ShantanuT01/DACTYL-Pretraining huggingface dataset:
It was suggested by Kontsevich that the Grothendieck-Teichmueller group GT should act on the Duflo isomorphism of su(2) but the corresponding realization of GT turned out to be trivial. We show that a solvable quotient of the motivic Galois group - which is supposed to agree with GT - is closely related to the quantum coadjoint action on U_q(sl_2) for q a root of unity, i.e. in the quantum group case one has a nontrivial realization of a quotient of the motivic Galois group. From a discussion of the algebraic properties of this realization we conclude that in more general cases than U_q(sl_2) it should be related to a quantum version of the motivic Galois group. Finally, we discuss the relation of our construction to quantum field and string theory and explain what we believe to be the "physical reason" behind this relation between the motivic Galois group and the quantum coadjoint action. This might be a starting point for the generalization of our construction to more involved examples.
A recently proposed renormalization scheme can be used to deal with nonrelativistic potential scattering exhibiting ultraviolet divergence in momentum space. A numerical application of this scheme is made in the case of potential scattering with $r^{-2}$ divergence for small r, common in molecular and nuclear physics, by the use of cut-offs in momentum and configuration spaces. The cut-off is finally removed in terms of a physical observable and model-independent result is obtained at low energies. The expected variation of the off-shell behavior of the t matrix arising from the renormalization scheme is also discussed.
For nearly seven decades astronomers have been studying active galaxies, that is to say galaxies with actively accreting central supermassive black holes, AGN. A small fraction of these are characterized by luminous, powerful radio emission: this class is known as radio-loud. A substantial fraction, the so-called radio-quiet AGN population, displays intermediate or weak radio emission. However, an appreciable fraction of strong X-rays emitting AGN are characterized by the absence of radio emission, down to an upper limit of about $10^{-7}$ times the luminosity of the most powerful radio-loud AGN.   We wish to address the nature of these - seemingly radio-silent - X-ray-luminous AGN and their host galaxies: is there any radio emission, and if so, where does it originate? Focusing on the GOODS-N field, we examine the nature of these objects employing stacking techniques on ultra-deep radio data obtained with the JVLA. We combine these radio data with Spitzer far-infrared data. We establish the absence, or totally insignificant contribution of jet-driven radio-emission in roughly half of the otherwise normal population of X-ray luminous AGN, which appear to reside in normal star-forming galaxies. We conclude that AGN- or jet-driven radio emission is simply a mechanism that may be at work or may be dormant in galaxies with actively accreting black holes. The latter can be classified as radio-silent AGN.
In this work, we use the numerical renormalization group (NRG) theory to study the thermodynamics of the two-impurity Anderson model. Two different methods are used to estimate the effect of the Dzyaloshiskii-Moriya (DM) interaction on the variation of the Kondo temperature. When the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is vanishing, the two different estimations give different tendency. If we use the peak of the specific heat to identify the variation of the Kondo temperature versus the Dzyaloshiskii-Moriya interaction, we get an almost linear function. However, if we use the low temperature universal curve of the impurity entropy, we get a quadratic function. These results indicate that the previous debates about the influence of the spin-orbit coupling on the Kondo temperature may come from the different definitions of the Kondo temperature. When the RKKY interaction is ferromagnetic, there are two stages of the Kondo screening. Both the two estimations demonstrate that the second stage of the Kondo temperature is exponentially dependent on the DM interaction. There results are dramatically different from those calculated via perturbation theory.
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a vector field" type constraints can always be put into linear first order hyperbolic form for which global existence and uniqueness of solutions to an initial-boundary value problem is guaranteed.
We report studies on temperature, field and time dependence of magnetization on cupric oxide nanoparticles of sizes 9 nm, 13 nm and 16 nm. The nanoparticles show unusual features in comparison to other antiferromagnetic nanoparticle systems. The field cooled (FC) and zero field cooled (ZFC) magnetization curves bifurcate well above the N\'eel temperature and the usual peak in the ZFC magnetization curve is absent.   The system does not show any memory effects which is in sharp contrast to the usual behavior shown by other antiferromagnetic nanoparticles. It turns out that the non-equilibrium behavior of CuO nanoparticles is very strange and is neither superparamagnetic nor spin glass-like.
