ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the transition from suppression to enhancement of J/psi mesons produced in ultra-relativistic nuclear collisions in the framework of the statistical hadronization model. The calculations are confronted with the most recent data from the RHIC accelerator. This comparison yields first direct evidence for generation of J/psi mesons at the phase boundary. Based on the success of this approach we make specific predictions for LHC energy.
In this paper we calculate the quark number susceptibility (QNS) of QCD at finite temperature under the rainbow-ladder and Ball-Chiu type truncation schemes of the Dyson-Schwinger approach. It is found that the difference between the result of the rainbow-ladder truncation and that of Ball-Chiu type truncation is small, which shows that the dressing effect of the quark-gluon vertex on the QNS at finite temperature is small. It is also found that at low temperature the quark number susceptibility is nearly zero and it increases sharply when the temperature approaches the chiral phase transition point. A comparison between the result in the present paper with those in the literature is made.
We discuss several topics related to polylogarithms with focus on dilogarithms. The topics are: a generating function with harmonic numbers coming from Ramanujan, extending the dilogarithm to complex numbers beyond the unit disk, and relating polylogarithms to Bernoulli polynomials and to solitons. Several improvements and corrections are made to existing representations.
The Galactic black hole candidate (BHC) 4U~1630-472 has gone through several outbursts (13 to be particular) in the last two and a half decades starting from the RXTE era till date. Like the outbursts of other transient BHCs, the outbursts of this source show variations in duration, peak numbers, highest peak flux, etc. However, unlike any other soft X-ray transients, this source showed outbursts of two types, such as normal and super. The normal outbursts of duration $\sim 100-200$~days are observed quasi periodically at an average recurrence/quiescence period of $\sim 500$~days. The super outbursts of duration $\sim 1.5-2.5$~years contain one or more normal outbursts other than one mega outburst. We make an effort to separate flux contribution of the normal and the mega outbursts from the super outbursts, and tried to understand the nature of evolution of both types (normal and mega) of outbursts, based on the quiescent period prior to the outbursts. Archival data of RXTE/ASM from January 1996 to June 2011, and MAXI/GSC from August 2009 to July 2020 are used for our study. A possible linear relation between the quiescent and outburstsing periods for both types of outbursts are observed. This makes the BHC a special source, and it may contain two companion binaries. Two companions might be responsible for two types of outbursts.
Using transfer-matrix method a correspondence between $2D$ classical spin systems ($2D$ Ising model and six-vertex model) and $1D$ quantum spin systems is considered. We find the transfer matrix in two limits - in a well-known strong-anisotropy limit and a novel strong-interaction limit. In contrast to the usual strong-anisotropy approximation, within the strong-interaction approximation we take into account the non-commutativity of transfer-matrix components. The latter approximation is valid for low temperatures or strong interaction in one spatial dimension. We observe that the Hamiltonian of the corresponding quantum chains contains multispin interactions.
N=2 supersymmetric WZNW models associated with finite-dimensional Manin triples is considered. Physical states in topological phase of these models are computed and them N=2 WZNW representatives are constracted. Ring structure of the physical states is computed.
We consider the semi-linear beam equation on the d dimensional irrational torus with smooth nonlinearity of order n -- 1 with n $\ge$ 3 and d $\ge$ 2. If $\epsilon$ $\ll$ 1 is the size of the initial datum, we prove that the lifespan T$\epsilon$ of solutions is O($\epsilon$ --A(n--2) --) where A $\not\equiv$ A(d, n) = 1 + 3 d--1 when n is even and A = 1 + 3 d--1 + max(4--d d--1 , 0) when n is odd. For instance for d = 2 and n = 3 (quadratic nonlinearity) we obtain T$\epsilon$ = O($\epsilon$ --6 --), much better than O($\epsilon$ --1), the time given by the local existence theory. The irrationality of the torus makes the set of differences between two eigenvalues of $\sqrt$ $\Delta$ 2 + 1 accumulate to zero, facilitating the exchange between the high Fourier modes and complicating the control of the solutions over long times. Our result is obtained by combining a Birkhoff normal form step and a modified energy step.
We construct a universal code for stationary and memoryless classical-quantum channel as a quantum version of the universal coding by Csisz\'{a}r and K\"{o}rner. Our code is constructed by the combination of irreducible representation, the decoder introduced through quantum information spectrum, and the packing lemma.
