ShantanuT01/DACTYL-Pretraining huggingface dataset:
The parity-nonconserving asymmetry in the deuteron photodisintegration, $\vec{\gamma}+d\to n+p$, is considered with the photon energy ranged up to 10 MeV above the threshold. The aim is to improve upon a schematic estimate assuming the absence of tensor as well as spin-orbit forces in the nucleon-nucleon interaction. The major contributions are due to the vector-meson exchanges, and the strong suppression of the pion-exchange contribution is confirmed. A simple argument, going beyond the observation of an algebraic cancellation, is presented. Contributions of meson-exchange currents are also considered, but found to be less significant.
Let $\mathbb{\hat{E}}$ be the upper expectation of a weakly compact but non-dominated family $\mathcal{P}$ of probability measures. Assume that $Y$ is a $d$-dimensional $\mathcal{P}$-semimartingale under $\mathbb{\hat{E}}$. Given an open set $Q\subset\mathbb{R}^{d}$, the exit time of $Y$ from $Q$ is defined by \[ {\tau}_{Q}:=\inf\{t\geq0:Y_{t}\in Q^{c}\}. \] The main objective of this paper is to study the quasi-continuity properties of ${\tau}_{Q}$ under the nonlinear expectation $\mathbb{\hat{E}}$. Under some additional assumptions on the growth and regularity of $Y$, we prove that ${\tau}_{Q}\wedge t$ is quasi-continuous if $Q$ satisfies the exterior ball condition. We also give the characterization of quasi-continuous processes and related properties on stopped processes. In particular, we get the quasi-continuity of exit times for multi-dimensional $G$-martingales, which nontrivially generalizes the previous one-dimensional result of Song.
Quantum radiation properties of Dirac particles in general nonstationary black holes in the general case is investigated by both using the method of generalized tortoise coordinate transformation and considering the asymptotic behaviors of both the first and second order forms of Dirac equations near the event horizon. It is generally shown that the temperature and shape of event horizon of this kind of black holes depend on both the time and different angles. Further, we give a general expression of the new extra coupling effect in thermal radiation spectrum of Dirac particles which is missing in that of scalar particles. Also, we reveal a relationship that is ignored before between thermal radiation and non-thermal radiation in the case of scalar particles, which is that the chemical potential in thermal radiation spectrum is equal to the highest energy of the negative energy state of scalar particles in non-thermal radiation for general nonstationary black holes.
Vortex dynamics in inhomogeneous Bose-Einstein condensates are studied numerically in two and three dimensions. We simulate the precession of a single vortex around the center of a trapped condensate, and use the Magnus force to estimate the precession frequency. Vortex ring dynamics in a spherical trap are also simulated, and we discover that a ring undergoes oscillatory motion around a circle of maximum energy. The position of this locus is calculated as a function of the number of condensed atoms. In the presence of dissipation, the amplitude of the oscillation will increase, eventually resulting in self-annihilation of the ring.
In this paper, we study the formation of finite time singularities in the form of super norm blowup for a spatially inhomogeneous hyperbolic system. The system is related to the variational wave equations as those in [18]. The system posses a unique $C^1$ solution before the emergence of vacuum in finite time, for given initial data that are smooth enough, bounded and uniformly away from vacuum. At the occurrence of blowup, the density becomes zero, while the momentum stays finite, however the velocity and the energy are both infinity.
Solar flares are explosive releases of magnetic energy. Hard X-ray (HXR) flare emission originates from both hot (millions of Kelvin) plasma and nonthermal accelerated particles, giving insight into flare energy release. The Nuclear Spectroscopic Telescope ARray (NuSTAR) utilizes direct focusing optics to attain much higher sensitivity in the HXR range than that of previous indirect imagers. This paper presents eleven NuSTAR microflares from two active regions (AR 12671 on 2017 August 21, and AR 12712 on 2018 May 29). The temporal, spatial, and energetic properties of each are discussed in context with previously published HXR brightenings. They are seen to display several 'large-flare' properties, such as impulsive time profiles and earlier peaktimes in higher energy HXRs. For two events where active region background could be removed, microflare emission did not display spatial complexity: differing NuSTAR energy ranges had equivalent emission centroids. Finally, spectral fitting showed a high energy excess over a single thermal model in all events. This excess was consistent with additional higher-temperature plasma volumes in 10/11 microflares, and consistent only with an accelerated particle distribution in the last. Previous NuSTAR studies focused on one or a few microflares at a time, making this the first to collectively examine a sizable number of events. Additionally, this paper introduces an observed variation in the NuSTAR gain unique to the extremely low-livetime (<1%) regime, and establishes a correction method to be used in future NuSTAR solar spectral analysis.
