ShantanuT01/DACTYL-Pretraining huggingface dataset:
A polynomial automorphism of $\mathbb{A}^n$ over a field of characteristic zero is called co-tame if, together with the affine subgroup, it generates the entire tame subgroup. We prove some new classes of automorphisms, including $3$-triangular automorphisms, are co-tame. Of particular interest, if $n=3$, we show that the statement "Every $m$-triangular automorphism is either affine or co-tame" is true if and only if $m \leq 3$; this improves upon positive results of Bodnarchuk (for $m \leq 2$, in any dimension $n$) and negative results of the authors (for $m \geq 6$, $n=3$). The main technical tool we introduce is a class of maps we term 'translation degenerate automorphisms'; we show that all of these are co-tame, a result that may be of independent interest in the further study of co-tame automorphisms.
With the recent availability of state-of-the-art heavy-ion stable and radioactive beams, there has been a renew interest in the investigation of nuclear reactions with heavy ions. I first present the role of inelastic and transfer channel couplings in fusion reactions induced by stable heavy ions. Analysis of experimental fusion cross sections by using standard coupled-channel calculations is discussed. The role of multi-neutron transfer is investigated in the fusion process below the Coulomb barrier by analyzing $^{32}$S+$^{90,96}$Zr as benchmark reactions. The enhancement of fusion cross sections for $^{32}$S+$^{96}$Zr is well reproduced at sub-barrier energies by NTFus code calculations including the coupling of the neutron-transfer channels following the Zagrebaev semi-classical model. Similar effects for $^{40}$Ca+$^{90}$Zr and $^{40}$Ca+$^{96}$Zr fusion excitation functions are found. The breakup coupling in both the elastic scattering and in the fusion process induced by weakly bound stable projectiles is also shown to be crucial. In this lecture, full coupled-channel calculations of the fusion excitation functions are performed by using the breakup coupling for the more neutron-rich reaction and for the more weakly bound projectiles. I clearly demonstrate that Continuum-Discretized Coupled-Channel calculations are capable to reproduce the fusion enhancement from the breakup coupling in $^{6}$Li+$^{59}$Co.
We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at $\sigma_{xy} = \pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at $\sigma_{xy} = \pm n(4e^2/h)$ starting from the edges of the band center regime towards the band center with an increasing ac field. Beyond a critical field strength, a Hall plateau with $\sigma_{xy} = 0$ can be realized at the band center, hence restoring fully a conventional integer QHE with particle-hole symmetry. Within a low-energy Hamiltonian for Dirac cones merging, we show a very good agreement with the tight-binding calculations for the Hall plateau transitions. We also obtain the band structure for driven graphene ribbons to provide a further understanding on the appearance of the new Hall plateaus, showing a trivial insulator behavior for the $\sigma_{xy} = 0$ state. In the presence of disorder, we numerically study the disorder-induced destruction of the quantum Hall states in a finite driven sample and find that qualitative features known in the undriven disordered case are maintained.
We investigate the possible accuracy that can be reached by analytical models for the matter density power spectrum and correlation function. Using a realistic description of the power spectrum that combines perturbation theory with a halo model, we study the convergence rate of several perturbative expansion schemes and the impact of nonperturbative effects, as well as the sensitivity to phenomenological halo parameters. We check that the simple reorganization of the standard perturbative expansion, with a Gaussian damping prefactor, provides a well-ordered convergence and a finite correlation function that yields a percent accuracy at the baryon acoustic oscillation peak (as soon as one goes to second order). Lagrangian-space expansions are somewhat more efficient, when truncated at low orders, but may diverge at high orders. We find that whereas the uncertainty on the halo-profile mass-concentration relation is not a strong limitation, the uncertainty on the halo mass function can severely limit the accuracy of theoretical predictions for $P(k)$ (this also applies to the power spectra measured in numerical simulations). The real-space correlation function provides a better separation between perturbative and nonperturbative effects, which are restricted to $x \lesssim 10 h^{-1}$Mpc at all redshifts.
