving the Gamma function and Bernoulli polynomials, namely $$ \sum_{k\leq x}\frac{1}{k^s} \sum_{j=1}^{k^s}\log\Gamma\left(\frac{j}{k^s}\right)   \sum_{\substack{d|k \\ d^{s}|j}}f*\mu(d) \quad {\rm and } \quad \sum_{k\leq x}\frac{1}{k^s}\sum_{j=0}^{k^{s}-1}   B_{m}\sum_{\substack{d|k \\ d^{s}|j}} f*\mu(d) $$ with any fixed integer $s> 1$ and any arithmetical function $f$. We give asymptotic formulas for them with various multiplicative functions $f$. We also consider several formulas of the Dirichlet series associated with the above identities. This paper is a continuation of an earlier work of the authors.
This paper explores optimal methods for obtaining one-dimensional (1D) powder pattern intensities from two-dimensional (2D) planar detectors with good estimates of their standard deviations. We describe methods to estimate uncertainties when the same image is measured in multiple frames as well as from a single frame. We show the importance of considering the correlation of diffraction points during the integration and the re-sampling process of data analysis. We find that correlations between adjacent pixels in the image can lead to seriously overestimated uncertainties if it is neglected in the integration process. Off-diagonal entries in the variance-covariance (VC) matrix are problematic as virtually all data processing and modeling programs cannot handle the full VC matrix. We show the off-diagonal terms come mainly from the pixel splitting algorithm used as the default integration algorithm in many popular 2D integration programs, as well as from re-binning and re-sampling steps later in the processing. When the full VC matrix can be propagated during the data reduction, it is possible to get accurate refined parameters and their uncertainties at the cost of increasing computational complexity. However, as this is not normally possible, we explore the best approximate methods for data processing in order to estimate uncertainties on refined parameters with the greatest accuracy from just the diagonal variance terms in the VC matrix.
We report on Hartree-Fock-Bogoliubov (HFB) calculations of the ground-state rotationnal band of the heavy nucleus $^{254}$No recently observed experimentally. The calculated quadrupole deformation is consistent with the experimental value of $\beta=0.27$ and is almost constant over the whole band. We also reproduce fairly well the excitation spectra and moments of inertia of this isotope up to the maximal experimentally observed state of spin 20. The rather high stability of this nucleus against fission is illustrated by the deformation energy curve providing very high fission barriers at zero spin within the HFB and HFB plus Lipkin-Nogami formalisms. The variation of these barriers with increased angular velocities is also studied.
The lifetimes of 17 even-parity levels (3d5s, 3d4d, 3d6s, and 4p$^2$) in the region 57743-77837 cm$^{-1}$ of singly ionised scandium (\ion{Sc}{ii}) were measured by two-step time-resolved laser induced fluorescence spectroscopy. Oscillator strengths of 57 lines from these highly excited upper levels were derived using a hollow cathode discharge lamp and a Fourier transform spectrometer. In addition, Hartree--Fock calculations where both the main relativistic and core-polarisation effects were taken into account were carried out for both low- and high-excitation levels. There is a good agreement for most of the lines between our calculated branching fractions and the measurements of Lawler and Dakin (1989) in the region 9000-45000 cm$^{-1}$ for low excitation levels and with our measurements for high excitation levels in the region 23500-63100 cm$^{-1}$. This, in turn, allowed us to combine the calculated branching fractions with the available experimental lifetimes to determine semi-empirical oscillator strengths for a set of 380 E1 transitions in \ion{Sc}{ii}. These oscillator strengths include the weak lines that were used previously to derive the solar abundance of scandium. The solar abundance of scandium is now estimated to $\log~\epsilon_\odot = 3.04\pm0.13$ using these semi-empirical oscillator strengths to shift the values determined by Scott et al. (2015). The new estimated abundance value is in agreement with the meteoritic value ($\log~\epsilon_{\text{met}}=3.05\pm0.02$) of Lodders et al. (2009).
We report the serendipitous detection of the planetary nebula NGC 5315 by the Chandra X-ray Observatory. The Chandra imaging spectroscopy results indicate that the X-rays from this PN, which harbors a Wolf-Rayet (WR) central star, emanate from a T_X ~ 2.5x10^6 K plasma generated via the same wind-wind collisions that have cleared a compact (~8000 AU radius) central cavity within the nebula. The inferred X-ray luminosity of NGC 5315 is ~2.5x10^{32} erg s^{-1} (0.3-2.0 keV), placing this object among the most luminous such ``hot bubble'' X-ray sources yet detected within PNe. With the X-ray detection of NGC 5315, objects with WR-type central stars now constitute a clear majority of known examples of diffuse X-ray sources among PNe; all such ``hot bubble'' PN X-ray sources display well-defined, quasi-continuous optical rims. We therefore assert that X-ray-luminous hot bubbles are characteristic of young PNe with large central star wind kinetic energies and closed bubble morphologies. However, the evidence at hand also suggests that processes such as wind and bubble temporal evolution, as well as heat conduction and/or mixing of hot bubble and nebular gas, ultimately govern the luminosity and temperature of superheated plasma within PNe.