We consider thermodynamic and transport properties of a long granular array with strongly connected grains (inter-grain conductance g>>1.) We find that the system exhibits activated behavior of conductance and thermodynamic density of states ~exp(-T*/T) where the gap, T*, is parametrically larger than the energy at which conventional perturbation theory breaks down. The scale T* represents energy needed to create a long single-electron charge soliton propagating through the array.
Details of the discovery of a new X-ray source, IGR J18462-0223, on October 12, 2007, during a short (several hours), intense (~ 35 mCrab at the peak) outburst of hard radiation by the IBIS/ISGRI gamma-ray telescope onboard the INTEGRAL observatory are given. The detection of another earlier outburst from this source occurred on April 28, 2006, in the archival data of the telescope is reported. We present the results of the source's localization and our spectral/timing analysis of the observational data. The source may turn out to be yet another representative of the continuously growing population of fast X-ray transients, which are the focus of attention because of the identification of their optical counterparts with early-type supergiants.
We use standard constructions in algebraic geometry and homological algebra to extend the decomposition and hard Lefschetz theorems of T. Mochizuki and C. Sabbah so that they remains valid without the quasi-projectivity assumptions.
Consider the second order divergence form elliptic operator $L$ with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calder\'{o}n-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some $L^p$ spaces.   In this work we generalize the classical approach and develop a theory of Hardy and BMO spaces associated to $L$, which includes, in particular, molecular decomposition, maximal function characterization, duality of Hardy and BMO spaces, John-Nirenberg inequality, and allows to handle aforementioned operators.
Traditional formulations of geometric problems from the Schubert calculus, either in Plucker coordinates or in local coordinates provided by Schubert cells, yield systems of polynomials that are typically far from complete intersections and (in local coordinates) typically of degree exceeding two. We present an alternative primal-dual formulation using parametrizations of Schubert cells in the dual Grassmannians in which intersections of Schubert varieties become complete intersections of bilinear equations. This formulation enables the numerical certification of problems in the Schubert calculus.
We consider a cosmological model starting from (1) the(1+3+6)-dimensional space-times consisting of the outer space (the 3-dimensional expanding section) and the inner space (the 6-dimensional section) and reaching (2) the Friedmann model after the decoupling between the outer space and the inner space, and derive fluctuations of the background radiation appearing in the above 10-dimensional space-times. For this purpose we first derive the fluid-dynamical perturbations in the above 10-dimensional space-times, corresponding to two kinds of curvature perturbations (in the scalar mode) in the non-viscous case, and next study the quantum fluctuations in the scalar and tensor modes, appearing at the stage when the perturbations are within the horizon of the inflating outer space. Lastly we derive the wave-number dependence of fluctuations (the power spectrum) in the two modes, which formed at the above decoupling epoch and are observed in the Friedmann stage. It is found that it can be consistent with the observed spectra of the cosmic microwave background radiation.
We consider a chiral one-loop hedgehog soliton of the bosonized SU(2)$_f$ Nambu & Jona-Lasinio model which is embedded in a hot medium of constituent quarks. Energy and radius of the soliton are determined in self-consistent mean-field approximation. Quasi-classical corrections to the soliton energy are derived by means of the pushing and cranking approaches. The corresponding inertial parameters are evaluated. It is shown that the inertial mass is equivalent to the total internal energy of the soliton. Corrected nucleon and $\Delta$ isobar masses are calculated in dependence on temperature and density of the medium. As a result of the self-consistently determined internal structure of the soliton the scaling between constituent quark mass, soliton mass and radius is noticeably disturbed.
Following the approach of Rota and Taylor \cite{SIAM}, we present an innovative theory of Sheffer sequences in which the main properties are encoded by using umbrae. This syntax allows us noteworthy computational simplifications and conceptual clarifications in many results involving Sheffer sequences. To give an indication of the effectiveness of the theory, we describe applications to the well-known connection constants problem, to Lagrange inversion formula and to solving some recurrence relations.
Motivated by recent success of local electron tunneling into heavy fermion materials, we study the local electronic structure around a single Kondo hole in an Anderson lattice model and the Fano interference pattern relevant to STM experiments. Within the Gutzwiller method, we find that an intragap bound state exists in the heavy Fermi liquid regime. The energy position of the intragap bound state is dependent on the on-site potential scattering strength in the conduction and $f$-orbital channels. Within the same method, we derive a new $dI/dV$ formulation, which includes explicitly the renormalization effect due to the $f$-electron correlation. It is found that the Fano interference gives asymmetric coherent peaks separated by the hybridization gap. The intragap peak structure has a Lorenzian shape, and the corresponding $dI/dV$ intensity depends on the energy location of the bound state.