The nonlinear Hall effect has opened the door towards deeper understanding of topological states of matter. It can be observed as the double-frequency Hall voltage response to an ac longitudinal current in the presence of time-reversal symmetry. Disorder plays indispensable roles in various linear Hall effects, such as the localization in the quantized Hall effects and the extrinsic mechanisms of the anomalous, spin, and valley Hall effects. Unlike in the linear Hall effects, disorder enters the nonlinear Hall effect even in the leading order. However, the disorder-induced contribution to the nonlinear Hall effect has not been addressed. Here, we derive the formulas of the nonlinear Hall conductivity in the presence of disorder scattering. We apply the formulas to calculate the nonlinear Hall response of the tilted 2D Dirac model, which is the symmetry-allowed minimal model for the nonlinear Hall effect and can serve as a building block in realistic band structures. More importantly, we construct the general scaling law of the nonlinear Hall effect, which may help in experiments to distinguish disorder-induced contributions to the nonlinear Hall effect. This work will be instructive for exploring unconventional responses upon breaking discrete or crystal symmetries in emergent physical systems and materials.
We present our results on soft gluon resummation in the invariant mass threshold applied to the associated production of a top quark pair with a W boson at the LHC in the Mellin space formalism.
We study the magnetic properties of the two-dimensional anisotropic antiferromagnetic spin-1/2 Heisenberg model with Dzyaloshinskii-Moriya interaction and in-plane frustration included. The method of spin Green functions within the framework of Tyablikov's random-phase-approximation decoupling scheme is used in order to derive expressions for the spin-wave spectrum, sublattice magnetization and transition temperature. Based on these expressions we perform a detailed analysis of the influence of varying values of model parameters on its magnetic properties. The model is also applied to the high-Tc superconducting parent compound La2Cuo4 and our results compared to available experimental data.
The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the framework of the Navier-Stokes-Poisson system with adiabatic exponent $6/5 < \gamma < 4/3$.
We formulate the standard model with an arbitrary number of colors N_c. The cancellation of Witten's global SU(2)_L anomaly requires N_c to be odd, while the cancellation of triangle anomalies determines the consistent N_c-dependent values of the quark charges. In this theory, the width of the neutral pion decay into two photons is not proportional to (N_c)^2. In fact, in the case of a single generation and hence for two quark flavors (N_f = 2), N_c does not appear explicitly in the low-energy effective theory of the standard model. Hence, contrary to common lore, it is impossible to see the number of colors in low-energy experiments with just pions and photons. For N_f > 2, on the other hand, N_c explicitly enters the chiral Lagrangian as the quantized prefactor of the Wess-Zumino-Witten term, but the contribution of this term to photon-pion vertices is completely canceled by the N_c-dependent part of a Goldstone-Wilczek term. However, the width of the eta decay into pi^+ pi^- gamma survives the cancellation and is indeed proportional to (N_c)^2. By detecting the emerging photon, this process thus allows one to literally see N_c for N_f > 2.
We present Atacama Large Millimeter/submillimeter Array (ALMA) line and continuum observations at 1.2mm with ~0.3" resolution that uncover a Keplerian-like disk around the forming O-type star AFGL 4176. The continuum emission from the disk at 1.21 mm (source mm1) has a deconvolved size of 870+/-110 AU x 330+/-300 AU and arises from a structure ~8 M_sun in mass, calculated assuming a dust temperature of 190 K. The first-moment maps, pixel-to-pixel line modeling, assuming local thermodynamic equilibrium (LTE), and position-velocity diagrams of the CH3CN J=13-12 K-line emission all show a velocity gradient along the major axis of the source, coupled with an increase in velocity at small radii, consistent with Keplerian-like rotation. The LTE line modeling shows that where CH3CN J=13-12 is excited, the temperatures in the disk range from ~70 to at least 300 K and that the H2 column density peaks at 2.8x10^24 cm^-2. In addition, we present Atacama Pathfinder Experiment (APEX) 12CO observations which show a large-scale outflow from AFGL 4176 perpendicular to the major axis of mm1, supporting the disk interpretation. Finally, we present a radiative transfer model of a Keplerian disk surrounding an O7 star, with a disk mass and radius of 12 M_sun and 2000 AU, that reproduces the line and continuum data, further supporting our conclusion that our observations have uncovered a Keplerian disk around an O-type star.