In the first part of this paper the notion of natural metric on the set of natural numbers is defined. It is such metric that the completion of N is a compact metric space that a probability borel measure exists in order that the sequence {n} is uniformly distributed. A necessary and sufficient condition where a given metric is natural. Later we study the properties of sequences uniformly continuous with respect to given natural metric. Inter alia Theorems 5 and 8 characterise the continuity of distribution function
We propose a general framework to study transformations that drive an underdamped Brownian particle in contact with a thermal bath from an equilibrium state to a new one in an arbitrarily short time. To this end, we make use of a time and space-dependent potential, that plays a dual role: confine the particle, and manipulate the system. In the special case of an isothermal compression or decompression of a harmonically trapped particle, we derive explicit protocols that perform this quick transformation, following an inverse engineering method. We focus on the properties of these protocols, which crucially depend on two key dimensionless numbers that characterize the relative values of the three timescales of the problem, associated with friction, oscillations in the confinement and duration of the protocol. In particular, we show that our protocols encompass the known overdamped version of this problem and extend it to any friction for decompression and to a large range of frictions for compression.
Supersonic turbulence generates distributions of shock waves. Here, we analyse the shock waves in three-dimensional numerical simulations of uniformly driven supersonic turbulence, with and without magnetohydrodynamics and self-gravity. We can identify the nature of the turbulence by measuring the distribution of the shock strengths.   We find that uniformly driven turbulence possesses a power law distribution of fast shocks with the number of shocks inversely proportional to the square root of the shock jump speed. A tail of high speed shocks steeper than Gaussian results from the random superposition of driving waves which decay rapidly. The energy is dissipated by a small range of fast shocks. These results contrast with the exponential distribution and slow shock dissipation associated with decaying turbulence.   A strong magnetic field enhances the shock number transverse to the field direction at the expense of parallel shocks. A simulation with self-gravity demonstrates the development of a number of highly dissipative accretion shocks. Finally, we examine the dynamics to demonstrate how the power-law behaviour arises.
We present a detailed comparison of the substructure properties of a single Milky Way sized dark matter halo from the Aquarius suite at five different resolutions, as identified by a variety of different (sub-)halo finders for simulations of cosmic structure formation. These finders span a wide range of techniques and methodologies to extract and quantify substructures within a larger non-homogeneous background density (e.g. a host halo). This includes real-space, phase-space, velocity-space and time- space based finders, as well as finders employing a Voronoi tessellation, friends-of-friends techniques, or refined meshes as the starting point for locating substructure.A common post-processing pipeline was used to uniformly analyse the particle lists provided by each finder. We extract quantitative and comparable measures for the subhaloes, primarily focusing on mass and the peak of the rotation curve for this particular study. We find that all of the finders agree extremely well on the presence and location of substructure and even for properties relating to the inner part part of the subhalo (e.g. the maximum value of the rotation curve). For properties that rely on particles near the outer edge of the subhalo the agreement is at around the 20 per cent level. We find that basic properties (mass, maximum circular velocity) of a subhalo can be reliably recovered if the subhalo contains more than 100 particles although its presence can be reliably inferred for a lower particle number limit of 20. We finally note that the logarithmic slope of the subhalo cumulative number count is remarkably consistent and <1 for all the finders that reached high resolution. If correct, this would indicate that the larger and more massive, respectively, substructures are the most dynamically interesting and that higher levels of the (sub-)subhalo hierarchy become progressively less important.
Similarity-preserving hashing is a widely-used method for nearest neighbour search in large-scale image retrieval tasks. There has been considerable research on generating efficient image representation via the deep-network-based hashing methods. However, the issue of efficient searching in the deep representation space remains largely unsolved. To this end, we propose a simple yet efficient deep-network-based multi-index hashing method for simultaneously learning the powerful image representation and the efficient searching. To achieve these two goals, we introduce the multi-index hashing (MIH) mechanism into the proposed deep architecture, which divides the binary codes into multiple substrings. Due to the non-uniformly distributed codes will result in inefficiency searching, we add the two balanced constraints at feature-level and instance-level, respectively. Extensive evaluations on several benchmark image retrieval datasets show that the learned balanced binary codes bring dramatic speedups and achieve comparable performance over the existing baselines.
We report a determination of the complex in-plane dielectric function of monolayers of four transition metal dichalcogenides: MoS2, MoSe2, WS2 and WSe2, for photon energies from 1.5 - 3 eV. The results were obtained from reflection spectra using a Kramers-Kronig constrained variational analysis. From the dielectric functions, we obtain the absolute absorbance of the monolayers. We also provide a comparison of the dielectric function for the monolayers with the corresponding bulk materials.
We develop a general method to "self-calibrate" observations of galaxy clustering with respect to systematics associated with photometric calibration errors. We first point out the danger posed by the multiplicative effect of calibration errors, where large-angle error propagates to small scales and may be significant even if the large-scale information is cleaned or not used in the cosmological analysis. We then propose a method to measure the arbitrary large-scale calibration errors and use these measurements to correct the small-scale (high-multipole) power which is most useful for constraining the majority of cosmological parameters. We demonstrate the effectiveness of our approach on synthetic examples and briefly discuss how it may be applied to real data.