Artificially increasing the luminosity and the thermal diffusivity of a model is a common tactic adopted in hydrodynamical simulations of stellar convection. In this work, we analyse the impact of these artificial modifications on the physical properties of stellar interiors and specifically on internal gravity waves. We perform two-dimensional simulations of solar-like stars with the MUSIC code. We compare three models with different luminosity enhancement factors to a reference model. The results confirm that properties of the waves are impacted by the artificial enhancement of the luminosity and thermal diffusivity. We find that an increase in the stellar luminosity yields a decrease in the bulk convective turnover timescale and an increase in the characteristic frequency of excitation of the internal waves. We also show that a higher energy input in a model, corresponding to a larger luminosity, results in higher energy in high frequency waves. Across our tests with the luminosity and thermal diffusivity enhanced together by up to a factor of 104, our results are consistent with theoretical predictions of radiative damping. Increasing the luminosity also has an impact on the amplitude of oscillatory motions across the convective boundary. One must use caution when interpreting studies of internal gravity waves based on hydrodynamical simulations with artificially enhanced luminosity.
AdS2 has an SL(2,R) isometry group. It is argued that in the context of quantum gravity on AdS2 this group is enlarged to the full infinite-dimensional 1+1 conformal group. Massive scalar fields are coupled to AdS2 gravity and shown to have associated conformal weights h(m) shifted by their mass. For integral values of h primary boundary operators are obtained as h normal derivatives of the scalar field. AdS2 string theories arise in the `very-near-horizon' limit of S1-compactified AdS3 string theories. This limit corresponds to energies far below the compactification scale. The dual conformal field theory has one null dimension and can in certain cases be described as the discrete light cone quantization of a two-dimensional deformed symmetric-product conformal field theory. Evidence is given that the AdS2 Virasoro algebra is related to the right-moving AdS3 Virasoro algebra by a topological twist which shifts the central charge to zero.
We study the possibility of experimental testing the manifestations of equivalence principle in spin-gravity interactions. We reconsider the earlier experimental data and get the first experimental bound on anomalous gravitomagnetic moment. The spin coupling to the Earth's rotation may also be explored at the extensions of neutron EDM and g-2 experiments. The spin coupling to the terrestrial gravity produces a considerable effect which may be discovered at the planned deuteron EDM experiment. The Earth's rotation should also be taken into account in optical experiments on a search for axionlike particles.
Two permutations of $[n]=\{1,2 \ldots n\}$ are \textit{$k$-neighbor separated} if there are two elements that are neighbors in one of the permutations and that are separated by exactly $k-2$ other elements in the other permutation. Let the maximal number of pairwise $k$-neighbor separated permutations of $[n]$ be denoted by $P(n,k)$. In a previous paper, the authors have determined $P(n,3)$ for every $n$, answering a question of K\"orner, Messuti and Simonyi affirmatively. In this paper we prove that for every fixed positive integer $\ell $, $$P(n,2^\ell+1) = 2^{n-o(n)}. $$ We conjecture that for every fixed even $k$, $P(n,k)=2^{n-o(n)}$. We also show that this conjecture is asymptotically true in the following sense $$\lim_{k \rightarrow \infty} \lim_{n \rightarrow \infty} \sqrt[n]{P(n,k)}=2.$$ Finally, we show that for even $n$, $P(n,n)= 3n/2$.
The $f(R)$ gravity can be cast into the form of a scalar-tensor theory, and scalar degree of freedom can be suppressed in high-density regions by the chameleon mechanism. In this article, for the general $f(R)$ gravity, using a scalar-tensor representation with the chameleon mechanism, we calculate the parameterized post-Newtonian parameters $\gamma$ and $\beta$, the effective gravitational constant $G_{\rm eff}$, and the effective cosmological constant $\Lambda_{\rm eff}$. In addition, for the general $f(R)$ gravity, we also calculate the rate of orbital period decay of the binary system due to gravitational radiation. Then we apply these results to specific $f(R)$ models (Hu-Sawicki model, Tsujikawa model and Starobinsky model) and derive the constraints on the model parameters by combining the observations in solar system, cosmological scales and the binary systems.
