ShantanuT01/DACTYL-Pretraining huggingface dataset:
Fermion propagator of the Schwinger Model is revisited from the point of view of its infrared behavior. The values of anomalous dimensions are found in arbitrary covariant gauge and in all contributing instanton sectors. In the case of a gauge invariant, but path dependent propagator, the exponential dependence, instead of power law one, is established for the special case when the path is a straight line. The leading behavior is almost identical in any sector, differing only by the slowly varying, algebraic prefactors. The other kind of the gauge invariant function, which is the amplitude of the dressed Dirac fermions, may be reduced, by the appropriate choice of the dressing, to the gauge variant one, if Landau gauge is imposed.
We perform a non-radial adiabatic perturbation analysis on homologous conventional polytropic stellar core collapses. The core collapse features a polytropic exponent $\Gamma=4/3$ relativistic gas under self-gravity of spherical symmetry while three-dimensional perturbations involve an adiabatic exponent $\gamma$ with $\gamma\neq\Gamma$ such that the Brunt-V$\ddot{\rm a}$is$\ddot{\rm a}$l$\ddot{\rm a}$ buoyancy frequency ${\cal N}$ does not vanish. With proper boundary conditions, we derive eigenvalues and eigenfunctions for different modes of oscillations. In reference to stellar oscillations and earlier results, we examine behaviours of different modes and the criterion for instabilities. The acoustic p$-$modes and surface f$-$modes remain stable. For $\gamma<\Gamma$, convective instabilities appear as unstable internal gravity g$^{-}-$modes. For $\gamma>\Gamma$, sufficiently low-order internal gravity g$^{+}-$modes are stable, whereas sufficiently high-order g$^{+}-$modes, which would have been stable in a static star, become unstable during self-similar core collapses. For supernova explosions, physical consequences of such inevitable g$-$mode instabilities are speculated.
The evidence for joint gamma and neutrino emission from the blazar TXS 0506+056 has renewed interest in blazars as neutrino sources. The detection of neutrinos from blazars can be seen as the smoking gun for the presence of relativistic protons in blazar's jets, and can thus help identify blazars, and active galactic nuclei in general, as cosmic-ray accelerators. In this contribution I first introduce blazars and blazar hadronic models, and then present the results of the multi-messenger modeling of both the 2017 gamma-neutrino flare, and the 2014-2015 neutrino-only flare of TXS 0506+056. For the first time it is possible to constrain blazar hadronic models using the information from neutrino detectors, and I discuss the implications of these neutrino observations on our understanding of the physics of relativistic jets from super-massive black-holes.
We prove the approach to equilibrium of quenched isolated quantum systems for which the change in the Hamiltonian brought about by the quench satisfies a certain closed commutator algebra with all the extensive integrals of motion of the system before the quench. The proof is carried out by following the exact unitary evolution of the entropy operator, defined as the negative of the logarithm of the nonequilibrium density matrix, and showing that, under the conditions implied by the assumed algebra, this entropy operator becomes, at infinite times, a linear combination of integrals of motion of the perturbed system. That is, we show how the nonequilibrium density matrix approaches a generalized Gibbs ensemble. The restricted class of systems for which the present results apply turn out to have degenerate spectra in general, as opposed to some generic systems for which a kind of ergodicity is expected, with a nontrivial dynamics believed to find instances in one-dimensional infinite super-integrable systems. Our findings constitute a direct demonstration of how a non-ergodic isolated quantum system may get to statistical equilibrium.
We study Diophantine arithmetic properties of birational divisors in conjunction with concepts that surround $\mathrm{K}$-stability for Fano varieties. There is also an interpretation in terms of the barycentres of Newton-Okounkov bodies. Our main results show how the notion of divisorial instability, in the sense of K. Fujita, implies instances of Vojta's Main Conjecture for Fano varieties. A main tool in the proof of these results is an arithmetic form of Cartan's Second Main Theorem that has been obtained by M. Ru and P. Vojta.
