ShantanuT01/DACTYL-Pretraining huggingface dataset:
For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltoninan of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization of the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach.
The significance of zero modes in the path-integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in (1+2) dimensions is studied, and with a BRST invariant gauge fixing a well defined transition amplitude is obtained in the one loop approximation. We also present an alternative method which does not necessitate evoking the time-dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the non-linear field equations. The considerations given here are particularly useful in - but also limited to - the one-loop approximation.
The recent discovery of a light CP-even Higgs in a region of masses consistent with the predictions of models with low energy supersymmetry have intensified the discussion of naturalness in these situations. The focus point solution alleviates the MSSM fine tuning problem. In a previous work, we showed the general form of the MSSM focus point solution, for different values of the messenger scale and of the ratio of gaugino and scalar masses. Here we study the possibility of inducing a light stop as a result of the renormalization group running from high energies. This scenario is highly predictive and leads to observables that may be constrained by future collider and flavor physics data.
Analysis of all-sky Planck submillimetre observations and the IRAS 100um data has led to the detection of a population of Galactic cold clumps. The clumps can be used to study star formation and dust properties in a wide range of Galactic environments. Our aim is to measure dust spectral energy distribution (SED) variations as a function of the spatial scale and the wavelength. We examine the SEDs at large scales using IRAS, Planck, and Herschel data. At smaller scales, we compare with JCMT/SCUBA-2 850um maps with Herschel data that are filtered using the SCUBA-2 pipeline. Clumps are extracted using the Fellwalker method and their spectra are modelled as modified blackbody functions. According to IRAS and Planck data, most fields have dust colour temperatures T_C ~ 14-18K and opacity spectral index values of beta=1.5-1.9. The clumps/cores identified in SCUBA-2 maps have T~ 13K and similar beta values. There are some indications of the dust emission spectrum becoming flatter at wavelengths longer than 500um. In fits involving Planck data, the significance is limited by the uncertainty of the corrections for CO line contamination. The fits to the SPIRE data give a median beta value slightly above 1.8. In the joint SPIRE and SCUBA-2 850um fits the value decreases to beta ~1.6. Most of the observed T-beta anticorrelation can be explained by noise. The typical submillimetre opacity spectral index beta of cold clumps is found to be ~1.7. This is above the values of diffuse clouds but lower than in some previous studies of dense clumps. There is only tentative evidence of T-beta anticorrelation and beta decreasing at millimetre wavelengths.
A new approach to the analysis of soft and semihard hadron processes is suggested. In the frame of the Quark-Gluon String Model the interaction of valence quarks and diquarks and sea quarks (antiquarks) of colliding hadrons is taken into account. This one is calculated as the exchange by one nonpertubative gluon, i.e., the cut-off parameter in the gluonic propagator is included. This one allows us to analise the inclusive hadron spectra in hadron collisions at transverse momenta up to 3-4 Gev/c.
We explore the phase diagram for an $SU(N)$ gauge theory in $2 + 1$ dimensions with three families of fermions with different masses, all in the fundamental representation. The phase diagram is three dimensional and contains cuboid, planar and linear quantum regions, depending on the values of the fermionic masses. Among other checks, we consider the consistency with boson/fermion dualities and verify the reduction of the phase diagram to the one and two-family diagrams.
It is well known that within self-consistent Random Phase Approximation (RPA) on top of Hartree-Fock (HF), the translational symmetry should be restored. Due to approximations at the level of the practical implementation, this restoration may be only partial. As a result, one has spurious contributions in the physical quantities that are extracted from RPA. While there are several recipes in the literature to overcome this drawback in order to produce transition densites or strength functions that are free from spurious contamination, there is no formalism associated with the full RPA response function. We present such formalism in this paper. Our goal is to avoid spurious contamination when the response function is used in many-body frameworks like the particle-vibration coupling theory.