We discuss the uncertainty relation for the azimuthal angle $\phi$ and the $z$-component of the angular momentum $L_z$. To this end we derive the uncertainty relation for an arbitrary pair of observables and discuss the conditions for its validity. By means of a simple parameter-dependent state we illustrate the well known fact that the standard uncertainty relation for the coordinate and its conjugate momentum does not apply the pair of observables $\phi-L_z$. This analysis is motivated by a discussion of the motion of an electron in a constant magnetic field appeared recently in this journal (Eur. J. Phys. \textbf{33} (2012) 1147) where the author assumed the validity of the standard uncertainty relation for the pair $\phi-L_z$.
We consider a fractal refinement of the Carleson problem for the Schr\"odinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with respect to the $\alpha$-Hausdorff measure ($\alpha$-a.e.). We extend to the fractal setting ($\alpha < n$) a recent counterexample of Bourgain \cite{Bourgain2016}, which is sharp in the Lebesque measure setting ($\alpha = n$). In doing so we recover the necessary condition from \cite{zbMATH07036806} for pointwise convergence~$\alpha$-a.e. and we extend it to the range $n/2<\alpha \leq (3n+1)/4$.
It is generally believed that isospin would diminish in its importance as we go towards heavy mass region due to isospin mixing caused by the growing Coulomb forces. However, it was realized quite early that isospin could become an important and useful quantum number for all nuclei including heavy nuclei due to neutron richness of the systems~\cite{robson}. Lane and Soper~\cite{lane} also showed in a theoretical calculation that isospin indeed remains quite good in heavy mass neutron rich systems. In this paper, we present isospin based calculations~\cite{jain,swati} for the fission fragment distributions obtained from heavy-ion fusion fission reactions. We discuss in detail the procedure adopted to assign the isospin values and the role of neutron multiplicity data in obtaining the total fission fragment distributions. We show that the observed fragment distributions can be reproduced rather reasonably well by the calculations based on the idea of conservation of isospin. This is probably the very first direct experimental evidence of the validity of isospin in heavy nuclei, which arises largely due to the neutron-rich nature of heavy nuclei and their fragments. This result may eventually become useful for the theories of nuclear fission and also in other practical applications.
This paper is concerned with the quantitative homogenization of $2m$-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp $O(\varepsilon)$ convergence rate in $W^{m-1, p_0}$ with $p_0=\frac{2d}{d-1}$ in a bounded Lipschitz domain in $\mathbb{R}^d$ as well as the uniform large-scale interior $C^{m-1, 1}$ estimate. With additional smoothness assumptions, the uniform interior $C^{m-1, 1}$, $W^{m,p}$ and $C^{m-1, \alpha}$ estimates are also obtained. As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions.
Most neutron stars (NSs) and black holes (BHs) are believed to be the final remnants in the evolution of massive stars. In this study, we propose a new formation channel for the formation of BHs and peculiar NSs (specifically, magnetars and Thorne-$\dot{\rm Z}$ytkow objects [T$\dot{\rm Z}$Os]), which we refer to as the core merger-induced collapse (CMIC) model. This model involves the merger at the end of a common-envelope phase of an oxygen/neon/magnesium composition white dwarf and the core of a hydrogen-rich or helium-rich non-degenerate star, leading to the creation of peculiar new types of objects. The results of binary population synthesis simulations show that the CMIC channel could make important contributions to the populations of (millisecond) pulsars, T$\dot{\rm Z}$Os, magnetars and BHs. The possibility of superluminous supernovae powered by T$\dot{\rm Z}$Os, magnetars and BHs formed through the CMIC model is also being investigated. Magnetars with immediate matter surroundings formed after the CMIC might be good sources for fast radio bursts.
