ShantanuT01/DACTYL-Pretraining huggingface dataset:
Nowadays quantum-mechanical theory allows one to reliably calculate the processes of 2p radioactivity (true three-body decays) and the corresponding energy and angular correlations up to distances of the order of 1000 fm. However, the precision of modern experiments has now become sufficient to indicate some deficiency of the predicted theoretical distributions. In this paper we discuss the extrapolation along the classical trajectories as a method to improve the convergence of the theoretical energy and angular correlations at very large distances (of the order of atomic distances), where only the long-range Coulomb forces are still operating. The precision of this approach is demonstrated using the "exactly" solvable semianalytical models with simplified three-body Hamiltonians. It is also demonstrated that for heavy 2p emitters, the 2p decay momentum distributions can be sensitive to the effect of the screening by atomic electrons. We compare theoretical results with available experimental data.
We announce the discovery of a quasar behind the disk of M31, which was previously classified as a remarkable nova in our neighbour galaxy. The paper is primarily aimed at the outburst of J004457+4123 (Sharov 21), with the first part focussed on the optical spectroscopy and the improvement in the photometric database. Both the optical spectrum and the broad band spectral energy distribution of Sharov 21 are shown to be very similar to that of normal, radio-quiet type 1 quasars. We present photometric data covering more than a century and resulting in a long-term light curve that is densely sampled over the past five decades. The variability of the quasar is characterized by a ground state with typical fluctuation amplitudes of ~0.2 mag around B~20.5, superimposed by a singular flare of ~2 yr duration (observer frame) with the maximum at 1992.81 where the UV flux has increased by a factor of ~20. The total energy in the flare is at least three orders of magnitudes higher than the radiated energy of the most luminous supernovae, provided that it comes from an intrinsic process and the energy is radiated isotropically. The profile of the flare light curve appears to be in agreement with the standard predictions for a stellar tidal disruption event where a ~10 M_sun giant star was shredded in the tidal field of a ~2...5 10^8 M_sun black hole. The short fallback time derived from the light curve requires an ultra-close encounter where the pericentre of the stellar orbit is deep within the tidal disruption radius. Gravitational microlensing provides an alternative explanation, though the probability of such a high amplification event is very low.
The weight spectra of MDS codes of length $ n $ and dimension $ k $ over the arbitrary alphabets are studied. For all $ q $-ary MDS codes of dimension $ k $ containing the zero codeword, it is shown that all $ k $ weights from $ n $ to $ n-k+1 $ are realized. The remaining case $ n=q+k-1 $ is also determined. Additionally, we prove that all binary MDS codes are equivalent to linear MDS codes. The proofs are combinatorial, and self contained.
We present an elementary type preserving bijection between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis.
Relativistic energy density functional approaches are known to well describe nuclear states which involve alpha clusters. Here, alpha emitting nuclei are analysed through the behavior of the spatial localisation of nucleonic states, calculated with an axially deformed RHB approach over the nuclear chart. The systematic occurrence of more localised valence states, having a n = 1 radial quantum number, allows to pinpoint nuclei in agreement with experimentally known alpha-emitters. The cases of 212Po and 104Te are investigated, showing the concomitant contributions of the pseudospin symmetry and the presence of n = 1 states, on the alpha preformation probability. The impact of the localisation of valence states, on alpha preformation probability, is then analysed. It allows to study shell effects on this probability, over isotopic and isotonic chains. Finally, a phenomenological law is also provided, relating this probability to the radial quantum number of the valence states.
To understand the conditions under which dense, molecular gas is able to form within a galaxy, we post-process a series of three-dimensional galactic-disk-scale simulations with ray-tracing based radiative transfer and chemical network integration to compute the equilibrium chemical and thermal state of the gas. In performing these simulations we vary a number of parameters, such as the ISRF strength, vertical scale height of stellar sources, cosmic ray flux, to gauge the sensitivity of our results to these variations. Self-shielding permits significant molecular hydrogen (H2) abundances in dense filaments around the disk midplane, accounting for approximately ~10-15% of the total gas mass. Significant CO fractions only form in the densest, n>~10^3 cm^-3, gas where a combination of dust, H2, and self-shielding attenuate the FUV background. We additionally compare these ray-tracing based solutions to photochemistry with complementary models where photo-shielding is accounted for with locally computed prescriptions. With some exceptions, these local models for the radiative shielding length perform reasonably well at reproducing the distribution and amount of molecular gas as compared with a detailed, global ray tracing calculation. Specifically, an approach based on the Jeans Length with a T=40K temperature cap performs the best in regards to a number of different quantitative measures based on the H2 and CO abundances.