This is a numerical study of thermoelectric properties of ballistic bilayer graphene in the presence of trigonal warping term in the effective Hamiltonian. We find, in the mesoscopic samples of the length $L>10\,\mu{}$m at sub-Kelvin temperatures, that both the Seebeck coefficient and the Lorentz number show anomalies (the additional maximum and minimum, respectively) when the electrochemical potential is close to the Lifshitz energy, which can be attributed to the presence of the van Hove singularity in a bulk density of states. At higher temperatures the anomalies vanish, but measurable quantities characterizing remaining maximum of the Seebeck coefficient still unveil the presence of massless Dirac fermions and make it possible to determine the trigonal warping strength. Behavior of the thermoelectric figure of merit ($ZT$) is also discussed.
Ultrasonic investigations of the single-site quadrupolar Kondo effect in diluted Pr system Y$_{0.966}$Pr$_{0.034}$Ir$_2$Zn$_{20}$ are reported. The elastic constant $(C_{11}-C_{12})/2$ is measured down to ~40 mK using ultrasound for the dilute system Y$_{0.966}$Pr$_{0.034}$Ir$_2$Zn$_{20}$ and the pure compound YIr$_2$Zn$_{20}$. We found that the elastic constant $(C_{11}-C_{12})/2$ of the Pr-dilute system exhibits a logarithmic temperature dependence below $T_0$ ~0.3 K, where non-Fermi-liquid (NFL) behavior in the specific heat and electrical resistivity is observed. This logarithmic temperature variation manifested in the $\Gamma_3$-symmetry quadrupolar susceptibility is consistent with the theoretical prediction of the quadrupolar Kondo effect by D. L. Cox. On the other hand, the pure compound YIr$_2$Zn$_{20}$ without $4f$-electron contributions shows nearly no change in its elastic constants evidencing negligible phonon contributions. In addition, clear acoustic de Haas-van Alphen (dHvA) oscillations in the elastic constant were detected for both compounds on applying magnetic field. This is mainly interpreted as contribution from the Fermi surface of YIr$_2$Zn$_{20}$.
We provide strong evidence that all tree-level 4-point holographic correlators in AdS$_3 \times S^3$ are constrained by a hidden 6D conformal symmetry. This property has been discovered in the AdS$_5 \times S^5$ context and noticed in the tensor multiplet subsector of the AdS$_3 \times S^3$ theory. Here we extend it to general AdS$_3 \times S^3$ correlators which contain also the chiral primary operators of spin zero and one that sit in the gravity multiplet. The key observation is that the 6D conformal primary field associated with these operators is not a scalar but a self-dual $3$-form primary. As an example, we focus on the correlators involving two fields in the tensor multiplets and two in the gravity multiplet and show that all such correlators are encoded in a conformal 6D correlator between two scalars and two self-dual $3$-forms, which is determined by three functions of the cross ratios. We fix these three functions by comparing with the results of the simplest correlators derived from an explicit supergravity calculation.
An action of a finite group on a smooth projective curve over an algebraically closed field of positive characteristic is called restrained, if all second ramification groups are trivial (e.g., every group action on an ordinary curve is restrained). When the ramification indices satisfy certain numerical criteria, we construct a degenerating equivariant quasi-projective family to which the given curve belongs, and which in a sense is the unique building block for all such restrained equivariant families that ramify above a fixed set of points. The result is used to inductively study automorphisms of ordinary curves.
We apply the $\delta$-expansion perturbation scheme to the $\lambda \phi_{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\delta$-expansion the interaction term is written as $\lambda (\phi^{2})^{1 + \delta}$ and $\delta$ is considered as the perturbation parameter. We compute, in this perturbation approach, the renormalized mass at finite temperature from which we get the critical temperature. The results are compared with the usual loop-expansion at finite temperature.
We study the irreducibility of the characteristic polynomial of the energy graph of the non linear Schr\"{o}dinger equation (NLS). This will be useful to the verification of the second Melnikov condition for NLS.
In the standard model, the top quark decay width \Gamma_t is computed from the exclusive t -> bW decay. We argue in favor of using the three body decays t-> bf_i\bar{f}_j to compute \Gamma_t as a sum over these exclusive modes. As dictated by the S-matrix theory, these three body decays of the top quark involve only asymptotic states and incorporate the width of the W boson resonance in a natural way. The convolution formula (CF) commonly used to include the finite width effects is found to be valid, in the general case, when the intermediate resonance couples to a conserved current (limit of massless fermions in the case of W bosons). The relation Gamma_t=\Gamma(t-> bW) is recovered by taking the limit of massless fermions followed by the W boson narrow width approximation. Although both calculations of \Gamma_t are different at the formal level, their results would differ only by tiny effects induced by light fermion masses and higher order radiative corrections.