We summarize recent results regarding single and double soft theorems of two different particles named dilatons, the Nambu-Goldstone boson of the spontaneously broken conformal field theories and the massless scalar particle of the closed string theories. Similarities and differences between the soft theorems of these two particles are discussed as well as their connections with the symmetries of the theories.
The teleparallel $T_{4}$ version of Riemannian geometry of acoustic spacetime in rotating $2-D$ Bose-Einstein condensates (BEC) is investigated. An experiment is proposed on the basis of phonon ray trajectory around a vortex. The deviation geodesic equation may be expressed in terms of Cartan acoustic torsion. The Riemann curvature is computed in terms of rotation of the fluid. The geodesic deviation equation shows that the acoustic torsion acts locally as a diverging lens and the stream lines on opposite sides of the BEC vortex flow apart from each other. We also show that the Magnus field is cancelled when the acoustic torsion coincides with the rotation of the condensate. This effect is equivalent to the Meissner effect in superconductors. It is interesting to note how the teleparallel acoustic spacetime constrains the physical parameters in the BEC. Here we use the term acoustic torsion since in teleparallelism it is derived from the acoustic metric.
We present a resonant x-ray diffraction study of the magnetic order in NdFe$_3$(BO$_3$)$_4$ and its coupling to applied electric fields. Our high-resolution measurements reveal A coexistence of two different magnetic phases, which can be triggered effectively by external electric fields. More in detail, the volume fraction of the collinear magnetic phase is found to strongly increase at the expense of helically ordered regions when an electric field is applied. These results confirm that the collinear magnetic phase is responsible for the ferroelectric polarization of NdFe$_3$(BO$_3$)$_4$ and, more importantly, demonstrate that magnetic phase coexistence provides an alternative route towards materials with a strong magnetoelectric response.
Motivated by the recently observed hypernucleus (Kiso event) $^{15}_{\Xi}$C ($^{14}$N$+\Xi^-$), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme-Hartree-Fock models. The $\Xi N$ interactions are constructed to reproduce the two possibly observed $\Xi^-$ removal energies, $4.38\pm 0.25$ MeV or $1.11\pm 0.25$ MeV. The present result is preferable to be $^{14}{\rm N}({\rm g.s.})+\Xi^-(1p)$, corresponding to the latter value.
We propose new gauge invariant actions for open NS, heterotic NS, and closed NS-NS superstring field theories. They are based on the large Hilbert space, and have Wess-Zumino-Witten-like expressions which are the $\mathbb{Z}_{2}$-reversed versions of the conventional WZW-like actions. On the basis of the procedure proposed in arXiv:1505.01659, we show that our new WZW-like actions are completely equivalent to $A_{\infty }/L_{\infty }$ actions proposed in arXiv:1403.0940 respectively.
In this note, we combine the two approaches of Billingsley (1998) and Cs\H{o}rg\H{o} and R\'ev\'esz (1980), to provide a detailed sequential and descriptive for creating s standard Brownian motion, from a Brownian motion whose time space is the class of non-negative dyadic numbers. By adding the proof of Etemadi's inequality to text, it becomes self-readable and serves as an independent source for researches and professors.
Particle acceleration is one of the most significant features that are ubiquitous among space and cosmic plasmas. It is most prominent during flares in the case of the Sun, with which huge amount of electromagnetic radiation and high-energy particles are expelled into the interplanetary space through acceleration of plasma particles in the corona. Though it has been well understood that energies of flares are supplied by the mechanism called magnetic reconnection based on the observations in X-rays and EUV with space telescopes, where and how in the flaring magnetic field plasmas are accelerated has remained unknown due to the low plasma density in the flaring corona. We here report the first observational identification of the energetic non-thermal electrons around the point of the ongoing magnetic reconnection (X-point); with the location of the X-point identified by soft X-ray imagery and the localized presence of non-thermal electrons identified from imaging-spectroscopic data at two microwave frequencies. Considering the existence of the reconnection outflows that carries both plasma particles and magnetic fields out from the X-point, our identified non-thermal microwave emissions around the X-point indicate that the electrons are accelerated around the reconnection X-point. Additionally, the plasma around the X-point was also thermally heated up to 10 MK. The estimated reconnection rate of this event is ~0.017.