For a skip-free Markov process on non-negative integers with generator matrix Q, we evaluate the joint Laplace transform of the occupation times before hitting the state n (starting at 0). This Laplace transform has a very straightforward and familiar expression. We investigate the properties of this Laplace transform, especially the conditions under which the occupation times form a Markov chain.
We study the kinetics of the first order phase separation transition in boson-fermion cold-atom mixtures. At sufficiently low temperatures such a transition is driven by quantum fluctuations responsible for the formation of critical nuclei of a stable phase. Based on a microscopic description of interacting boson-fermion mixtures we derive an effective action for the critical droplet and obtain an asymptotic expression for the nucleation rate in the vicinity of the phase transition and near the spinodal instability of the mixed phase. We also discuss effects of dissipation which play a dominant role close to the transition point, and identify the regimes where quantum nucleation can be experimentally observed in cold-atom systems.
Multiple tracers of the cosmic density field, with different bias, number and luminosity evolution, can be used to measure the large-scale properties of the Universe. We show how an optimal combination of tracers can be used to detect general-relativistic effects in the observed density of sources. We forecast for the detectability of these effects, as well as measurements of primordial non-Gaussianity and large-scale lensing magnification with current and upcoming large-scale structure experiments. In particular we quantify the significance of these detections in the short term with experiments such as the Dark Energy Survey (DES), and in the long term with the Large Synoptic Survey Telescope (LSST) and the Square Kilometre Array (SKA). We review the main observational challenges that must be overcome to carry out these measurements.
Recent data from Reticulum II (RetII) require the energy range of the FermiLAT $\gamma$-excess to be $\sim$ $2-10$ GeV. We adjust our unified nonthermal Dark Matter (DM) model to accommodate this. We have two extra scalars beyond the Standard Model to also explain 3.55 keV X-ray line. Now the mass of the heavier of them has to be increased to lie around 250 GeV, while that of the lighter one remains at 7.1 keV. This requires a new seed mechanism for the $\gamma$-excess and new Boltzmann equations for the generation of the DM relic density. All concerned data for RetII and the X-ray line can now be fitted well and consistency with other indirect limits attained.
Outflows in active galactic nuclei (AGNs) are crucial to understand in investigating the co-evolution of supermassive black holes (SMBHs) and their host galaxies since outflows may play an important role as an AGN feedback mechanism. Based on the archival UV spectra obtained with HST and IUE, we investigate outflows in the broad-line region (BLR) in low-redshift AGNs (z < 0.4) through the detailed analysis of the velocity profile of the CIV emission line. We find a dependence of the outflow strength on the Eddington ratio and the BLR metallicity in our low-redshift AGN sample, which is consistent with the earlier results obtained for high-redshift quasars. These results suggest that the BLR outflows, gas accretion onto SMBH, and past star-formation activity in the host galaxies are physically related in low-redshift AGNs as in powerful high-redshift quasars.
Density-functional theory calculations are used to verify the atomic structure of the $\sqrt{3}$$\times$$\sqrt{3}$ silicene phase grown on the Ag(111) surface. Recent experimental studies strongly suggested that the previous double-layer silicene model should be replaced with a Ag-mixed double-layer model resembling the top layers of the Ag/Si(111)-($\sqrt{3}$$\times$$\sqrt{3}$) surface. In our calculations, the Ag-mixed double-layer model is indeed energetically favored over the double-layer silicene model and well reproduces the reported scanning-tunneling microscopy and spectroscopy data. Especially, the structural origin of the experimental band structure is clarified as the top Ag-Si mixed layer, unlike the experimental interpretations as either a silicene layer or the Ag(111) substrate.
We consider the $\mathcal{N}=2$ SYM theory with gauge group SU($N$) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large-$N$ 't Hooft expansion and is dual to a particular orientifold of $AdS_{5}\times S^{5}$. We analyze this gauge theory relying on the matrix model provided by localization a la Pestun. Even though this matrix model has very non-trivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the 't Hooft coupling $\lambda$. These exact expressions can be used to generate the perturbative expansions at high orders in a very efficient way, and also to study analytically the leading behavior at strong coupling. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to the Pad\'e resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk $|\lambda|<\pi^2$ of the latter.
In this work the shear viscosity of strongly interacting matter is calculated within a two-flavor Nambu--Jona-Lasinio model as a function of temperature and chemical potential. The general Kubo formula is applied, incorporating the full Dirac structure of the thermal quark spectral function and avoiding commonly used on-shell approximations. Mesonic fluctuations contributing via Fock diagrams provide the dominant dissipative processes. The resulting ratio $\eta/s$ (shear viscosity over entropy density) decreases with temperature and chemical potential. Interpolating between our NJL results at low temperatures and hard-thermal-loop results at high temperatures a minimum slightly above the AdS/CFT benchmark $\eta/s=1/4\pi$ is obtained.
