ShantanuT01/DACTYL-Pretraining huggingface dataset:
We analyse two new versions of \theta-expanded non-commutative quantum electrodynamics up to first order in \theta and first loop order. In the first version we expand the bosonic sector using the Seiberg-Witten map, leaving the fermions unexpanded. In the second version we leave both bosons and fermions unexpanded. The analysis shows that the Seiberg-Witten map is a field redefinition at first order in \theta. However, at higher order in \theta the Seiberg-Witten map cannot be regarded as a field redefinition. We find that the initial action of any \theta-expanded massless non-commutative QED must include one extra term proportional to \theta which we identify by loop calculations.
We consider point sets in $\mathbb{Z}_n^2$ where no three points are on a line - also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small $n$.
We consider long-time behavior of dynamical systems perturbed by a small noise. Under certain conditions, a slow component of such a motion, which is most important for long- time evolution, can be described as a motion on the cone of invariant measures of the non- perturbed system. The case of a finite number of extreme points of the cone is considered in this paper. As is known, in the generic case, the long-time evolution can be described by a hierarchy of cycles defined by the action functional for corresponding stochastic processes. This, in particular, allows to study metastable distributions and such effects as stochastic resonance. If the system has some symmetry in the logarithmic asymptotics of transition probabilities (rough symmetry),the hierarchy of cycles should be replaced by a hierarchy of Markov chains and their invariant measures.
Primordial or big bang nucleosynthesis (BBN) is one of the three historical strong evidences for the big bang model. The recent results by the Planck satellite mission have slightly changed the estimate of the baryonic density compared to the previous WMAP analysis. This article updates the BBN predictions for the light elements using the cosmological parameters determined by Planck, as well as an improvement of the nuclear network and new spectroscopic observations. There is a slight lowering of the primordial Li/H abundance, however, this lithium value still remains typically 3 times larger than its observed spectroscopic abundance in halo stars of the Galaxy. According to the importance of this "lithium problem", we trace the small changes in its BBN calculated abundance following updates of the baryonic density, neutron lifetime and networks. In addition, for the first time, we provide confidence limits for the production of 6Li, 9Be, 11B and CNO, resulting from our extensive Monte Carlo calculation with our extended network. A specific focus is cast on CNO primordial production. Considering uncertainties on the nuclear rates around the CNO formation, we obtain CNO/H \approx (5-30) x 10^{-15}. We further improve this estimate by analyzing correlations between yields and reaction rates and identified new influential reaction rates. These uncertain rates, if simultaneously varied could lead to a significant increase of CNO production: CNO/H \sim 10^{-13}. This result is important for the study of population III star formation during the dark ages.
We present new X-ray (Chandra) and radio (ATCA) observations of the z=0.09 radio galaxy PKS B1416-493, a member of the southern equivalent of the 3CRR sample. We find the source to be embedded in a previously unrecognized bright kT=4.6 keV non cool-core cluster. The discovery of new clusters of such high temperature and luminosity within z=0.1 is rare. The radio source was chosen for observation based on its intermediate FRI/II morphology. We identify a cavity coincident with the northeast lobe, and excess counts associated with the southwest lobe that we interpret as inverse Compton X-ray emission. The jet power, at 5.3 x 10^44 erg/s, when weighted by radio source density, supports suggestions that radio sources of intermediate morphology and radio power may dominate radio-galaxy heating in the local Universe.
We examine the dissipative dynamics of N00N states with an arbitrary photon number N in two architectures of fiber-coupled optical ring resonators (RRs) interacting with two-level quantum emitters. One architecture consists of a two-way cascaded array of emitter-cavity systems, while in the other architecture we consider two fiber-coupled RRs each coupled to multiple dipole-dipole interacting (DDI) quantum emitters (QEs). Our focus in this paper is to study how am initially prepared multiple excitation atomic N00N states transfers to the RRs and then how rapidly it decays in these open cavity quantum electrodynamics (CQED) setups while varying the emitter-cavity coupling strengths, emitter-cavity detuning, and backscattering from cavity modes. We present a general theoretical formalism valid for any arbitrary numbers of QEs, RRs, and N number in the N00N state for both schemes. As examples, we discuss the cases of single and two-excitation N00N states and report the comparison of our findings in both schemes. As one of the main results, we conclude that the array scheme tends to store N00N for longer times while the DDI scheme supports higher fidelity values. The results of this study may find applications in designing new multiparty entanglement-based protocols in quantum metrology and quantum lithography.