The lattice dynamics of Ba$_2$CuGe$_2$O$_7$, a compound which develops Dzyaloshinsky-Moriya (DM) helical magnetism below $T_N$ = 3.2 K, has been studied by measuring the infrared reflectivity of a single crystal with the radiation polarized both in the $ab$ plane and along the $c$ axis of its tetragonal cell, from 7 K to 300 K. In this compound, where the unit cell has no inversion symmetry, fourteen $E$ phonon modes of the $ab$ plane, out of the eighteen predicted, and all the ten $B_2$ modes of the $c$ axis, have been observed. They have been assigned to the atomic motions by a comparison with shell-model calculations, which provided vibrational frequencies in good agreement with the experiment, while most calculated intensities turned to be much lower than the experimental values. This discrepancy has been tentatively explained by assuming strong electron-phonon interactions, a hypothesis supported by the failure of the $f$- sum rule if restricted to the phonon region. Indeed, we observe a remarkable increase in the oscillator strengths at $T$'s low but higher than $T_N$, which suggests that the dielectric constant of Ba$_2$CuGe$_2$O$_7$ may increase at those temperatures.
We obtain an asymptotic formula for the smoothly weighted first moment of primitive quadratic Dirichlet L-functions at the central point, with an error term that is "square-root" of the main term. Our approach uses a recursive technique that feeds the result back into itself, successively improving the error term.
We discuss some results related to a phase transition model in which the potential energy induced by a double-well function is balanced by a fractional elastic energy. In particular, we present asymptotic results (such as $\Gamma$-convergence, energy bounds and density estimates for level sets), flatness and rigidity results, and the construction of planelike minimizers in periodic media.   Finally, we consider a nonlocal equation with a multiwell potential, motivated by models arising in crystal dislocations, and we construct orbits exhibiting symbolic dynamics, inspired by some classical results by Paul Rabinowitz.
In this work we prove a criterion for an algebraic continued fraction to have a proper palindromic symmetry in dimension $4$. As a multidimensional generalization of continued fractions, we consider Klein polyhedra.
The emission nebula around the subdwarf B (sdB) star PHL 932 is currently classified as a planetary nebula (PN) in the literature. Based on a large body of multi-wavelength data, both new and previously published, we show here that this low-excitation nebula is in fact a small Stromgren sphere (HII region) in the interstellar medium around this star. We summarise the properties of the nebula and its ionizing star, and discuss its evolutionary status. We find no compelling evidence for close binarity, arguing that PHL 932 is an ordinary sdB star. We also find that the emission nebulae around the hot DO stars PG 0108+101 and PG 0109+111 are also Stromgren spheres in the ISM, and along with PHL 932, are probably associated with the same extensive region of high-latitude molecular gas in Pisces-Pegasus.
The most reliable method to estimate the residence time of cosmic rays in the Galaxy is based on the study of the suppression, due to decay, of the flux of unstable nuclei such as beryllium-10, that have lifetime of appropriate duration. The Cosmic Ray Isotope Spectrometer (CRIS) collaboration has measured the ratio between the fluxes of beryllium-10 and beryllium-9 in the energy range E_0 \simeq 70-145 MeV/nucleon, and has used the data to estimate an escape time tau_{ esc} = 15.0 +- 1.6 Myr. This widely quoted result has been obtained in the framework of a simple leaky-box model where the distributions of escape time and age for stable particles in the Galaxy are identical and have exponential form. In general, the escape time and age distributions do not coincide, they are not unique (because they depend on the injection or observation point), and do not have a simple exponential shape. It is therefore necessary to discuss the measurement of the beryllium ratio in a framework that is more general and more realistic than the leaky-box model.   In this work we compute the escape time and age distributions of cosmic rays in the Galaxy in a model based on diffusion that is much more realistic than the simple leaky-box, but that remains sufficiently simple to have exact analytic solutions. Using the age distributions of the model to interpret the measurements of the beryllium-10 suppression, one obtains a cosmic ray residence time that is significantly longer (a factor 2 to 4 depending on the extension of the cosmic ray halo) than the leaky-box estimate. This revised residence time implies a proportional reduction of the power needed to generate the galactic cosmic rays.