In this work, layered perovskite SBN was investigated in a new doped form for hole as well as electron transport layer (HTL/ETL) in perovskite solar cells. This work was targeted to conclude the effect of tin doping in lanthanum-bismuth layer SBN on optical energy band gap besides dominant electron-hole transportation to assist in perovskite solar cell applications. Thoroughly hard ball-milled compositions Sr1-xSnxBi1.95La0.05Nb2O9 (x=0.0, 0.01, 0.03, 0.05, 0.1 and 0.2) were prepared by special microwave synthesis to obtain fine (~10-60nm) mesoporous particle network of atomic level substitutions. Microwave synthesis was crucial in modifying dielectric, semiconducting and optical characteristics of prepared SBN materials. The band gap reduced in continuous manner and carrier mobility was increased by 112% for maximum tin doping. Nano particle formation assisted in raising carrier mobility by bridging bigger grains through nano particles. The effect of macro-sized grains and nano-sized grain boundaries on carrier transport were further investigated in detail using impedance spectroscopy.
We have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multi-point correlation function characterizing the ground state. This work presents a successful application of this procedure to the string order parameter of the S = 1 XXZ chain with uniaxial single-ion anisotropy. The finite-size string correlation function is estimated by the density matrix renormalization group method. We focus on the gradient of the inversedsystem- size dependence of the correlation function on a logarithmic plot. This quantity shows that the finite-size scaling sensitively changes at the critical point. The behavior of the gradient with increasing system size is divergent, stable at a finite value, or rapidly decreases to zero when the system is in the disordered phase, at the critical point, or in the ordered phase, respectively. The analysis of the finite-size string correlation functions allows precise determination of the boundary of the Haldane phase and estimation of the critical exponent of the correlation length. Our estimates of the transition point and the critical exponents, which are determined only by the ground-state quantities, are consistent with results obtained from the analysis of the energy-level structure. Our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long-range order. The quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned. This work will assist in the development of a method to directly observe quantum phase transitions.
The oscillating magnetic interlayer coupling of Fe over spacer layers consisting of Cu$_{x}$Pd$_{1-x}$ alloys is investigated by first principles density functional theory. The amplitude, period and phase of the coupling, as well as the disorder-induced decay, are analyzed in detail and the consistency to the Ruderman-Kittel-Kasuya-Yoshida (RKKY) theory is discussed. For the first time an effect of the Fermi surface nesting strength on the amplitude is established from first principles calculations. An unexpected variation of the phase and disorder-induced decay is obtained and the results are discussed in terms of asymptotics.
Radio observations were used to detect the `active' galaxy population within rich clusters of galaxies in a non-biased manner that is not plagued by dust extinction or the K-correction. We present wide-field radio, optical (imaging and spectroscopy), and ROSAT All-Sky Survey (RASS) X-ray data for a sample of 30 very rich Abell (R > 2) cluster with z < 0.25. The VLA radio data samples the ultra-faint radio (L(1.4 GHz) > 2E22 W/Hz) galaxy population within these extremely rich clusters for galaxies with M_R < -21. This is the largest sample of low luminosity 20 cm radio galaxies within rich Abell clusters collected to date. The radio-selected galaxy sample represents the starburst (Star formation rate > 5 M_sun/yr) and active galactic nuclei (AGN) populations contained within each cluster. Archival and newly acquired redshifts were used to verify cluster membership for most (~95%) of the optical identifications. Thus we can identify all the starbursting galaxies within these clusters, regardless of the level of dust obscuration that would affect these galaxies being identified from their optical signature. Cluster sample selection, observations, and data reduction techniques for all wavelengths are discussed.