Frustration in spin system can give rise to unique ordered states and as a consequence several physical phenomena are expected such as multiferroics, high temperature superconductors and anomalous hall effect. Here we report the "new magnetic orders" induced by anisotropic spin exchanges on pyrochlore spinels as the interplay of spin orbit coupling and geometrical frustration. Due to complicated superexchange paths of B-site spinels, we claim that anisotropic interaction between next-nearest neighbors play an important role. Based on the systematic studies of generic spin model, we argue that several classical spin states can be explored in spinel systems; local XY state, all-in all-out state, Palmer-Chalker state and coplanar spiral state. In addition, we reveal new types of magnetic phases with finite ordering wavevectors, labeled as 'octagonal (prism)' state and '(distorted) cubic' states. When the 'octagonal prism' state is stabilized, non-zero scalar spin chirality induces alternating net current in addition to finite orbital current and orbital magnetization even in Mott insulators. Finally, we also discuss the relevance of 'distorted cubic' state to the magnetic order of spinel compound GeCo2O4.
A class of exact analytic solutions in the modified cubic fermionic string field theory with the GSO(-) sector is presented. This class contains the GSO(-) tachyon field and reproduces the correct value for the nonBPS D-brane tension.
The population of millisecond pulsars (MSPs) has been expanded considerably in the last decade. Not only is their number increasing, but also various classes of them have been revealed. Among different classes of MSPs, the behaviour of black widows and redbacks are particularly interesting. These systems consist of an MSP and a low-mass companion star in compact binaries with an orbital period of less than a day. In this article, we give an overview of the high energy nature of these two classes of MSPs. Updated catalogues of black widows and redbacks are presented and their X ray/$\gamma$-ray properties are reviewed. Besides the overview, using the most updated eight-year Fermi Large Area Telescope point source catalog, we have compared the $\gamma$-ray properties of these two MSP classes. The results suggest that the X-rays and $\gamma$-rays observed from these MSPs originate from different mechanisms. Lastly, we will also mention the future prospects of studying these spider pulsars with the novel methodologies as well as upcoming observing facilities.
Let f be a modular form of weight 2 and trivial character. Fix also an imaginary quadratic field K. We use work of Bertolini-Darmon and Vatsal to study the mu-invariant of the p-adic Selmer group of f over the anticyclotomic Zp-extension of K. In particular, we verify the mu-part of the main conjecture in this context. The proof of this result is based on an analysis of congruences of modular forms, leading to a conjectural quantitative version of level-lowering (which we verify in the case that Mazur's principle applies).
We compare [O IV] 25.89 micron emission line luminosities with very hard (10-200 keV) X-rays from Swift, Integral, and BeppoSAX for a complete sample of 89 Seyferts from the Revised Shapley-Ames sample. Using Seyfert 1s, we calibrate [O IV] as a measure of AGN intrinsic luminosity, for particular use in high-obscuration environments. With this calibration, we measure the average decrement in 14-195 keV X-ray to [O IV] luminosity ratio for Seyfert 2s compared to type 1s. We find a decrement of 3.1 +- 0.8 for Seyfert 2s, and a decrement of 5.0 +- 2.7 for known Compton-thick Seyfert 2s. These decrements imply column densities of approximately log N(H)=24.6 and 24.7 cm^-2, respectively. Thus, we infer that the average Seyfert 2 is more highly obscured and intrinsically more luminous than would be inferred even from the very hard X-rays. We demonstrate two applications of the hard X-ray to [O IV] ratio. We measure a column density for the extremely obscured NGC 1068 of log N(H)=25.3-25.4 cm^-2. Finally, by comparing [O IV] luminosities to total infrared luminosities for twelve bright ultraluminous infrared galaxies, we find that four have substantial AGN contributions.
We propose a ``channelization'' architecture to achieve wide-band electromagnetically induced transparency (EIT) and ultra-slow light propagation in atomic Rb-87 vapors. EIT and slow light are achieved by shining a strong, resonant ``pump'' laser on the atomic medium, which allows slow and unattenuated propagation of a weaker ``signal'' beam, but only when a two-photon resonance condition is satisfied. Our wideband architecture is accomplished by dispersing a wideband signal spatially, transverse to the propagation direction, prior to entering the atomic cell. When particular Zeeman sub-levels are used in the EIT system, then one can introduce a magnetic field with a linear gradient such that the two-photon resonance condition is satisfied for each individual frequency component. Because slow light is a group velocity effect, utilizing differential phase shifts across the spectrum of a light pulse, one must then introduce a slight mismatch from perfect resonance to induce a delay. We present a model which accounts for diffusion of the atoms in the varying magnetic field as well as interaction with levels outside the ideal three-level system on which EIT is based. We find the maximum delay-bandwidth product decreases with bandwidth, and that delay-bandwidth product ~1 should be achievable with bandwidth ~50 MHz (~5 ns delay). This is a large improvement over the ~1 MHz bandwidths in conventional slow light systems and could be of use in signal processing applications.