We develop an analytical forward model based on perturbation theory to predict the redshift-space galaxy overdensity at the field level given a realization of the initial conditions. We find that the residual noise between the model and simulated galaxy density has a power spectrum that is white on large scales, with size comparable to the shot noise. In the mildly nonlinear regime, we see a $k^2\mu^2$ correction to the noise power spectrum, corresponding to larger noise along the line of sight and on smaller scales. The parametric form of this correction has been predicted on theoretical grounds before, and our simulations provide important confirmation of its presence. We have also modeled the galaxy velocity at the field-level and compared it against simulated galaxy velocities, finding that about $10\%$ of the galaxies are responsible for half of the rms velocity residual for our simulated galaxy sample.
Charge sensing in quantum-dot structures is studied by an exactly solvable reduced model and numerical density-matrix renormalization group methods. Charge sensing is characterized by the repeated cycling of the occupation of current-carrying states due to the capacitive coupling to trap states which are weakly coupled to the leads. In agreement with recent experiments, it results in a variety of characteristic behaviors ranging from asymmetric Coulomb-blockade peaks to sawtooth- and dome-like structures. Temperature introduces distinct asymmetric smearing of these features and correlations in the conductance provide a fingerprint of charge-sensing behavior.
We present a simple model of how quasars occupy dark matter halos from z=0 to z=5 using the observed mBH-sigma relation and quasar luminosity functions. This provides a way for observers to statistically infer host halo masses for quasar observations using luminosity and redshift alone. Our model is deliberately simple and sidesteps any need to explicitly describe the physics. In spite of its simplicity, the model reproduces many key observations and has predictive power: 1) model quasars have the correct luminosity function (by construction) and spatial clustering (by consequence); 2) we predict high redshift quasars of a given luminosity live in less massive dark matter halos than the same luminosity quasars at low redshifts; 3) we predict a factor of ~5 more 10^8.5Msun black holes at z~2 than is currently observed; 4) we predict a factor of ~20 evolution in the amplitude of the mBH-Mhalo relation between z=5 and the present day; 5) we expect luminosity dependent quasar lifetimes of between tQ~10^(7-8)yr, but which may become as short as 10^(5-6)yr for quasars brighter than L*; 6) while little luminosity dependent clustering evolution is expected at z<1, increasingly strong evolution is predicted for L>L* quasars at higher redshifts. These last two results arise from the narrowing distribution of halo masses that quasars occupy as the Universe ages. We also deconstruct both "downsizing" and "upsizing" trends predicted by the model at different redshifts and space densities. Importantly, this work illustrates how current observations cannot distinguish between more complicated physically motivated quasar models and our simple phenomenological approach. It highlights the opportunities such methodologies provide.
We investigate an interacting fermion model with boundary potential by using Bethe ansatz method. The ground state properties of the system and the boundary effect are discussed. It is found that attractive boundary potential leads to the boundary bound state. An interesting phenomenon is that the slidding collective charges in a periodic system, which is formed due to the attractive interaction among the fermions, will be pinned around the boundary, as long as the negative boundary potential is strong enough.
In this paper we consider the one-dimensional quantum random walk X^{varphi} _n at time n starting from initial qubit state varphi determined by 2 times 2 unitary matrix U. We give a combinatorial expression for the characteristic function of X^{varphi}_n. The expression clarifies the dependence of it on components of unitary matrix U and initial qubit state varphi. As a consequence of the above results, we present a new type of limit theorems for the quantum random walk. In contrast with the de Moivre-Laplace limit theorem, our symmetric case implies that X^{varphi}_n /n converges in distribution to a limit Z^{varphi} as n to infty where Z^{varphi} has a density 1 / pi (1-x^2) sqrt{1-2x^2} for x in (- 1/sqrt{2}, 1/sqrt{2}). Moreover we discuss some known simulation results based on our limit theorems.
In this paper we study the asymptotic behavior of a quadratic Schr\"{o}dinger equation with electromagnetic potentials. We prove that small solutions scatter. The proof builds on earlier work of the author for quadratic NLS with a non magnetic potential. The main novelty is the use of various smoothing estimates for the linear Schr\"{o}dinger flow in place of boundedness of wave operators to deal with the loss of derivative. As a byproduct of the proof we obtain boundedness of the wave operator of the linear electromagnetic Schr\"{o}dinger equation on an $L^2$ weighted space for small potentials, as well as a dispersive estimate for the corresponding flow.