This paper is concerned with the sharp interface limit for the Allen-Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain $\Omega\subset\mathbb{R}^2$. We assume that a diffuse interface already has developed and that it is in contact with the boundary $\partial\Omega$. The boundary condition is designed in such a way that the limit problem is given by the mean curvature flow with constant $\alpha$-contact angle. For $\alpha$ close to $90${\deg} we prove a local in time convergence result for well-prepared initial data for times when a smooth solution to the limit problem exists. Based on the latter we construct a suitable curvilinear coordinate system and carry out a rigorous asymptotic expansion for the Allen-Cahn equation with the nonlinear Robin boundary condition. Moreover, we show a spectral estimate for the corresponding linearized Allen-Cahn operator and with its aid we derive strong norm estimates for the difference of the exact and approximate solutions using a Gronwall-type argument.
We conduct 24.4~fps optical observations of repeating Fast Radio Burst (FRB) 20190520B using Tomo-e Gozen, a high-speed CMOS camera mounted on the Kiso 105-cm Schmidt telescope, simultaneously with radio observations carried out using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). We succeeded in the simultaneous optical observations of 11 radio bursts that FAST detected. However, no corresponding optical emission was found. The optical fluence limits as deep as 0.068 Jy ms are obtained for the individual bursts (0.029 Jy ms on the stacked data) corrected for the dust extinction in the Milky Way. The fluence limit is deeper than those obtained in the previous simultaneous observations for an optical emission with a duration $\gtrsim 0.1$ ms. Although the current limits on radio--optical spectral energy distribution (SED) of FRBs are not constraining, we show that SED models based on observed SEDs of radio variable objects such as optically detected pulsars, and a part of parameter spaces of theoretical models in which FRB optical emission is produced by inverse-Compton scattering in a pulsar magnetosphere or a strike of a magnetar blastwave into a hot wind bubble, can be ruled out once a similar fluence limit as in our observation is obtained for a bright FRB with a radio fluence $\gtrsim 5$ Jy ms.
Let $W_{\infty}(\beta)$ be the limit of the Biggins martingale $W_n(\beta)$ associated to a supercritical branching random walk with mean number of offspring $m$. We prove a functional central limit theorem stating that as $n\to\infty$ the process $$ D_n(u):= m^{\frac 12 n} \left(W_{\infty}\left(\frac{u}{\sqrt n}\right) - W_{n}\left(\frac{u}{\sqrt n}\right) \right) $$ converges weakly, on a suitable space of analytic functions, to a Gaussian random analytic function with random variance. Using this result we prove central limit theorems for the total path length of random trees. In the setting of binary search trees, we recover a recent result of R. Neininger [Refined Quicksort Asymptotics, Rand. Struct. and Alg., to appear], but we also prove a similar theorem for uniform random recursive trees. Moreover, we replace weak convergence in Neininger's theorem by the almost sure weak (a.s.w.) convergence of probability transition kernels. In the case of binary search trees, our result states that $$ L\left\{\sqrt{\frac{n}{2\log n}} \left(EPL_{\infty} - \frac{EPL_n-2n\log n}{n}\right)\Bigg | G_{n}\right\} \to \{\omega\mapsto N_{0,1}\}, \quad \text{a.s.w.},$$ where $EPL_n$ is the external path length of a binary search tree $X_n$ with $n$ vertices, $EPL_{\infty}$ is the limit of the R\'egnier martingale, and $L(\,\cdot\, |G_n)$ denotes the conditional distribution w.r.t. the $\sigma$-algebra $G_n$ generated by $X_1,\ldots,X_n$. A.s.w. convergence is stronger than weak and even stable convergence. We prove several basic properties of the a.s.w. convergence and study a number of further examples in which the a.s.w. convergence appears naturally. These include the classical central limit theorem for Galton-Watson processes and the P\'olya urn.