Let C be a smooth curve, and M_r(C) the coarse moduli space of vector bundles of rank r and trivial determinant on C. We examine the generalized Verschiebung map V_r: M_r(C^(p)) --> M_r(C) induced by pulling back under Frobenius. Our main result is a computation of the degree of V_2 for a general C of genus 2, in characteristic p>2. We also give several general background results on the Verschiebung in an appendix.
We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the c-random walks. Such walks are used, e.g., in population genetics. The number variance problem consists in investigating if the variance of the number of "particles" N_n(L) lying in the ball of radius L at a given time n remains bounded, or even better, converges to a finite limit, as $L\to \infty$. We give a necessary and sufficient condition and discuss its relationship to transience/recurrence property of the walk. Next we consider normalized fluctuations of N_n(L) around the mean as $n\to \infty$ and L is increased in an appropriate way. We prove convergence of finite dimensional distributions to a Gaussian process whose properties are discussed. As the c-random walks mimic symmetric stable processes on R, we compare our results to those obtained by Hambly and Jones (2007,2009), where the number variance problem for an infinite system of symmetric stable processes on R was studied. Since the hierarchical group is an ultrametric space, corresponding results for symmetric stable processes and hierarchical random walks may be analogous or quite different, as has been observed in other contexts. An example of a difference in the present context is that for the stable processes a fluctuation limit process is a centered Gaussian process which is not Markovian and has long range dependent stationary increments, but the counterpart for hierarchical random walks is Markovian, and in a special case it has independent increments.
We investigate the dependence of the galaxy properties on cosmic web environments using the most up-to-date hydrodynamic simulation: Evolution and Assembly of Galaxies and their Environments (EAGLE). The baryon fractions in haloes and the amplitudes of the galaxy luminosity function decrease going from knots to filaments to sheets to voids. Interestingly, the value of L$^*$ varies dramatically in different cosmic web environments. At z = 0, we find a characteristic halo mass of $10^{12} h^{-1}\rm M_{\odot}$, below which the stellar-to-halo mass ratio is higher in knots while above which it reverses. This particular halo mass corresponds to a characteristic stellar mass of $1.8\times 10^{10} h^{-1}\rm M_{\odot}$. Below the characteristic stellar mass central galaxies have redder colors, lower sSFRs and higher metallicities in knots than those in filaments, sheets and voids, while above this characteristic stellar mass, the cosmic web environmental dependences either reverse or vanish. Such dependences can be attributed to the fact that the active galaxy fraction decreases along voids, sheets, filaments and knots. The cosmic web dependences get weaker towards higher redshifts for most of the explored galaxy properties and scaling relations, except for the gas metallicity vs. stellar mass relation.
Let $\mathfrak{S}_n$ and $\mathfrak{B}_n$ denote the respective sets of ordinary and bigrassmannian (BG) permutations of order $n$, and let $(\mathfrak{S}_n,\leq)$ denote the Bruhat ordering permutation poset. We study the restricted poset $(\mathfrak{B}_n,\leq)$, first providing a simple criterion for comparability. This criterion is used to show that that the poset is connected, to enumerate the saturated chains between elements, and to enumerate the number of maximal elements below $r$ fixed elements. It also quickly produces formulas for $\beta(\omega)$ ($\alpha(\omega)$ respectively), the number of BG permutations weakly below (weakly above respectively) a fixed $\omega\in\mathfrak{B}_n$, and is used to compute the M\"obius function on any interval in $\mathfrak{B}_n$.   We then turn to a probabilistic study of $\beta=\beta(\omega)$ ($\alpha=\alpha(\omega)$ respectively) for the uniformly random $\omega\in\mathfrak{B}_n$. We show that $\alpha$ and $\beta$ are equidistributed, and that $\beta$ is of the same order as its expectation with high probability, but fails to concentrate about its mean. This latter fact derives from the limiting distribution of $\beta/n^3$.   We also compute the probability that randomly chosen BG permutations form a 2- or 3-element multichain.
We obtain, by a direct computation, explicit descriptions of all principally polarized semi-abelic varieties of torus rank up to 3. We describe the geometry of their symmetric theta divisors and obtain explicit formulas for the involution and its fixed points. These results allow us to give a new proof of the statements about the dimensions, for small genus, of the loci of ppav with theta divisor containing two-torsion points of multiplicity three. We also prove a result about the closure of this set. Our computations used in our work arXiv:1103.1857 to compute the class of the closure of the locus of intermediate jacobians of cubic threefolds in the Chow ring of the perfect cone compactification of the moduli space of principally polarized abelian fivefolds.
There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations.
The scaling dimensions of large operators in N=4 supersymmetric Yang-Mills theory are dual to energies of semiclassical strings in AdS(5)xS(5). At one loop, the dimensions of large operators can be computed with the help of Bethe ansatz and can be directly compared to the string energies. We study finite-size corrections for Bethe states which should describe quantum corrections to energies of extended semiclassical strings.