We develop a theory for the electronic excitations in UPt$_3$ which is based on the localization of two of the $5f$ electrons. The remaining $f$ electron is delocalized and acquires a large effective mass by inducing intra-atomic excitations of the localized ones. The measured deHaas-vanAlphen frequencies of the heavy quasiparticles are explained as well as their anisotropic heavy mass. A model calculation for a small cluster reveals why only the largest of the different $5f$ hopping matrix elements is operative causing the electrons in other orbitals to localize.
We describe the classical and quantum two dimensional nonlinear dynamics of large blue-detuned eveanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modualtion period and integrate the signals.   For quantum dynamics, quantum collapses and revivals appear . For periodically modulated optical potential, the variance of atomic position will be supressed compared to the no modulation case. The atomic angular momentum will influnce the evolution of wave function in two dimensional quantum system of hollow fiber.
We extend previous work of the author using an idea of Buzzard and give an elementary construction of non-ordinary $p$-adic families of Hilbert Modular Eigenforms.
We first give a summary of the history of transcendental numbers then use a nice technique by G. Dresden to prove a new transcendental number. In particular, while previous work looked at the last non-zero digit of $n^n$, we consider the digit right before its last non-zero digit and show that the infinite decimal built from these digits is transcendental.
A dynamical coupled-channel study of K* K*bar state with isospin 0 and omega phi state is performed within both the chiral SU(3) quark model and the extended chiral SU(3) quark model by solving a resonating group method (RGM) equation. The model parameters are taken from our previous work, which gave a satisfactory description of the energies of the octet and decuplet baryon ground states, the binding energy of the deuteron, the nucleon-nucleon (NN) scattering phase shifts, and the hyperon-nucleon (YN) cross sections. The results show that the interactions of K* K*bar states are attractive, which consequently result in K* K*bar bound states with the binding energies of about 10-70 MeV, and contrarily, no omega phi bound state is obtained. The channel coupling effect of K* K*bar and omega phi is found to be considerably large, which makes the binding of K* K*bar 5-45 MeV deeper. The plausible interpretation of f_0(1710) and X(1812) being K* K*bar dominated states is briefly discussed.
The mean field approach to the Nambu-Jona-Lasinio model is developed systematically. Approximate mean field action is obtained, based on the study of divergencies in the mean field action. A special scalar case of the approximate motion equations is studied and inhomogenouous solutions are discussed. It is shown that the model can have inhomogeneous vacuum configurations which leads to bound fermionic states.
Consider the ensemble of real symmetric Toeplitz matrices whose entries are i.i.d random variables chosen from a fixed probability distribution p of mean 0, variance 1 and finite higher moments. Previous work [BDJ,HM] showed that the limiting spectral measures (the density of normalized eigenvalues) converge weakly and almost surely to a universal distribution almost that of the Gaussian, independent of p. The deficit from the Gaussian distribution is due to obstructions to solutions of Diophantine equations and can be removed (see [MMS]) by making the first row palindromic. In this paper, we study the case where there is more than one palindrome in the first row of a real symmetric Toeplitz matrix. Using the method of moments and an analysis of the resulting Diophantine equations, we show that the moments of this ensemble converge to an universal distribution with a fatter tail than any previously seen limiting spectral measure.
We introduce the notion of isolated genus two curves. As there is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap, the discrete log problem (DLP) cannot be efficiently carried over from an isolated curve to a large set of isogenous curves. Thus isolated genus two curves might be more secure for DLP based hyperelliptic curve cryptography. We establish results on explicit expressions for the index of an endomorphism ring in the maximal CM order, and give conditions under which the index is a prime number or an almost prime number for three different categories of quartic CM fields. We also derived heuristic asymptotic results on the densities and distributions of isolated genus two curves with CM by any fixed quartic CM field. Computational results, which are also shown for three explicit examples, agree with heuristic prediction with errors within a tolerable range.
A subset in a group $G \leq Sym(n)$ is intersecting if for any pair of permutations $\pi,\sigma$ in the subset there is an $i \in \{1,2,\dots,n\}$ such that $\pi(i) = \sigma(i)$. If the stabilizer of a point is the largest intersecting set in a group, we say that the group has the Erd\H{o}s-Ko-Rado (EKR) property. Moreover, the group has the strict EKR property if every intersecting set of maximum size in the group is either the stabilizer of a point or the coset of the stabilizer of a point. In this paper we look at several families of permutation groups and determine if the groups have either the EKR property or the strict EKR property. First, we prove that all cyclic groups have the strict EKR property. Next we show that all dihedral and Frobenius groups have the EKR property and we characterize which ones have the strict EKR property. Further, we show that if all the groups in an external direct sum or an internal direct sum have the EKR (or strict EKR) property, then the product does as well. Finally, we show that the wreath product of two groups with EKR property also has the EKR property.