Motivated by the close analogy with the fractional quantum Hall states (FQHSs), fractional Chern insulators (FCIs) are envisioned as strongly correlated, incompressible states emerging in a fractionally filled, (nearly) flat band with non-trivial Chern number. Built upon this vision, fractional topological insulators (FTIs) have been proposed as being composed of two independent copies of the FCI with opposite Chern numbers for different spins, preserving the time-reversal symmetry as a whole. An important question is if the correlation between electrons with different spins can be really ignored. To address this question, we investigate the effects of correlation in the presence of spin-dependent holomorphicity, i.e., electrons of one spin species reside in the holomorphic lowest Landau level, while those of the other in the antiholomorphic counterpart. By constructing and performing exact diagonalization of an appropriate model Hamiltonian, here, we show that generic, strongly correlated, fractionally filled states with spin-dependent holomorphicity cannot be described as two independent copies of the FQHS, suggesting that FTIs in the lattice cannot be described as those of the FCI either. Fractionally filled states in this system are generally compressible except at half filling, where an insulating state called the half-filled spin-holomorphic FTI occurs. It is predicted that the half-filled spin-holomorphic FTI is susceptible to an inherent spontaneous symmetry breaking, leading to the spatial separation of spins.
Solar flares are one of the most energetic events in the solar atmosphere. It is widely accepted that flares are powered by magnetic reconnection in the corona. An eruptive flare is usually accompanied by a coronal mass ejection, both of which are probably driven by the eruption of a magnetic flux rope (MFR). Here we report an eruptive flare on 2016 March 23 observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The extreme-ultraviolet imaging observations exhibit the clear rise and eruption of an MFR. In particular, the observations reveal solid evidence for magnetic reconnection from both the corona and chromosphere during the flare. Moreover, weak reconnection is observed before the start of the flare. We find that the preflare weak reconnection is of tether-cutting type and helps the MFR to rise slowly. Induced by a further rise of the MFR, strong reconnection occurs in the rise phases of the flare, which is temporally related to the MFR eruption. We also find that the magnetic reconnection is more of 3D-type in the early phase, as manifested in a strong-to-weak shear transition in flare loops, and becomes more 2D-like in the later phase, as shown by the apparent rising motion of an arcade of flare loops.
We consider electrostatically coupled quantum dots in topological insulators, otherwise confined and gapped by a magnetic texture. By numerically solving the (2+1) Dirac equation for the wave packet dynamics, we extract the energy spectrum of the coupled dots as a function of bias-controlled coupling and an external perpendicular magnetic field. We show that the tunneling energy can be controlled to a large extent by the electrostatic barrier potential. Particularly interesting is the coupling via Klein tunneling through a resonant valence state of the barrier. The effective three-level system nicely maps to a model Hamiltonian, from which we extract the Klein coupling between the confined conduction and valence dots levels. For large enough magnetic fields Klein tunneling can be completely blocked due to the enhanced localization of the degenerate Landau levels formed in the quantum dots.
We study the local topological zeta function associated to a complex function that is holomorphic at the origin of C^2 (respectively C^3). We determine all possible poles less than -1/2 (respectively -1). On C^2 our result is a generalization of the fact that the log canonical threshold is never in ]5/6,1[. Similar statements are true for the motivic zeta function.