This work is focused in the study of analytic anisotropic solutions to Einstein's field equations, describing spherically symmetric and static configurations by way of the gravitational decoupling through the method of Minimal Geometric Deformation (MGD). For this we apply MGD to Heintzmann's solution obtaining two new analytic and well behaved anisotropic solutions, in which all their parameters such as the effective density, the effective radial and tangential pressure, as well as radial and tangential sound speed, fulfill each of the requirements for the physical acceptability available in the literature.
In the Luttinger model with non-local interaction we investigate, by exact analytical methods, the time evolution of an inhomogeneous state with a localized fermion added to the non interacting ground state. In absence of interaction the averaged density has two peaks moving in opposite directions with constant velocities. If the state is evolved with the interacting Hamiltonian two main effects appear. The first is that the peaks have velocities which are not constant but vary between a minimal and maximal value. The second is that a dynamical `Landau quasi-particle weight' appears in the oscillating part of the averaged density, asymptotically vanishing with time, as consequence of the fact that fermions are not excitations of the interacting Hamiltonian.
We explore the recoverability of gas physical conditions with the Large Velocity Gradient (LVG) model, using the public code RADEX and the molecules HCN and CO. Examining a wide parameter range with a series of models of increasing complexity we use both grid and Monte Carlo Markov Chain (MCMC) methods to recover the input conditions, and quantify the inherent and noise induced uncertainties in the model results. We find that even with the benefit of generous assumptions the LVG models struggle to recover any parameter better than to within half a dex, although we find no evidence of systemic offsets. Examining isotopologue lines we demonstrate that it is always preferable to model the isotopologue abundance ratio as a free parameter, due to large biases introduced in all other parameters when an incorrect ratio is assumed. Finally, we explore the effects of the background radiation temperature on CO and HCN line ratios, with an emphasis on the effect of the CMB at $z>4$, and show that while the effect on the line ratios is minor, the effect on the SLED peak is significant and that the CO$(1-0)$ line luminosity to H$_2$ mass conversion factor ($\alpha_{\rm CO}$) needs to be altered to account for the loss of contrast against the hotter CMB as redshift increases.
A set of Mo/Si periodic multilayers is studied by non destructive analysis methods. The thickness of the Si layers is 5 nm while the thickness of the Mo layers changes from one multilayer to another, from 2 to 4 nm. This enables us to probe the effect of the transition between the amorphous to crystalline state of the Mo layers near the interfaces with Si on the optical performances of the multilayers. This transition results in the variation of the refractive index (density variation) of the Mo layers, as observed by x-ray reflectivity (XRR) at a wavelength of 0.154 nm. Combining x-ray emission spectroscopy and XRR, the parameters (composition, thickness and roughness) of the interfacial layers formed by the interaction between the Mo and Si layers are determined. However, these parameters do not evolve significantly as a function of the Mo thickness. It is observed by diffuse scattering at 1.33 nm that the lateral correlation length of the roughness strongly decreases when the Mo thickness goes from 2 to 3 nm. This is due to the development of Mo crystallites parallel to the multilayer surface.
We classify globally generated vector bundles on $\mathbf{P}^1 \times \mathbf{P}^1 \times \mathbf{P}^1$ with small first Chern class, i.e. $c_1= (a_1, a_2, a_3)$, $a_i \le 2$. Our main method is to investigate the associated smooth curves to globally generated vector bundles via the Hartshorne-Serre correspondence.
We study Markov chains which model genome rearrangements. These models are useful for studying the equilibrium distribution of chromosomal lengths, and are used in methods for estimating genomic distances. The primary Markov chain studied in this paper is the top-swap Markov chain. The top-swap chain is a card-shuffling process with $n$ cards divided over $k$ decks, where the cards are ordered within each deck. A transition consists of choosing a random pair of cards, and if the cards lie in different decks, we cut each deck at the chosen card and exchange the tops of the two decks. We prove precise bounds on the relaxation time (inverse spectral gap) of the top-swap chain. In particular, we prove the relaxation time is $\Theta(n+k)$. This resolves an open question of Durrett.
