ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the ground-state properties of the one-dimensional two-band Hubbard model with different bandwidths. The density-matrix renormalization group method is applied to calculate the averaged electron occupancies $n$ as a function of the chemical potential $\mu$. Both at quarter and half fillings, "charge plateaux" appear in the $n$-$\mu$ plot, where $d\mu/dn$ diverges and the Mott insulating states are realized. To see how the orbital polarization in the one-quarter charge plateau develops, we apply the second-order perturbation theory from the strong-coupling limit at quarter filling. The resultant Kugel-Khomskii spin-orbital model includes a $magnetic$ field coupled to orbital pseudo-spins. This field originates from the discrepancy between the two bandwidths and leads to a finite orbital pseudo-spin magnetization.
We present results of a 90 ksec Chandra X-ray observation of the young sigma Orionis cluster (age ~3 Myr) obtained with the High Energy Transmission Grating Spectrometer. We use the high resolution grating spectrum and moderate resolution CCD spectrum of the massive central star sigma Ori AB (O9.5V + B0.5V) to test wind shock theories of X-ray emission and also analyze the high spatial resolution zero-order ACIS-S image of the central cluster region. Chandra detected 42 X-ray sources on the primary CCD (ACIS-S3). All but five have near-IR or optical counterparts and about one-fourth are variable. Notable high-mass stellar detections are sigma Ori AB, the magnetic B star sigma Ori E, and the B5V binary HD 37525. Most of the other detections have properties consistent with lower mass K or M-type stars. We present the first X-ray spectrum of the unusual infrared source IRS1 located 3.3 arc-sec north of sigma Ori AB, which is likely an embedded T Tauri star whose disk/envelope is being photoevaporated by sigma Ori AB. We focus on the radiative wind shock interpretation of the soft luminous X-ray emission from sigma Ori AB, but also consider possible alternatives including magnetically-confined wind shocks and colliding wind shocks. Its emission lines show no significant asymmetries or centroid shifts and are moderately broadened to HWHM ~ 264 km/s, or one-fourth the terminal wind speed. Forbidden lines in He-like ions are formally undetected, implying strong UV suppression. The Mg XI triplet forms in the wind acceleration zone within one stellar radius above the surface. These X-ray properties are consistent in several respects with the predictions of radiative wind shock theory for an optically thin wind, but explaining the narrow line widths presents a challenge to the theory.
Let $\mathcal{S}_{n}$ be the symmetric group on $[n]=\{1, \ldots, n\}$. The $k$-point fixing graph $\mathcal{F}(n,k)$ is defined to be the graph with vertex set $\mathcal{S}_{n}$ and two vertices $g$, $h$ of $\mathcal{F}(n,k)$ are joined if and only if $gh^{-1}$ fixes exactly $k$ points. In this paper, we derive a recurrence formula for the eigenvalues of $\mathcal{F}(n,k)$. Then we apply our result to determine the sign of the eigenvalues of $\mathcal{F}(n,1)$.
Here we present a critical view of practical problems in the analysis of optical Fe II emission lines of Type 1 AGN spectra. Besides the very complex and unclear physical interpretation of the Fe II template shape, there are other issues that might affect the results of Fe II contribution as well (like the S/N, the AGN continuum component modelling, the complex shapes of other broad and narrow emission lines that are blending in the same part of the spectrum, the galactic host stellar component that could lead to mimicking of the Fe II template shape on some parts of spectrum, etc.). In this paper we concentrate particularly on the claims of possibility that in some objects Fe II could be strongly shifted to the red. We examine the effects in the fitting procedure that could artificially lead to such results.
This talk is dedicated to Alberto Sirlin in celebration of his seventieth birthday. I wish to convey my deep appreciation of his many important contributions to particle physics over 40 years and look forward to many more years of productive research.
We give a brief re-exposition of the theory due to Pauli and Sinclair of ramification polygons of Eisenstein polynomials over p-adic fields, their associated residual polynomials and an algorithm to produce all extensions for a given ramification polygon. We supplement this with an algorithm to produce all ramification polygons of a given degree, and hence we can produce all totally ramified extensions of a given degree.