In a recent publication, we derived the mesoscale continuum theory of plasticity for multiple-slip systems of parallel edge dislocations, motivated by the statistical-based nonlocal continuum crystal plasticity theory for single-glide due to Yefimov et al. (2004b). In this dislocation field theory (DiFT) the transport equations for both the total dislocation densities and geometrically necessary dislocation densities on each slip system were obtained from the Peach-Koehler interactions through both single and pair dislocation correlations. The effect of pair correlation interactions manifested itself in the form of a back stress in addition to the external shear and the self-consistent internal stress. We here present the study of size effects in single crystalline thin films with symmetric double slip using the novel continuum theory. Two boundary value problems are analyzed: (1) stress relaxation in thin films on substrates subject to thermal loading, and (2) simple shear in constrained films. In these problems, earlier discrete dislocation simulations had shown that size effects are born out of layers of dislocations developing near constrained interfaces. These boundary layers depend on slip orientations and applied loading but are insensitive to the film thickness. We investigate stress response to changes in controlled parameters in both problems. Comparisons with previous discrete dislocation simulations are discussed.
We characterize the formulas that are avoided by every $\alpha$-free word for some $\alpha>1$. We study the avoidability index of formulas whose fragments are of the form $XYX$. The largest avoidability index of an avoidable palindrome pattern is known to be at least $4$ and at most $16$. We make progress toward the conjecture that every avoidable palindrome pattern is $4$-avoidable.
We examine a generalized script{PT}-Symmetric quartic anharmonic oscillator model to determine the various physical variables perturbatively in powers of a small quantity {\epsilon}. We make use of the Bender-Dunne operator basis elements and exploit the properties of the totally symmetric operator T_{m,n}.
We consider directed last-passage percolation on the random graph G = (V,E) where V = Z and each edge (i,j), for i < j, is present in E independently with some probability 0 < p <= 1. To every present edge (i,j) we attach i.i.d. random weights v_{i,j} > 0. We are interested in the behaviour of w_{0,n}, which is the maximum weight of all directed paths from 0 to n, as n tends to infinity. We see two very different types of behaviour, depending on whether E[v_{i,j}^2] is finite or infinite. In the case where E[v_{i,j}^2] is finite we show that the process has a certain regenerative structure, and prove a strong law of large numbers and, under an extra assumption, a functional central limit theorem. In the situation where E[v_{i,j}^2] is infinite we obtain scaling laws and asymptotic distributions expressed in terms of a "continuous last-passage percolation" model on [0,1]; these are related to corresponding results for two-dimensional last-passage percolation with heavy-tailed weights obtained by Hambly and Martin.
The nonlinear model of pionic condensate in nuclei by G. Preparata can be efficiently verified by investigation of the quasielastic knockout process of pions out of nuclei by high energy electrons. First, a momentum distribution (MD) of the collective pions has a bright maximum at q=0.3 Gev.Second the excitation spectrum of a recoil nucleus is concentrated at low energies E lesser than 1MeV. The results for the pion knockout from mesonic clouds of individual nucleons are absolutely different. The latter results are presented both for pion and rho-meson clouds localized on nucleons.
In this paper we study a nonlocal diffusion problem on a manifold. These kind of equations can model diffusions when there are long range effects and have been widely studied in Euclidean space.   We first prove existence and uniqueness of solutions and a comparison principle. Then, for a convenient rescaling we prove that the operator under consideration converges to a multiple of the usual Heat-Beltrami operator on the manifold. Next, we look at the long time behavior on compact manifolds by studying the spectral properties of the operator. Finally, for the model case of hyperbolic space we study the long time asymptotics and find a different and interesting behavior.
Specific dark energy models with a linear inhomogeneous time-dependent equation of state, within the framework of 4d Friedman-Robertson-Walker (FRW) cosmology, are investigated. It is demonstrated that such 4d inhomogeneous fluid models may lead to a turbulence FRW cosmology. Both one-component and two-component models from 4d inhomogeneous dark fluid models are considered. In the one-component model the universe may develop from a viscous era with, for instance, a constant bulk viscosity, into a turbulent era. In the two-component model the fluid can be decomposed into two components, one non-turbulent (ideal) and another turbulent part, obeying two different equations of state. Conditions for the appearance of the turbulent dark energy universe in terms of the parameters in the equation of state (EoS) without introducing the turbulence concept explicitly are are obtained. An equivalent description in terms of an inhomogeneous fluid for the viscous Little Rip (LR) cosmology is also developed.
When scale symmetry is combined with chiral symmetry in a scale-chiral Lagrangian, it can be shown in Fermi-liquid fixed point theory that $g_A^{\rm eff}\approx 1$ in finite nuclei {\it as well as} in dense baryonic matter. This is suggested as a signal for emergence of hidden symmetries of QCD in baryonic matter from low to very high density. This calculation throws doubt on the "first principles" explanation of the quenching of $g_A$ in nuclei with two-body meson-exchange currents. It also has relevance to Gamow-Teller matrix elements in neutrinoless double $\beta$ decay.