We prove that Kelly-Ulam conjecture is true for p-disconnected graphs.
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical particle model descriptions exhibiting either Galileian or Lorentzian symmetry. The structures of fundamental importance are the relevant (Lie) groups of symmetries and their homogeneous (and associated) spaces that, in the situations of interest, also possess Hamiltonian structures. Comments are made on the relation between the theory outlined and a recent paper by Carmeli, Cassinelli, Toigo, and Vacchini.
We describe CPMC-Lab, a Matlab program for the constrained-path and phaseless auxiliary-field Monte Carlo methods. These methods have allowed applications ranging from the study of strongly correlated models, such as the Hubbard model, to ab initio calculations in molecules and solids. The present package implements the full ground-state constrained-path Monte Carlo (CPMC) method in Matlab with a graphical interface, using the Hubbard model as an example. The package can perform calculations in finite supercells in any dimensions, under periodic or twist boundary conditions. Importance sampling and all other algorithmic details of a total energy calculation are included and illustrated. This open-source tool allows users to experiment with various model and run parameters and visualize the results. It provides a direct and interactive environment to learn the method and study the code with minimal overhead for setup. Furthermore, the package can be easily generalized for auxiliary-field quantum Monte Carlo (AFQMC) calculations in many other models for correlated electron systems, and can serve as a template for developing a production code for AFQMC total energy calculations in real materials. Several illustrative studies are carried out in one- and two-dimensional lattices on total energy, kinetic energy, potential energy, and charge- and spin-gaps.
We simulate automotion, the spontaneous transport of a magnetic domain wall under the influence of demagnetization and magnetic anisotropy, in nanoscale spintronic interconnects. In contrast to spin transfer driven magnetic domain wall motion, the proposed interconnects operate with only a transient current pulse and provide favorable scaling down to the 20nm scale. Cases of both in-plane and perpendicular magnetization are considered. Analytical dependence of the velocity of domain walls on the angle of magnetization are compared with full micromagnetic simulations. Deceleration, disappearance, and reflection of domain walls are demonstrated. Dependences of the magnetization angle on the current pulse parameters are studied. The energy and delay analysis suggests that automotion is an attractive option for spintronic logic interconnects.
The multiplicity distributions of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the large volume limit. The microscopic correlator method is used to enforce conservation of three charges - baryon number, electric charge, and strangeness - in the canonical ensemble. In addition, in the micro-canonical ensemble energy conservation is included. An analytical method is used to account for resonance decays. The multiplicity distributions and the scaled variances for negatively, positively, and all charged hadrons are calculated along the chemical freeze-out line of central Pb+Pb (Au+Au) collisions from SIS to LHC energies. Predictions obtained within different statistical ensembles are compared with the preliminary NA49 experimental results on central Pb+Pb collisions in the SPS energy range. The measured fluctuations are significantly narrower than the Poisson ones and clearly favor expectations for the micro-canonical ensemble. Thus this is a first observation of the recently predicted suppression of the multiplicity fluctuations in relativistic gases in the thermodynamical limit due to conservation laws.
We study the "stiff pressure limit" of a nonlinear drift-diffusion equation, where the density is constrained to stay below the maximal value one. The challenge lies in the presence of a drift and the consequent lack of monotonicity in time. In the limit a Hele-Shaw-type free boundary problem emerges, which describes the evolution of the congested zone where density equals one. We discuss pointwise convergence of the densities as well as the $BV$ regularity of the limiting free boundary.
Ring diagram analysis is a standard local helioseismic technique. Data from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) are routinely used for Ring-diagram analysis, and fits to the power spectra as well as inversion results are standard data products. In this paper we examine the effects of different tracking rates, noise, and resolution on ring-diagram results. Most of the analysis is for $15^\circ$ tiles, but we also examine the effects of different tile sizes. The largest effect we find is that of resolution. Doppler noise has very little effect on the results, except perhaps at the deepest regions for which the tiles can give reliable results; variations in the tracking rate have a similar effect.