Shimura curves are moduli spaces of abelian surfaces with quaternion multiplication. Models of Shimura curves are very important in number theory. Klein's icosahedral invariants $\mathfrak{A},\mathfrak{B}$ and $\mathfrak{C}$ give the Hilbert modular forms for $\sqrt{5}$ via the period mapping for a family of $K3$ surfaces. Using the period mappings for several families of $K3$ surfaces, we obtain explicit models of Shimura curves with small discriminant in the weighted projective space ${\rm Proj} (\mathbb{C}[\mathfrak{A},\mathfrak{B},\mathfrak{C}])$.
Low dimensional material systems provide a unique set of properties useful for solid-state devices. The building block of these devices is the PN junction. In this work, we present a dramatic difference in the electrostatics of PN junctions in lower dimensional systems, as against the well understood three dimensional systems. Reducing the dimensionality increases the fringing fields and depletion width significantly. We propose a novel method to derive analytic equations in 2D and 1D that considers the impact of neutral regions. The analytical results show an excellent match with both the experimental measurements and numerical simulations. The square root dependence of the depletion width on the ratio of dielectric constant and doping in 3D changes to a linear and exponential dependence for 2D and 1D respectively. This higher sensitivity of 1D PN junctions to its control parameters can be used towards new sensors.
Graphene, a flat monolayer of carbon atoms packed tightly into a two dimensional hexagonal lattice, has unusual electronic properties which have many promising nanoelectronic applications. Recent Low Energy Electron Microscopy (LEEM) experiments show that the step edge velocity of epitaxially grown 2D graphene islands on Ru(0001) varies with the fifth power of the supersaturation of carbon adatoms. This suggests that graphene islands grow by the addition of clusters of five atoms rather than by the usual mechanism of single adatom attachment.   We have carried out Kinetic Monte Carlo (KMC) simulations in order to further investigate the general scenario of epitaxial growth by the attachment of mobile clusters of atoms. We did not seek to directly replicate the Gr/Ru(0001) system but instead considered a model involving mobile tetramers of atoms on a square lattice. Our results show that the energy barrier for tetramer break up and the number of tetramers that must collide in order to nucleate an immobile island are the important parameters for determining whether, as in the Gr/Ru(0001) system, the adatom density at the onset of island nucleation is an increasing function of temperature. A relatively large energy barrier for adatom attachment to islands is required in order for our model to produce an equilibrium adatom density that is a large fraction of the nucleation density. A large energy barrier for tetramer attachment to islands is also needed for the island density to dramatically decrease with increasing temperature. We show that islands grow with a velocity that varies with the fourth power of the supersaturation of adatoms when tetramer attachment is the dominant process for island growth.
A mesoscopic evolution equation for an ensemble of mesoparticles follows after the elimination of internal degrees of freedom. If the system is composed of a hierarchy of scales, the reduction procedure could be worked repeatedly and the characterization of this iterating method is carried out. Namely, a prescription describing a discrete hierarchy of master equations for the density operator is obtained. Decoherence follows from the irreversible coupling of the systems, defined by mesoscopic variables, to internal degrees of freedom. We discuss briefly the existence of systems with the same dynamics laws at different scales. We made an explicit calculation for an ensemble of particles with internal harmonic interaction in an external anharmonic field. New conditions related to the semiclassical limit for mesoscopic systems (Wigner-function) are conjectured.
A theoretical model of the coherent precession of magnetization excited by a picosecond acoustic pulse in a ferromagnetic semiconductor layer of (Ga,Mn)As is developed. The short strain pulse injected into the ferromagnetic layer modifies the magnetocrystalline anisotropy resulting in a tilt of the equilibrium orientation of magnetization and subsequent magnetization precession. We derive a quantitative model of this effect using the Landau-Lifshitz equation for the magnetization that is precessing in the time-dependent effective magnetic field. After developing the general formalism, we then provide a numerical analysis for a certain structure and two typical experimental geometries in which an external magnetic field is applied either along the hard or the easy magnetization axis. As a result we identify three main factors, which determine the precession amplitude: the magnetocrystalline anisotropy of the ferromagnetic layer, its thickness, and the strain pulse parameters.