In this paper, we consider the averaging principle for a class of McKean-Vlasov stochastic differential equations with slow and fast time-scales. Under some proper assumptions on the coefficients, we first prove that the slow component strongly converges to the solution of the corresponding averaged equation with convergence order $1/3$ using the approach of time discretization. Furthermore, under stronger regularity conditions on the coefficients, we use the technique of Poisson equation to improve the order to $1/2$, which is the optimal order of strong convergence in general.
We have conducted sensitive (1 sigma<30 uJy) 1.4 GHz radio observations with the Australia Telescope Compact Array of a field largely coincident with infrared observations of the Spitzer Wide-Area Extragalactic Survey. The field is centred on the European Large Area ISO Survey S1 region and has a total area of 3.9 deg. We describe the observations and calibration, source extraction, and cross-matching to infrared sources. Two catalogues are presented; one of the radio components found in the image and one of radio sources with counterparts in the infrared and extracted from the literature. 1366 radio components were grouped into 1276 sources, 1183 of which were matched to infrared sources. We discover 31 radio sources with no infrared counterpart at all, adding to the class of Infrared-Faint Radio Sources.
In the paper Sato (2006) there are introduced two families of improper random integrals and the corresponding two convolution semigroups of infinitely divisible laws on $\Rset^d$. Theorem 3.1 gives a relation (a factorization property) between those two integrals. Here, using \emph{the random integral mappings} $I^{h,r}_{(a,b]}$ (cf. the survey article Jurek (2011)), we give a simpler proof that is also valid for measures on Banach spaces. Furthermore, using our technique we establish yet other relations between those two families of improper stochastic integrals.
We analytically study the non-linear stability of a spherically symmetric wormhole supported by an infinitesimally thin brane of negative tension, which has been devised by Barcelo and Visser. We consider a situation in which a thin spherical shell composed of dust falls into an initially static wormhole; The dust shell plays a role of the non-linear disturbance. The self-gravity of the falling dust shell is completely taken into account through Israel's formalism of the metric junction. When the dust shell goes through the wormhole, it necessarily collides with the brane supporting the wormhole. We assume the interaction between these shells is only gravity and show the condition under which the wormhole stably persists after the dust shell goes through it.
Ab initio electronic structure calculations based on density functional theory and tight-binding methods for the thermoelectric properties of p-type Sb$_2$Te$_3$ films are presented. The thickness-dependent electrical conductivity and the ther- mopower are computed in the diffusive limit of transport based on the Boltzmann equation. Contributions of the bulk and the surface to the transport coefficients are separated which enables to identify a clear impact of the topological surface state on the thermoelectric properties. By tuning the charge carrier concentration, a crossover between a surface-state-dominant and a Fuchs-Sondheimer transport regime is achieved. The calculations are corroborated by thermoelectric transport measurements on Sb$_2$Te$_3$ films grown by atomic layer deposition.
Let $C\subset \mathbb {P}^n$ be a smooth curve and $N_C$ its normal bundle. $N_C$ satisfies strong interpolation if for all integers $s>0$ and $\lambda _i\in \{0,1,\dots ,n-1\}$, $1\le i \le s$, there are distinct points $P_1,\dots ,P_s\in C$ and linear subspaces $U_i\subseteq E|P_i$ such that $\dim (U_i)= \lambda _i$ for all $i$ and the evaluation map $H^0(E)\to \oplus _{i=1}^{s} U_i$ has maximal rank (A. Atanasios). We prove that $C$ satisfies strong interpolation if either $C$ is a linearly normal elliptic curve or $C$ is a general embedding of degree $d\ge (5n-8)g+2n^2-5n+4$ of a smooth curve $X$ of genus $g\ge 2$.
In this article, we summarize two agnostic approaches in the framework of spatially curved Friedmann-Robertson-Walker (FRW) cosmologies discussed in detail in (Kerachian et al., 2020, 2019). The first case concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS), for which the only assumption made is the non-negativity of the fluid's energy density. The second case concerns the dynamics of a non-minimally coupled real scalar field with unspecified positive potential. For each of these models, we define a new set of dimensionless variables and a new evolution parameter. In the framework of these agnostic setups, we are able to identify several general features, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation.