The growth history of large-scale structure in the Universe is a powerful probe of the cosmological model, including the nature of dark energy. We study the growth rate of cosmic structure to redshift $z = 0.9$ using more than $162{,}000$ galaxy redshifts from the WiggleZ Dark Energy Survey. We divide the data into four redshift slices with effective redshifts $z = [0.2,0.4,0.6,0.76]$ and in each of the samples measure and model the 2-point galaxy correlation function in parallel and transverse directions to the line-of-sight. After simultaneously fitting for the galaxy bias factor we recover values for the cosmic growth rate which are consistent with our assumed $\Lambda$CDM input cosmological model, with an accuracy of around 20% in each redshift slice. We investigate the sensitivity of our results to the details of the assumed model and the range of physical scales fitted, making close comparison with a set of N-body simulations for calibration. Our measurements are consistent with an independent power-spectrum analysis of a similar dataset, demonstrating that the results are not driven by systematic errors. We determine the pairwise velocity dispersion of the sample in a non-parametric manner, showing that it systematically increases with decreasing redshift, and investigate the Alcock-Paczynski effects of changing the assumed fiducial model on the results. Our techniques should prove useful for current and future galaxy surveys mapping the growth rate of structure using the 2-dimensional correlation function.
We introduce layered controllable video generation, where we, without any supervision, decompose the initial frame of a video into foreground and background layers, with which the user can control the video generation process by simply manipulating the foreground mask. The key challenges are the unsupervised foreground-background separation, which is ambiguous, and ability to anticipate user manipulations with access to only raw video sequences. We address these challenges by proposing a two-stage learning procedure. In the first stage, with the rich set of losses and dynamic foreground size prior, we learn how to separate the frame into foreground and background layers and, conditioned on these layers, how to generate the next frame using VQ-VAE generator. In the second stage, we fine-tune this network to anticipate edits to the mask, by fitting (parameterized) control to the mask from future frame. We demonstrate the effectiveness of this learning and the more granular control mechanism, while illustrating state-of-the-art performance on two benchmark datasets. We provide a video abstract as well as some video results on https://gabriel-huang.github.io/layered_controllable_video_generation
The isocyanic acid (HNCO) presents an extended distribution in the centers of the Milky Way and the spiral galaxy IC342. Based on the morphology of the emission and the HNCO abundance with respect to H2, several authors made the hypothesis that HNCO could be a good tracer of interstellar shocks. Here we test this hypothesis by observing a well-known Galactic source where the chemistry is dominated by shocks. We have observed several transitions of HNCO towards L1157-mm and two positions (B1 and B2) in the blue lobe of the molecular outflow. The HNCO line profiles exhibit the same characteristics of other well-known shock tracers like CH3OH, H2CO, SO or SO2. HNCO, together with SO2 and OCS, are the only three molecules detected so far whose emission is much more intense in B2 than in B1, making these species valuable probes of chemical differences along the outflow. The HNCO abundance with respect to H2 is 0.4-1.8 10^-8 in B1 and 0.3-1 10^-7 in B2. These abundances are the highest ever measured, and imply an increment with respect to L1157-mm of a factor up to 83, demonstrating that this molecule is actually a good shock tracer. Our results probe that shocks can actually produce the HNCO abundance measured in galactic nuclei and even higher ones. We propose that the gas phase abundance of HNCO is due both to grain mantles erosion by the shock waves and by neutral-neutral reactions in gas phase involving CN and O2. The observed anticorrelation of CN and HNCO fluxes supports this scenario. The observed similarities of the HNCO emission and the sulfured molecules may arise due to formation pathways involving also O2.
Electronic and magnetic structures of the newly synthesized cobalt oxyselenide La2Co2Se2O3 (structurally similar to the superconducting iron pnictides) are studied through density functional calculations. The obtained results show that this material is a Mott insulator, and that it has a very stable Co2+ high-spin ground state with a t2g-like orbital ordering, which is substantiated by the calculated crystal-field excitation energies. The square lattice of the Co2+ spins is found to have a strong antiferro (a weak ferro) magnetic coupling for the second nearest neighbors (2nn) via O (Se2) and an intermediate antiferro one for the 1nn, with the strength ratio about 10:1:3. The present results account for the available experimental data of magnetism, and the prediction of a planar frustrated (2x2) antiferromagnetic structure would motivate a new experiment.