Emerging dimming occurs in isolated solar active regions (ARs) during the early stages of magnetic flux emergence. Observed by the Atmospheric Imaging Assembly, it features a rapid decrease in extreme-ultraviolet (EUV) emission in the 171 \r{A} channel images, and a simultaneous increase in the 211 \r{A} images. Here, we analyze the coronal thermodynamic and magnetic properties to probe its physical origin. We calculate the time-dependent differential emission measures for a sample of 18 events between 2010 and 2012. The emission measure (EM) decrease in the temperature range $5.7 \le \log_{10}T \le 5.9$ is well correlated with the EM increase in $6.2 \le \log_{10}T \le 6.4$ over eight orders of magnitude. This suggests that the coronal plasma is being heated from the quiet-Sun, sub-MK temperature to 1-2 MK, more typical for ARs. Potential field extrapolation indicates significant change in the local magnetic connectivity: the dimming region is now linked to the newly emerged flux via longer loops. We conclude that emerging dimming is likely caused by coronal heating episodes, powered by reconnection between the emerging and the ambient magnetic fields.
We investigate the quantum tunneling of a Bose-Einstein condensate confined in a optical trap. We show that periodic pulses of coherent matter are emitted from the trap by using an oscillating energy barrier. Moreover, the emitted fraction of condensed atoms strongly increases if the period of oscillation of the height of the energy barrier is in parametric resonance with the period of oscillation of the center of mass of the condensate inside the potential well. Our model is analyzed by numerically solving the nonpolynomial Schrodinger equation (NPSE), an effective one-dimensional equation which describes the macroscopic wavefunction of Bose condensates under transverse harmonic confinement. The range of validity of NPSE is discussed and compared with that of Gross-Pitaevskii equation.
A combinatorial formula is derived which expresses free cumulants in terms of classical comulants. As a corollary, we give a combinatorial interpretation of free cumulants of classical distributions, notably Gaussian and Poisson distributions. The latter count connected pairings and connected set partitions respectively. The proof relies on Moebius inversion on the partition lattice.
The various aspects of antiproton physics are shortly reviewed, and its relevance for the possible discovery of new particles and effects is pointed out. Then a survey of the nucleon-antinucleon interactions is given. In the nucleon-antinucleon annihilations, there is a big amount of experimental data that call for theoretical explanation. Importance of specific spin and isospin channels for our understanding of antiproton physics is stressed.
We study closed string tachyon condensation using the RG flow of the worldsheet theory. In many cases the worldsheet theory enjoys N=2 supersymmetry, which provides analytic control over the flow, due to non-renormalization theorems. Moreover, Mirror symmetry sheds light on the RG flow in such cases.   We discuss the relevant tachyon condensation in the context of both compact and non-compact situations which lead to very different conclusions. Furthermore, the tachyon condensation leads to non-trivial dualities for non-supersymmetric probe theories.
We investigate experimentally and theoretically few-particle effects in the optical spectra of single quantum dots (QDs). Photo-depletion of the QD together with the slow hopping transport of impurity-bound electrons back to the QD are employed to efficiently control the number of electrons present in the QD. By investigating structurally identical QDs, we show that the spectral evolutions observed can be attributed to intrinsic, multi-particle-related effects, as opposed to extrinsic QD-impurity environment-related interactions.   From our theoretical calculations we identify the distinct transitions related to excitons and excitons charged with up to five additional electrons, as well as neutral and charged biexcitons.