We show that the quantum super-minisuperspace of N=1 supergravity with $\Lambda \ne 0 $ has no non-trivial physical states for class A Bianchi models. Hence, in super quantum cosmology, the vanishing of $\Lambda$ is a condition for the existence of the universe. We argue that this result implies that in full supergravity with $\Lambda$ there are no non-trivial physical states with a finite number of fermionic fields. We use the Jacobson canonical formulation.
We carry out an analytic study of odd-parity perturbations of the self-similar Vaidya space-times that admit a naked singularity. It is found that an initially finite perturbation remains finite at the Cauchy horizon. This holds not only for the gauge invariant metric and matter perturbation, but also for all the gauge invariant perturbed Weyl curvature scalars, including the gravitational radiation scalars. In each case, `finiteness' refers to Sobolev norms of scalar quantities on naturally occurring spacelike hypersurfaces, as well as pointwise values of these quantities.
We propose a simple, fast, and accurate one-stage approach to visual grounding, inspired by the following insight. The performances of existing propose-and-rank two-stage methods are capped by the quality of the region candidates they propose in the first stage --- if none of the candidates could cover the ground truth region, there is no hope in the second stage to rank the right region to the top. To avoid this caveat, we propose a one-stage model that enables end-to-end joint optimization. The main idea is as straightforward as fusing a text query's embedding into the YOLOv3 object detector, augmented by spatial features so as to account for spatial mentions in the query. Despite being simple, this one-stage approach shows great potential in terms of both accuracy and speed for both phrase localization and referring expression comprehension, according to our experiments. Given these results along with careful investigations into some popular region proposals, we advocate for visual grounding a paradigm shift from the conventional two-stage methods to the one-stage framework.
Emission line observations of circumnuclear gas disks in the ALMA era have begun to resolve molecular gas tracer kinematics near supermassive black holes (BHs), enabling highly precise mass determination in the best cases. The ngVLA is capable of extremely high spatial resolution imaging of the CO(1-0) transition at 115 GHz for nearby galaxies. Furthermore, its high (anticipated) emission line sensitivity suggests this array can produce benchmark BH mass measurements. We discuss lessons learned from gas-dynamical modeling of recent ALMA data sets and also compare ALMA and ngVLA CO simulations of a dynamically cold disk. While only a fraction of all local galaxies likely possess sufficiently bright, regularly-rotating nuclear molecular gas, in such cases the ngVLA is expected to more efficiently resolve such emission arising at a projected 50-100 mas from the central BH.
In this paper, we study finite symplectic actions on K3 surfaces X, i.e. actions of finite groups G on X which act on H^{2,0}(X) trivially. We show that the action on the K3 lattice H^2(X,Z) induced by a symplectic action of G on X depends only on G up to isomorphism, except for five groups.
We study the X-ray variability of SS433 based on data from the ASCA observatory and the MAXI and RXTE/ASM monitoring missions. Based on the ASCA data, we have constructed the power spectrum of SS433 in the frequency range from $10^{-6}$ to 0.1 Hz, which confirms the presence of a flat portion (flat-topped noise) in the spectrum at frequencies $3\times 10^{-5}$ - $10^{-3}$ Hz. The periodic variability (precession, nutation, eclipses) begins to dominate significantly over the stochastic variability at lower frequencies, which does not allow the stochastic variability to be studied reliably. The best agreement with the observations is reached by the model with the flat portion extending to $9.5\times10^{-6}$ Hz and a power-law spectrum with index of 2.6 below that frequency. The jet nutation with a period of about three days suggests that the time for the passage of material through the disk is less than this value. Therefore, at frequencies below $4\times10^{-6}$ Hz, the power spectrum probably does not reflect the disk structure. It may depend on other factors, for example, a variable mass accretion rate supplied by the donor. The flat portion may arise from a rapid decrease in the viscous time in the supercritical or radiative disk zones. It could be related to the variability of the X-ray jets that are formed in the supercritical region.