We analyse the sensitivity to physics beyond the SM of T-odd correlations in $K_{\ell 4}$ decays, which do not involve the lepton polarization. We show that a combined analysis of $K^+_{\mu 4}$ and $K^-_{\mu 4}$ decays can lead to new constraints about CP violation in $\Delta S=1$ charged-current interactions, complementary to those obtained from the transverse muon polarization in $K_{\mu 3}$ and of comparable accuracy.
We present an investigation of the lattice dynamics of the charge-density-wave compound 2H-NbSe2. We analyze the precise nature of the wave vector dependent electron-phonon coupling (EPC) and derive the bare dispersion of the charge-density-wave (CDW) soft phonon mode using inelastic x-ray scattering combined with ab-initio calculations. Experimentally, phonon modes along the {\Gamma} - M line, i.e. q = (h, 0, 0) with 0 <= h <= 0.5, with the same longitudinal symmetry ({\Sigma}1) as the CDW soft mode were investigated up to 32 meV. In agreement with our calculations we observe significant EPC in the optic modes at h <= 0.2. We analyze the EPC in the optic as well as acoustic modes and show that the q dependences stem from scattering processes between two bands at the Fermi surface both having Nb 4d character. Finally, we demonstrate that the soft mode dispersion at T = 33 K (= {T_{CDW}}) can be well described on the basis of a strongly q dependent EPC matrix element and an acoustic-like bare phonon dispersion in agreement with observations near room temperature.
The main purpose of this paper is to obtain strong laws of large numbers for arrays or weighted sums of random variables under a scenario of dependence. Namely, for triangular arrays $\{X_{n,k}, \, 1 \leqslant k \leqslant n, \, n \geqslant 1 \}$ of row-wise extended negatively dependent random variables weakly mean dominated by a random variable $X \in \mathscr{L}_{1}$ and sequences $\{b_{n} \}$ of positive constants, conditions are given to ensure $\sum_{k=1}^{n} \left(X_{n,k} - \mathbb{E} \, X_{n,k} \right)/b_{n} \overset{\textnormal{a.s.}}{\longrightarrow} 0$. Our statements also allow us to improve recent results about complete convergence.
Context: The Ophiuchus cluster of galaxies, located at low latitudes in the direction of the Galactic bulge, has been relatively poorly studied in comparison with other rich galaxy clusters like Coma, Virgo and Fornax, in spite of being the 2nd brightest X-ray cluster in the sky. Methods: Deep near-infrared images and photometry from the VISTA Variables in the V\'ia L\'actea eXtended survey (VVVX) were used to detect galaxy member candidates of Ophiuchus cluster up to 2 Mpc from the cD galaxy 2MASX J17122774-2322108 using the Galdeano et al. criteria to select the galaxies among the foreground sources. We also perform a morphological visual classification, color-magnitude diagram and density profiles. Results: We identified 537 candidate galaxy members of the Ophiuchus cluster up to 2 Mpc from the cD galaxy, increasing 7 times the number of galaxies reported in previous catalogs. In addition, we performed a morphological classification of these galaxy candidates finding that the fraction of Ellipticals reaches more than the 60% in the central region of the cluster. On the other hand the Spirals fraction is lower than the 20% remaining almost constant throughout the cluster. Moreover, we study the red sequence of galaxy member candidates and use mock catalogs to explore the density profile of the cluster, finding that the value derived from the mock catalog towards an overdense region is in agreement with the galaxy excess of the central zone of the Ophiuchus cluster. Conclusions: Our investigation of the hidden population of Ophiuchus galaxies underscores the importance of this cluster as a prime target for future photometric and spectroscopic studies. Moreover the results of this work highlights the potential of VVVX survey to study extragalactic objects in the Zone of Avoidance.