This Fifth International WEIN Symposium is devoted to physics beyond the standard model. This talk is about tau lepton physics, but I begin with the question: do we know how to find new physics in the world of elementary particles? This question is interwoven with the various tau physics topics. These topics are: searching for unexpected tau decay modes; searching for additional tau decay mechanisms; radiative tau decays; tau decay modes of the W, B, and D; decay of the Z^0 to tau pairs; searching for CP violation in tau decay; the tau neutrino, dreams and odd ideas in tau physics; and tau research facilities in the next decades.
We propose a new approach to vague convergence of measures based on the general theory of boundedness due to Hu (1966). The article explains how this connects and unifies several frequently used types of vague convergence from the literature. Such an approach allows one to translate already developed results from one type of vague convergence to another. We further analyze the corresponding notion of vague topology and give a new and useful characterization of convergence in distribution of random measures in this topology.
We present a moderately-deep JK photometry for three selected areas of the dwarf irregular galaxy IC1613. The color-magnitude diagrams contain a mixture of red supergiants, asymptotic giant branch stars and the brightest red giant stars. The red supergiants are massive (20 - 25 M_\odot) and young -with ages between 8 and 25 Myr. The most important result is the evidence of the decreasing density of the intermediate age AGB population in the vicinity of the HII regions in the galaxy. We also find age differences between AGB stars in the main body of the galaxy and those near the HII regions in the North-East. The former span a range in ages between 1 and 10 Gyr, while the latter are younger than 1 Gyr. Using the period-luminosity relation derived by Madore & Freedman (1991) and JK magnitudes of the Cepheid variable V20, we calculated (m-M)_K = 24.37+-0.2. The recently discovered Nova (King et al. 1999) was identified in Field III. Its presence of our images and its brightness questioned its classification as a nova.
We study the relationship between the well-known Carleman's condition guaranteeing that a probability distribution is uniquely determined by its moments, and a recent easily checkable condition on the rate of growth of the moments. We use asymptotic methods in theory of integrals and involve properties of the Lambert $W$-function to show that the quadratic rate of growth of the ratios of consecutive moments, as a sufficient condition for uniqueness, is more restrictive than Carleman's condition. We derive a series of statements, one of them showing that Carleman's condition does not imply Hardy's condition, although the inverse implication is true. Related topics are also discussed.
We present in this paper the first near infrared study of the young open cluster NGC 2244, which is well known for its partially embedded nature in the Rosette Nebula. Based on the spatially complete 2 Micron All Sky Survey, the young OB cluster indicates apparent substructures. It is surprisingly resolved into a compact core that matches well the congregation of massive OB stars in the optical, a satellite cluster at a distance of 6.6 pc in its west and probably a major stellar aggregate resembling an arc in structure right below the core. This infrared study provides various new updates on its nature of the young open cluster, including its central position, physical scale and stellar population. A disk fraction of $\sim 20.5\pm2.8%$ is achieved for its members with masses above 0.8 $M_{\odot}$. NGC 2244 is hence a unique example for the study of embedded clusters.
A continuous mass population model with local competition is constructed where every emigrant colonizes an unpopulated island. The population founded by an emigrant is modeled as excursion from zero of an one-dimensional diffusion. With this excursion measure, we construct a process which we call Virgin Island Model. Furthermore, a necessary and sufficient condition for extinction of the total population is obtained for finite initial total mass.
Practical expressions are derived for a rapid and accurate evaluation of electric and thermal conductivities and thermopower of degenerate relativistic electrons along quantizing magnetic fields in outer neutron star crusts. The electron Coulomb scattering on ions is considered in liquid matter, and on high-temperature phonons or charged impurities in solid matter. A semi-quantitative treatment of low-temperature phonons is also proposed. The transport properties are expressed through the energy dependent effective electron relaxation time, which is calculated using the theoretical formalism of the previous work (astro-ph/9603133). Accurate fitting expressions for the relaxation time are obtained, and an efficient energy averaging procedure proposed. A Fortran code, which calculates the longitudinal transport properties of degenerate electrons in strong magnetic fields for any parameters of dense stellar matter of practical interest, is available from the authors upon request.