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the anisotropy factor. The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star. Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astrophysical objects like neutron stars.
The orientation of the disk of material accreting onto supermassive black holes that power quasars is one of most important quantities that are needed to understand quasars -- both individually and in the ensemble average. We present a hypothesis for determining comparatively edge-on orientation in a subset of quasars (both radio loud and radio quiet). If confirmed, this orientation indicator could be applicable to individual quasars without reference to radio or X-ray data and could identify some 10-20% of quasars as being more edge-on than average, based only on moderate resolution and signal-to-noise spectroscopy covering the CIV 1549A emission feature. We present a test of said hypothesis using X-ray observations and identify additional data that are needed to confirm this hypothesis and calibrate the metric.
In this note we present some of the most basic aspects of the fractional Laplacean with a self-contained and purely didactic intent, and with a somewhat different slant from the several excellent existing references. Given the interest that nonlocal operators have generated since the 2007 extension paper of Caffarelli and Silvestre, we feel it is appropriate offering to young researchers a quick additional guide to the subject which, we hope, will nicely complement the existing ones.
Suppose that $C\subset\mathbb P^2$ is a general enough nodal plane curve of degree $>2$, $\nu\colon \hat C\to C$ is its normalization, and $\pi\colon \hat C\to\mathbb P^1$ is a finite morphism simply ramified over the same set of points as a projection $\mathrm{pr}_p\circ \nu\colon\hat C \to\mathbb P^1$, where $p\in\mathbb P^2\setminus C$ (if $\mathrm{deg}\, C=3$, one should assume in addition that $\deg\pi\ne4$). We prove that the morphism $\pi$ is equivalent to such a projection if and only if it extends to a finite morphism $X\to(\mathbb P^2)^*$ ramified over $C^*$, where $X$ is a smooth surface.   As a by-product, we prove the Chisini conjecture for mappings ramified over duals to general nodal curves of any degree $\ge3$ except for duals to smooth cubics; this strengthens one of Victor Kulikov's results.
Ferroic magnetic quadrupole order exhibiting macroscopic magnetoelectric activity is discovered in the novel compound $A$(TiO)Cu$_4$(PO$_4$)$_4$ with $A$ = Pb, which is in contrast with antiferroic quadrupole order observed in the isostructural compounds with $A$ = Ba and Sr. Unlike the famous lone-pair stereochemical activity which often triggers ferroelectricity as in PbTiO$_3$, the Pb$^{2+}$ cation in Pb(TiO)Cu$_4$(PO$_4$)$_4$ is stereochemically inactive but dramatically alters specific magnetic interactions and consequently switches the quadrupole order from antiferroic to ferroic. Our first-principles calculations uncover a positive correlation between the degree of $A$-O bond covalency and a stability of the ferroic quadrupole order.
We place limits on semiclassical fluctuations that might be present in the primordial perturbation spectrum. These can arise if some signatures of pre-inflationary features survive the expansion, or could be created by whatever mechanism ends inflation. We study two possible models for such remnant fluctuations, both of which break the isotropy of CMB on large scales. We first consider a semiclassical fluctuation in one Fourier mode of primordial perturbations. The second scenario we analyze is a semiclassical Gaussian bump somewhere in space. These models are tested with the seven-year WMAP data using a Markov Chain Monte Carlo Bayesian analysis, and we place limits on these fluctuations. The upper bound for the amplitude of a fluctuation in a single Fourier mode is a<=10^(-4), while for the Gaussian bump a<=10^(-3).
A field-theoretic approach is applied to describe behavior of homogeneous three-dimensional systems with long-range interactions defined by two order parameters at bicritical and tetracritical points. Renormalization- group equations are analyzed in the two-loop approximation by using the Pade-Borel summation technique. The fixed points corresponding to various types of multicritical behavior are determined. It is shown that effects due to long-range interactions can be responsible for a change from bicritical to tetracritical behavior.