High dispersion near-infrared spectra have been taken of seven highly-evolved, variable, intermediate-mass (4-6 Msun) AGB stars in the LMC and SMC in order to look for C, N and O variations that are expected to arise from third dredge-up and hot-bottom burning. The pulsation of the objects has been modelled, yielding stellar masses, and spectral synthesis calculations have been performed in order to derive abundances from the observed spectra. For two stars, abundances of C, N, O, Na, Al, Ti, Sc and Fe were derived and compared with the abundances predicted by detailed AGB models. Both stars show very large N enhancements and C deficiencies. These results provide the first observational confirmation of the long-predicted production of primary nitrogen by the combination of third dredge-up and hot-bottom burning in intermediate-mass AGB stars. It was not possible to derive abundances for the remaining five stars: three were too cool to model, while another two had strong shocks in their atmospheres which caused strong emission to fill the line cores and made abundance determination impossible. The latter occurrence allows us to predict the pulsation phase interval during which observations should be made if successful abundance analysis is to be possible.
We deal with the following closely related problems: (i) For a germ of a reduced plane analytic curve, what is the minimal degree of an algebraic curve with a singular point analytically equivalent (isomorphic) to the given one? (ii) For a germ of a holomorphic function in two variables with an isolated critical point, what is the minimal degree of a polynomial, equivalent to the given function up to a local holomorphic coordinate change? Classically known estimates for such a degree $d$ in these questions are $\sqrt{\mu}+1\le d\le \mu+1$, where $\mu$ is the Milnor number. Our result in both the problems is $d\le a\sqrt{\mu}$ with an absolute constant $a$. As a corollary, we obtain asymptotically proper sufficient conditions for the existence of algebraic curves with prescribed singularities on smooth algebraic surfaces.
A well-known model due to J.-M. Lasry and P.L. Lions that presents the evolution of prices in a market as the evolution of a free boundary in a diffusion equation is suggested to be modified in order to show instabilities for some values of the parameters. This loss of stability is associated to the appearance of new types of solutions, namely periodic solutions, due to a Hopf bifurcation and representing price oscillations, and traveling waves, that represent either inflationary or deflationary behavior.
A toric arrangement is an arrangement of subtori of codimension one in a real or complex torus. The poset of layers is the set of connected components of non-empty intersections of these subtori, partially ordered by reverse inclusion. In this note we present an algorithm that computes this poset in the central case.
Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential equations (PDE). A systematic framework for the study of probabilities of deviations of the stochastic PDE from the deterministic PDE is through the theory of large deviations. The goal of this work is to develop the large deviation theory for small Poisson noise perturbations of a general class of deterministic infinite dimensional models. Although the analogous questions for finite dimensional systems have been well studied, there are currently no general results in the infinite dimensional setting. This is in part due to the fact that in this setting solutions may have little spatial regularity, and thus classical approximation methods for large deviation analysis become intractable. The approach taken here, which is based on a variational representation for nonnegative functionals of general PRM, reduces the proof of the large deviation principle to establishing basic qualitative properties for controlled analogues of the underlying stochastic system. As an illustration of the general theory, we consider a particular system that models the spread of a pollutant in a waterway.
A linear operator in a Hilbert space defined through the form of Riesz representation naturally introduces a reproducing kernel Hilbert space structure over the range space. Such formulation, called H-HK formulation in this paper, possesses a built-in mechanism to solve some basic type problems in the formulation by using the basis method, that include identification of the range space, the inversion problem, and the Moore-Penrose pseudo- (generalized) inversion problem. After a quick survey of the existing theory, the aim of the article is to establish connection between this formulation with sparse series representation, and in particular with one called pre-orthogonal adaptive Fourier decomposition (POAFD), the latter being one, most recent and well developed, with great efficiency and wide and deep connections with traditional analysis. Within the matching pursuit methodology the optimality of POAFD is theoretically guaranteed. In practice POAFD offers fast converging numerical solutions.
Here, we address a dimension-reduction problem in the context of nonlinear elasticity where the applied external surface forces induce bending-torsion moments. The underlying body is a multi-structure in $\mathbb{R}^3$ consisting of a thin tube-shaped domain placed upon a thin plate-shaped domain. The problem involves two small parameters, the radius of the cross-section of the tube-shaped domain and the thickness of the plate-shaped domain. We characterize the different limit models, including the limit junction condition, in the membrane-string regime according to the ratio between these two parameters as they converge to zero.