Suppose we have k matrices of size n by n. We are given an oracle that knows all the entries of k matrices, that is, we can query the oracle an (i,j) entry of the l-th matrix. The goal is to test if each pair of k matrices commute with each other or not with as few queries to the oracle as possible. In order to solve this problem, we use a theorem of Mario Szegedy (quant-ph/0401053) that relates a hitting time of a classical random walk to that of a quantum walk. We also take a look at another method of quantum walk by Andris Ambainis (quant-ph/0311001). We apply both walks into triangle finding problem (quant-ph/0310134) and matrix verification problem (quant-ph/0409035) to compare the powers of the two different walks. We also present Ambainis's method of lower bounding technique (quant-ph/0002066) to obtain a lower bound for this problem. It turns out Szegedy's algorithm can be generalized to solve similar problems. Therefore we use Szegedy's theorem to analyze the problem of matrix set commutativity. We give an O(k^{4/5}n^{9/5}) algorithm as well as a lower bound of Omega(k^{1/2}n). We generalize the technique used in coming up with the upper bound to solve a broader range of similar problems. This is probably the first problem to be studied on the quantum query complexity using quantum walks that involves more than one parameter, here, k and n.
Following Hasse's example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefully examining the analytic class number formula. In this paper we will show how to generalize these results to CM-fields by using class field theory. Although we will only need some special cases, we have also decided to include a few results on Hasse's unit index for CM-fields as well, because it seems that our proofs are more direct than those given by Hasse.
The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theorem for these stratifications in terms of complex tori and convex rational polytopes, generalizing to the quasi-projective case results of Green-Lazarsfeld and Simpson. As an application we show the polynomial periodicity of Hodge numbers of congruence covers in any dimension, generalizing results of E. Hironaka and Sakuma. We extend the structure theorem and polynomial periodicity to the setting of cohomology of unitary local systems. In particular, we obtain a generalization of the polynomial periodicity of Betti numbers of unbranched congruence covers due to Sarnak-Adams. We derive a geometric characterization of finite abelian covers, which recovers the classic one and the one of Pardini. We use this, for example, to prove a conjecture of Libgober about Hodge numbers of abelian covers.
The concept of Hausdorff continuous interval valued functions, developed within the theory of Hausdorff approximations and originaly defined for interval valued functions of one real variable is extended to interval valued functions defined on a topological space X. The main result is that the set of all finite Hausdorff continuous functions on any topological space X is Dedekind order complete. Hence it contains the Dedekind order completion of the set C(X) of all continuous real functions defined on X as well as the Dedekind order completion of the set C_b(X) of all bounded continuous functions on X. Under some general assumptions about the topological space X the Dedekind order completions of both C(X) and C_b(X) are characterised as subsets of the set of all Hausdorff continuous functions. This solves a long outstanding open problem about the Dedekind order completion of C(X). In addition, it has major applications to the regularity of solutions of large classes of nonlinear PDEs.
The intrinsic anomalous Nernst effect in a magnetic material is governed by the Berry curvature at the Fermi energy and can be realized in non-collinear antiferromagnets with vanishing magnetization. Thin films of (001)-oriented Mn$_{3}$NiN have their chiral antiferromagnetic structure located in the (111) plane facilitating the anomalous Nernst effect unusually in two orthogonal in-plane directions. The sign of each component of the anomalous Nernst effect is determined by the local antiferromagnetic domain state. In this work, a temperature gradient is induced in a 50 nm thick Mn$_{3}$NiN two micron-size Hall cross by a focused scanning laser beam, and the spatial distribution of the anomalous Nernst voltage is used to image and identify the octupole macrodomain arrangement. Although the focused laser beam width may span many individual domains, cooling from room temperature through the antiferromagnetic transition temperature in an in-plane magnetic field prepares the domain state producing a checkerboard pattern resulting from the convolution of contributions from each domain. These images together with atomistic and micromagnetic simulations suggest an average macrodomain of the order of $1 {\mu}m^{2}$.