We consider $n\times n$ real symmetric and Hermitian Wigner random matrices $n^{-1/2}W$ with independent (modulo symmetry condition) entries and the (null) sample covariance matrices $n^{-1}X^*X$ with independent entries of $m\times n$ matrix $X$. Assuming first that the 4th cumulant (excess) $\kappa_4$ of entries of $W$ and $X$ is zero and that their 4th moments satisfy a Lindeberg type condition, we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem (CLT) as $n\to\infty$, $m\to\infty$, $m/n\to c\in[0,\infty)$ with the same variance as for Gaussian matrices if the test functions of statistics are smooth enough (essentially of the class $\mathbf{C}^5$). This is done by using a simple ``interpolation trick'' from the known results for the Gaussian matrices and the integration by parts, presented in the form of certain differentiation formulas. Then, by using a more elaborated version of the techniques, we prove the CLT in the case of nonzero excess of entries again for essentially $\mathbb{C}^5$ test function. Here the variance of statistics contains an additional term proportional to $\kappa_4$. The proofs of all limit theorems follow essentially the same scheme.
We report the redshift of an unlensed, highly obscured submillimetre galaxy (SMG), HS1700.850.1, the brightest SMG (S850um =19.1 mJy) detected in the JCMT/SCUBA-2 Baryonic Structure Survey, based on the detection of its CO line emission. Using the IRAM PdBI-WIDEX with 3.6GHz band width, we serendipitously detect an emission line at 150.6 GHz. From a search over 14.5 GHz in the 3-mm and 2-mm atmospheric windows, we confirm the identification of this line as CO(5-4) at z = 2.816, meaning that it does not reside in the z~2.30 proto-cluster in this field. Measurement of the 870um source size (<0.85") from the Sub-Millimeter Array (SMA) confirms a compact emission in a S870um =14.5mJy, LIR~10^13 Lsun component, suggesting an Eddington-limited starburst. We use the double-peaked CO line profile measurements along with the SMA size constraints to study the gas dynamics of a HyLIRG, estimating the gas and dynamical masses of HS1700.850.1. While HS1700.850.1 is one of the most extreme galaxies known in the Universe, we find that it occupies a relative void in the Lyman-Break Galaxy distribution in this field. Comparison with other extreme objects at similar epochs (HyLIRG Quasars), and cosmological simulations, suggests such an anti-bias of bright SMGs could be relatively common, with the brightest SMGs rarely occupying the most overdense regions at z=2-4.
The Stellar Observation Network Group (SONG) is an initiative to build a worldwide network of 1m telescopes with highprecision radial-velocity spectrographs. Here we analyse the first radial-velocity time series of a red-giant star measured by the SONG telescope at Tenerife. The asteroseismic results demonstrate a major increase in the achievable precision of the parameters for redgiant stars obtainable from ground-based observations. Reliable tests of the validity of these results are needed, however, before the accuracy of the parameters can be trusted.   We analyse the first SONG time series for the star 46 LMi, which has a precise parallax and an angular diameter measured from interferometry, and therefore a good determination of the stellar radius. We use asteroseismic scaling relations to obtain an accurate mass, and modelling to determine the age.   A 55-day time series of high-resolution, high S/N spectra were obtained with the first SONG telescope. We derive the asteroseismic parameters by analysing the power spectrum. To give a best guess on the large separation of modes in the power spectrum, we have applied a new method which uses the scaling of Kepler red-giant stars to 46 LMi.   Several methods have been applied: classical estimates, seismic methods using the observed time series, and model calculations to derive the fundamental parameters of 46 LMi. Parameters determined using the different methods are consistent within the uncertainties. We find the following values for the mass M (scaling), radius R (classical), age (modelling), and surface gravity (combining mass and radius): M = 1.09 +- 0.04Msun, R = 7.95 +- 0.11 Rsun, age t = 8.2 +- 1.9Gy, and log g = 2.674 +- 0.013.