It is well known that the dynamics of a quantum system is always non-adiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching. However, we propose here a possible situation where the dynamics of a quantum system in passage across quantum critical regions is adiabatic and the defect density decays exponentially. This is achieved by incorporating additional interactions which lead to quantum critical behavior and gapless phases but do not participate in the time evolution of the system. To illustrate the general argument, we study the defect generation in the quantum critical dynamics of a spin-1/2 anisotropic quantum XY spin chain with three spin interactions and a linearly driven staggered magnetic field.
The electronic properties of quarter-filled organic materials showing spin-Peierls transition are investigated theoretically. By studying the one-dimensional extended Peierls-Hubbard model analytically as well as numerically, we find that there is a competition between two different spin-Peierls states due to the tetramized lattice distortion in the strongly correlated regime. One is accompanied by lattice dimerization which can be interpreted as a spontaneous Mott insulator, while the other shows the existence of charge order of Wigner crystal-type. Results of numerical density matrix renormalization group computations on sufficiently large system sizes show that the latter is stabilized in the ground state when both the on-site and the inter-site Coulomb interactions are large.
An explicit construction of the proton wave function is outlined in the high momentum limit of QCD dominated by a direct $qqq$ force, one generated by hooking the ends of a $ggg$ vertex to 3 distinct ${\bar q}gq$ vertices, thus making up a $Y$-shaped diagram (see fig.1). The high degree of $S_3$ symmetry thus involved ensures that the $qqq$ wave function is a mixture of $56, 0^+$ and $20,1^+$ components, rather than the traditional $56, 0^+$ and $70, 0^+$ type. Some results of this paradigm shift are offered.
Since the Maxwell theory of electromagnetic phenomena is a gauge theory, it is quite important to evaluate the zero-point energy of the quantized electromagnetic field by a careful assignment of boundary conditions on the potential and on the ghost fields. Recent work by the authors has shown that, for a perfectly conducting spherical shell, it is precisely the contribution of longitudinal and normal modes of the potential which enables one to reproduce the result first due to Boyer. This is obtained provided that one works with the Lorenz gauge-averaging functional, and with the help of the Feynman choice for a dimensionless gauge parameter. For arbitrary values of the gauge parameter, however, covariant and non-covariant gauges lead to an entangled system of three eigenvalue equations. Such a problem is crucial both for the foundations and for the applications of quantum field theory.
We computed proper motions of a selected sample of globular clusters projected on the central bulge, employing CCD images gathered along the last 25 years at the ESO-NTT, ESO-Danish and HST telescopes. We presented a method to derive their proper motions, and a set of coordinate transformations to obtain 3D Galactic velocity vectors of the clusters. We analysed 10 globular clusters, namely Terzan 1, Terzan 2, Terzan 4, Terzan 9, NGC 6522, NGC 6558, NGC 6540, AL~3,ESO456--SC38 and Palomar 6. For comparison purposes we also studied the outer bulge cluster NGC 6652. We discuss the general properties of the proper-motion-cleaned Colour-Magnitude Diagrams, derived for the first time for most of them. A general conclusion is that the inner bulge globular clusters have clearly lower transverse motions (and spatial velocities) than halo clusters, and appear to be trapped in the bulge bar.
We report a spectropolarimetric study of the post-AGB binary system 89 Herculis, based on data acquired with the high-resolution Catania Astrophysical Observatory Spectropolarimeter, the HArps-North POlarimeter and the Echelle SpectroPolarimetric Device for the Observation of Stars.   The linear polarization clearly detected across single atmospheric lines in absorption is characterized by complex Q and U morphologies that are variable with the orbital period of the system. Gauss-level magnetic fields, continuum depolarization due to pulsations, hot spots and scattering in the circumstellar environment were excluded as possible origin of the observed polarization.   In the context of the optical pumping mechanism, we suggest that the anisotropy of the stellar radiation field, fuelled by the close binary companion, can be responsible of the observed periodic properties of the spectral line polarization.   We conclude that high resolution linear spectropolarimetry could be an important diagnostic tool in the study of aspherical envelopes of cool and evolved stars.