In each dimension n >= 2, we construct a class of nonnegative potentials that are homogeneous of order -sigma, chosen from the range 0 < sigma < 2, and for which the perturbed Schrodinger equation does not satisfy global in time Strichartz estimates.
We explore a more general class of soft supersymmetry-breaking masses and interactions than that usually considered, both in general and in the MSSM context, where our results for the one-loop $\beta$-functions correct some errors in the literature. We identify a new class of one-loop finite supersymmetric theories.
Blazars are the established sources of an intense and variable non-thermal radiation extending from radio wavelengths up to HE and VHE gamma-rays. Understanding the spectral evolution of blazars in selected frequency ranges, as well as multi-frequency correlations in various types of blazar sources, is of a primary importance for constraining the blazar physics. Here we present the results of a long-term optical monitoring of a sample of 30 blazars of the BL Lac type. We study the optical color-magnitude correlation patterns emerging in the analyzed sample, and compare the optical properties of the targets with the high-energy gamma-ray and high-frequency radio data. The optical observations were carried out in R and B filters using ATOM telescope. Each object was observed during at least 20 nights in the period 2007-2012. We find significant global color-magnitude correlations in 40 % of the sample. The sources which do not display any clear chromatism often do exhibit bluer-when-brighter (bwb) behavior but only in isolated shorter time intervals. We also discovered spectral state transitions at optical wavelengths in several sources. Finally, we find that the radio, optical, and gamma-ray luminosities of the sources obey almost linear correlations, which seem however induced, at least partly, by the redshift dependance, and may be also affected by non-simultaneousness of the analyzed dataset. We argue that the observed bwb behavior is intrinsic to the jet emission regions, at least for some of the analyzed blazars, rather than resulting from the contamination of the measured flux by the starlight of host galaxies. We also conclude that the significance of color-magnitude scalings does not correlate with the optical color, but instead seems to depend on the source luminosity, in a sense that these are the lowest-luminosity BL Lac objects which display the strongest correlations.
The Eichler-Shimura isomorphism realizes the automorphic representation generated by an automorphic newform in certain cohomology of an arithmetic group. In this short note, we give a cohomological interpretation of the Eichler-Shimura isomorphism as a connection morphism of certain exact sequence of G-modules, for the multiplicative group G of any quaternion algebra over a totally real field.
We carry out a comprehensive investigation comparing the three-dimensional magnetic field restructuring, flare energy release, and the helioseismic response, of two homologous flares, the 2011 September 6 X2.1 (FL1) and September 7 X1.8 (FL2) flares in NOAA AR 11283. In our analysis, (1) a twisted flux rope (FR) collapses onto the surface at a speed of 1.5 km/s after a partial eruption in FL1. The FR then gradually grows to reach a higher altitude and collapses again at 3 km/s after a fuller eruption in FL2. Also, FL2 shows a larger decrease of the flux-weighted centroid separation of opposite magnetic polarities and a greater change of the horizontal field on the surface. These imply a more violent coronal implosion with corresponding more intense surface signatures in FL2. (2) The FR is inclined northward, and together with the ambient fields, it undergoes a southward turning after both events. This agrees with the asymmetric decay of the penumbra observed in the peripheral regions. (3) The amounts of free magnetic energy and nonthermal electron energy released during FL1 are comparable to those of FL2 within the uncertainties of the measurements. (4) No sunquake was detected in FL1; in contrast, FL2 produced two seismic emission sources S1 and S2 both lying in the penumbral regions. Interestingly, S1 and S2 are connected by magnetic loops, and the stronger source S2 has weaker vertical magnetic field. We discuss these results in relation to the implosion process in the low corona and the sunquake generation.