Recent studies of core-level X-ray photoelectron spectroscopy (XPS) spectra of silicene on ZrB$_2$(0001) were found to be inconsistent with the density of states (DOS) of a planar-like structure that has been proposed as the ground state by density functional theory (DFT). To resolve the discrepancy, a reexamination of the XPS spectra and direct theoretical access of accurate single-particle excitation energies are desired. By analyzing the XPS data using symmetric Voigt functions, different binding energies and its sequence of Si $2p$ orbitals can be assigned from previously reported ones where asymmetric pseudo-Voigt functions are adopted. Theoretically, we have adopted an approach developed very recently, which follows the sophisticated $\Delta$ self-consistent field ($\Delta$SCF) methods, to study the single-particle excitation of core states. In the calculations, each single-particle energy and the renormalized core-hole charge density are calculated straightforwardly via two SCF calculations. By comparing the results, the theoretical core-level absolute binding energies including the splitting due to spin-orbit coupling are in good agreement with the observed high-resolution XPS spectra. The good agreement not only resolves the puzzling discrepancy between experiment and theory (DOS) but also advocates the success of DFT in describing many-body interactions of electrons at the surface.
In 2016, in the work related to Galois representations, Greenberg conjectured the existence of multi-quadratic $p$-rational number fields of degree $2^{t}$ for any odd prime number $p$ and any integer $t \geq 1$. Using the criteria provided by him to check $p$-rationality for abelian number fields, certain infinite families of quadratic, biquadratic and triquadratic $p$-rational fields have been shown to exist in recent years. In this article, for any integer $k \geq 1$, we build upon the existing work and prove the existence of infinitely many prime numbers $p$ for which the imaginary quadratic fields $\mathbb{Q}(\sqrt{-(p - 1)}),\ldots,\mathbb{Q}(\sqrt{-(p - k)})$ and $\mathbb{Q}(\sqrt{-p(p - 1)}),\ldots, \mathbb{Q}(\sqrt{-p(p - k)})$ are all $p$-rational. This can be construed as analogous results in the spirit of Iizuka's conjecture on the divisibility of class numbers of consecutive quadratic fields. We also address a similar question of $p$-rationality for two consecutive real quadratic fields by proving the existence of infinitely many $p$-rational fields of the form $\mathbb{Q}(\sqrt{p^{2} + 1})$ and $\mathbb{Q}(\sqrt{p^{2} + 2})$. The result for imaginary quadratic fields is accomplished by producing infinitely many primes for which the corresponding consecutive discriminants have large square divisors and the same for real quadratic fields is proven using a result of Heath-Brown on the density of square-free values of polynomials at prime arguments.
We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density of states becomes infinite, for the value of the magnetic field equal to the inverse of the noncommutativity parameter. The Landau problem on the noncommutative two-sphere is also solved and compared to the plane problem.
Exoplanet transit and Doppler surveys discover many binary stars during their operation that can be used to conduct a variety of ancillary science. Specifically, eclipsing binary stars can be used to study the stellar mass-radius relationship and to test predictions of theoretical stellar evolution models. By cross-referencing 24 binary stars found in the MARVELS Pilot Project with SuperWASP photometry, we find two new eclipsing binaries, TYC 0272-00458-1 and TYC 1422-01328-1, which we use as case studies to develop a general approach to eclipsing binaries in survey data. TYC 0272-00458-1 is a single-lined spectroscopic binary for which we calculate a mass of the secondary and radii for both components using reasonable constraints on the primary mass through several different techniques. For a primary mass of M_1 = 0.92 +/- 0.1 M_solar, we find M_2 = 0.610 +/- 0.036 M_solar, R_1 = 0.932 +/- 0.076 R_solar and R_2 = 0.559 +/- 0.102 R_solar, and find that both stars have masses and radii consistent with model predictions. TYC 1422-01328-1 is a triple-component system for which we can directly measure the masses and radii of the eclipsing pair. We find that the eclipsing pair consists of an evolved primary star (M_1 = 1.163 +/- 0.034 M_solar, R_1 = 2.063 +/- 0.058 R_solar) and a G-type dwarf secondary (M_2 = 0.905 +/- 0.067 M_solar, R_2 = 0.887 +/- 0.037 R_solar). We provide the framework necessary to apply this analysis to much larger datasets.
The ad\`eles of a scheme have local components - these are topological higher local fields. The topology plays a large role since Yekutieli showed in 1992 that there can be an abundance of inequivalent topologies on a higher local field and no canonical way to pick one. Using the datum of a topology, one can isolate a special class of continuous endomorphisms. Quite differently, one can bypass topology entirely and single out special endomorphisms (global Beilinson-Tate operators) from the geometry of the scheme. Yekutieli's "Conjecture 0.12" proposes that these two notions agree. We prove this.