Consider weakly nonlinear complex Ginzburg--Landau (CGL) equation of the form: $$ u_t+i(-\Delta u+V(x)u)=\epsilon\mu\Delta u+\epsilon \mathcal{P}( u),\quad x\in {R^d}\,, \quad(*)   $$ under the periodic boundary conditions, where $\mu\geqslant0$ and $\mathcal{P}$ is a smooth function. Let $\{\zeta_1(x),\zeta_2(x),\dots\}$ be the $L_2$-basis formed by eigenfunctions of the operator $-\Delta +V(x)$. For a complex function $u(x)$, write it as $u(x)=\sum_{k\geqslant1}v_k\zeta_k(x)$ and set $I_k(u)=\frac{1}{2}|v_k|^2$. Then for any solution $u(t,x)$ of the linear equation $(*)_{\epsilon=0}$ we have $I(u(t,\cdot))=const$. In this work it is proved that if equation $(*)$ with a sufficiently smooth real potential $V(x)$ is well posed on time-intervals $t\lesssim \epsilon^{-1}$, then for any its solution $u^{\epsilon}(t,x)$, the limiting behavior of the curve $I(u^{\epsilon}(t,\cdot))$ on time intervals of order $\epsilon^{-1}$, as $\epsilon\to0$, can be uniquely characterized by a solution of a certain well-posed effective equation: $$ u_t=\epsilon\mu\triangle u+\epsilon F(u), $$ where $F(u)$ is a resonant averaging of the nonlinearity $\mathcal{P}(u)$. We also prove a similar results for the stochastically perturbed equation, when a white in time and smooth in $x$ random force of order $\sqrt\epsilon$ is added to the right-hand side of the equation.   The approach of this work is rather general. In particular, it applies to equations in bounded domains in $R^d$ under Dirichlet boundary conditions.
In this article, we consider the basic contact process in a static random environment on the half space $Z^d\times Z^+$ where the recovery rates are constants and the infection rates are independent and identically distributed random variables. We show that, for almost every environment, the complete convergence theorem holds. This is a generalization of the known result for the classical contact process in the half space case.
We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra process $(y_t)_{t\geq 0}$ in the rough path topology. As an application, we establish weak convergence as $\varepsilon\to 0$ of the solution of the random ordinary differential equation (ODE) $\frac{d}{dt}x^\varepsilon_t=\frac{1}{\sqrt \varepsilon} f(x_t^\varepsilon,y_{\frac{t}{\varepsilon}})$ and show that its limit solves a rough differential equation driven by a Gaussian field with a drift coming from the L\'evy area correction of the limiting rough driver. Furthermore, we prove that the stochastic flows of the random ODE converge to those of the Kunita type It\^o SDE $dx_t=G(x_t,dt)$, where $G(x,t)$ is a semi-martingale with spatial parameters.
We show that a two-dimensional (2D) isotropic Fermi liquid harbors two new types of collective modes, driven by quantum fluctuations, in addition to conventional zero sound: "hidden" and "mirage" modes. The hidden modes occur for relatively weak attractive interaction both in the charge and spin channels with any angular momentum $l$. Instead of being conventional damped resonances within the particle-hole continuum, the hidden modes propagate at velocities larger than the Fermi velocity and have infinitesimally small damping in the clean limit, but are invisible to spectroscopic probes. The mirage modes are also propagating modes outside the particle-hole continuum that occur for sufficiently strong repulsion interaction in channels with $l\geq 1$. They do give rise to peaks in spectroscopic probes, but are not true poles of the dynamical susceptibility. We argue that both hidden and mirage modes occur due to a non-trivial topological structure of the Riemann surface, defined by the dynamical susceptibility. The hidden modes reside below a branch cut that glues two sheets of the Riemann surface, while the mirage modes reside on an unphysical sheet of the Riemann surface. We show that both types of modes give rise to distinct features in time dynamics of a 2D Fermi liquid that can be measured in pump-probe experiments.