We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically-divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat. We show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size, in the critical region.
This paper is a continuation of an ongoing study of the evolutionary processes affecting cluster galaxies. Both CCD R band and H alpha narrow-band imaging was used to determine photometric parameters (m_(r), r_(24), H alpha flux and equivalent width) and derive star formation rates for 227 CGCG galaxies in 8 low-redshift clusters. The galaxy sample is a subset of CGCG galaxies in an objective prism survey of cluster galaxies for H alpha emission. It is found that detection of emission-line galaxies in the OPS is 85%, 70%, and 50% complete at the mean surface brightness values of 1.25 x 10^(-19), 5.19 x 10^(-20), and 1.76 x 10^(-20) W m^(-2) arcsec^(-2), respectively, measured within the R band isophote of 24 mag arcsec^(-2) for the galaxy. The CCD data, together with matched data from a recent H alpha galaxy survey of UGC galaxies within 3000 km s^(-1), will be used for a comparative study of R band and H alpha surface photometry between cluster and field spirals.
Extraction of spin observables from vector meson photoproduction on a nucleon target is described. Starting from density matrix elements in the vector meson's rest frame, we transform to spin observables in the photon-nucleon c.m. frame.   Several constraints on the transformed density matrix and on the spin observables follow from requiring that the angular distribution and the density matrix be positive definite. A set of constraints that are required in order to extract meaningful spin observables from forthcoming data are enunciated.
We examine problem of existence of stationary random fields with linear regressions and quadratic conditional variances, introduced by Bryc in "Stationary random fields with linear regressions" (Annals of Probability 29, No. 1, 504-519). Distributions of the fields are identified and almost complete description of the possible sets of parameters defining the first two conditional moments is given. This note almost solves Bryc's problem concerning fields undetermined by moments - the only remaining set of parameters for which the existence of Bryc's fields is unclear has Lebesgue measure zero.
The purpose of this work is to characterize the diffuse Galactic polarized synchrotron. We present EE, BB, and EB power spectra estimated cross-correlating Planck and WMAP polarization frequency maps at 23 and 30 GHz, for a set of six sky regions covering from 30% to 94% of the sky. The EE and BB angular power spectra show a steep decay of the spectral amplitude as a function of multipole, approximated by a power law with power indices around -2.9 for both components. The B/E ratio is about 0.22. The EB cross-component is compatible with zero at 1$\sigma$, with upper constraint on the EB/EE ratio of 1.2% at the 2$\sigma$ level. The recovered SED, in the frequency range 23-30 GHz, shows E and B power-law spectral indices compatible between themselves with a value of about -3.
We adopted the procedure of Carney to obtain a metallicity calibration for dwarfs for the RGU-photometry. For this purpose we selected 76 dwarfs of different metallicities from Carney, and Strobel et al., and evaluated their \delta(U-G) ultra-violet excess relative to Hyades by transforming their UBV magnitudes to RGU via metallicity dependent equations of Ak-Gungor. The \delta_{0.6}/\deltaM normalized factors of Sandage transform \delta(U-G) excess at any G-R to \delta=\delta_{1.08}, i.e.: the ultra-violet excess at G-R=1.08 mag, corresponding to B-V = 0.60 mag in the UBV-system. Finally, the (\delta, [Fe/H]) couples were fitted by the equation [Fe/H] = 0.11-2.22d-7.95d^2. This calibration covers the metallicity interval (-2.20, +0.20) dex.
We have used the Parkes Multibeam system and the Sloan Digital Sky Survey (SDSS) to assemble a sample of 195 galaxies selected originally from their HI signature to avoid biases against unevolved or low surface brightness objects. For each source 9 intrinsic properties are measured homogeneously, as well as inclination and an optical spectrum. The sample, which should be almost entirely free of either misidentification or confusion, includes a wide diversity of galaxies ranging from inchoate, low surface brightness dwarfs to giant spirals. Despite this diversity there are 5 clear correlations among their properties. They include a common dynamical mass-to-light ratio within their optical radii, a correlation between surface-brightness and Luminosity and a common HI surface-density. Such correlation should provide strong constrains on models of galaxy formation and evolution.
This is a write-up of my talk at the Conference on algebraic structures in Montreal, July 2003. I try to give a brief informal introduction to the proof of Y. Ruan's conjecture on orbifold cohomology multiplication for symplectic quotient singularities given in V. Ginzburg and D. Kaledin, math.AG/0212279. Version 2: minor changes, added some references.
We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for semi-stable objects on product varieties. The leading quadratic inequality can be viewed as a weak version of Bogomolov's inequality holding in arbitrary characteristics.
A one-dimensional Klein-Gordon problem, which is a physical model for a quantum particle submitted to a potential barrier, is studied numerically : using a variational formulation and a Newmark numerical method, we compute the mean position and standard deviation of the particle as well as their time evolution.
Evidence is provided for a conjecture that, in the continuum limit, the mean of the causal set action of a causal set sprinkled into a globally hyperbolic Lorentzian spacetime, M, of finite volume equals the Einstein Hilbert action of M plus the volume of the co-dimension 2 intersection of the future boundary with the past boundary. We give the heuristic argument for this conjecture and analyse some examples in 2 dimensions and one example in 4 dimensions.
We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we prove that there exists a global weak solution, if the order of the fractional diffusion $\alpha \in (1-c_1, 2]$, where $c_1>0$ is an explicit constant depending on the physical parameters present in the problem (chemosensitivity and strength of logistic damping). Furthermore, in the range $1-c_2<\alpha\leq 2$ with $0<c_2<c_1$, the solution is globally smooth. Let us emphasize that when $\alpha<1$, the diffusion is in the supercritical regime.
The Luttinger model was introduced to illustrate the theory of Tomonaga via an exactly soluble model. It became soon the subject of great interest also on the part of Mathematical Physics and a key to the investigations of the mathematical properties of Condensed Matter Physics. This paper reviews aspects of the above developments relevant for renormalization group methods.
We investigate several definitions of the time-dependent spectral function $A(\omega,t)$ of the Anderson impurity model following a quench and within the time-dependent numerical renormalization group method. In terms of the two-time retarded Green function $G^r(t_1,t_2)$, the definitions differ in the choice of the time variable $t$ with respect to $t_1$ and/or $t_2$. In a previous study [Nghiem {\it et al.} Phys. Rev. Lett. 119, 156601 (2017)], we investigated the spectral function, obtained from the Fourier transform of ${\rm Im}[G^r(t_1,t_2)]$ w.r.t. the time difference $t'=t_1-t_2$, with $t=t_2$. Here, we derivie expressions for the retarded Green function for the choices $t=t_1$ and the average time $t=(t_1+t_2)/2$, within the TDNRG approach. We compare and contrast the resulting $A(\omega,t)$ for the different choices of time reference. Expressions for the lesser, greater and advanced Green functions are also derived within TDNRG for all choices of time reference. The average time lesser Green function $G^<(\omega,t)$ is particularly interesting, as it determines the time-dependent occupied density of states $N(\omega,t)=G^<(\omega,t)/(2\pi i)$, a quantity that determines the photoemission current in time-resolved pump-probe photoemission spectroscopy. We present calculations for $N(\omega,t)$ for the Anderson model following a quench, and discuss the resulting time evolution of the spectral features, such as the Kondo resonance and high-energy peaks. We also discuss the issue of thermalization at long times for $N(\omega,t)$. Finally, we use the results for $N(\omega,t)$ to calculate the time-resolved photoemission current for the Anderson model following a quench (acting as the pump) and study the different behaviors that can be observed for different resolution times of a Gaussian probe pulse.