ShantanuT01/DACTYL-Pretraining huggingface dataset:
The presence of two photon exchange in $ep$ elastic scattering and in the crossed processes ($\bar p +p\leftrightarrow \ell^+ +\ell^-$, $\ell=e$ or $\mu$) is discussed in terms of three complex amplitudes which are functions of two kinematical variables, the momentum transfer squared $q^2$ and the polarization of the virtual photon, $\epsilon$. Model independent expressions of the differential cross section and of polarization observables are derived. Particular attention is devoted to the extraction of hadron electromagnetic form factors which becomes much more difficult in presence of two photon exchange, and to the relevant experimental observables which could give evidence for such mechanism.
This paper aims to invalidate the hypothesis that consciousness is necessary for the quantum measurement process. To achieve this target, I propose a considerable modification of the Schroedinger cat and the Dead-Alive Physicist thought experiments, called 'PIAR', short for Physicist Inside the Ambiguous Room. A specific strategy has enabled me to plan the experiment in such a way as to logically justify the inconsistency of the above hypothesis and to oblige its supporters to rely on an alternative interpretation of quantum mechanics in which the real-world phenomena exist independently of our conscious mind and where observers play no special role. Moreover, in my description, the measurement apparatus will be complete, in the sense that the experiment, given that it includes also the experimenter, will begin and end exclusively within a sealed room. Hence, my analysis provides a logical explanation of the relationship between the observer and the objects of her/his experimental observation; this and a few other implications are discussed in the fifth section and the conclusions.
We have developed an efficient isospin projection method in the shell model Monte Carlo approach for isospin-conserving Hamiltonians. For isoscalar observables this projection method has the advantage of being exact sample by sample. The isospin projection method allows us to take into account the proper isospin dependence of the nuclear interaction, thus avoiding a sign problem that such an interaction introduces in unprojected calculations. We apply our method in the calculation of the isospin dependence of level densities in the complete $pf+g_{9/2}$ shell. We find that isospin-dependent corrections to the total level density are particularly important for $N \sim Z$ nuclei.
It is possible that narrow-line Seyfert 1 galaxies (NLS1s) are in the early stage of active galactic nuclei (AGNs) evolution. It is important to estimate the mass of supermassive black hole (SBH) in NLS1s. Here we considered the different kinds of methods to estimate the SBH masses in NLS1s. The virial mass from the H$\beta$ linewidth assuming random orbits of broad line regions (BLRs) is consistent with that from the statured soft X-ray luminosity, which showed that most of NLS1s are in the super-Eddington accretion state. The mass from the [O III] linewidth is systematically larger than that from above two methods. It is necessary to measure he bulge stellar dispersion and/or bulge luminosity in NLS1s.
We show that the numerical renormalization group (NRG) is a viable multi-band impurity solver for Dynamical Mean Field Theory (DMFT), offering unprecedent real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund's metal problem for a three-orbital model with filling factor $n_d=2$. The ground state is a Fermi liquid. The one-particle spectral function has a strong particle-hole asymmetry, with a clear apparent power law for positive frequencies only. With increasing temperature it shows a coherence-incoherence crossover with spectral weight transfered from low to high energies and evolves qualitatively differently from a doped Mott insulator. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.
Theoretical study of systematics of neutron scattering cross sections on various materials for neutron energies up to several hundred MeV are of practical importance. In this paper, we analysed the experimental neutron scattering total cross sections from 20MeV to 550MeV using Ramsauer model for nuclei ranging from Be to Pb.
We consider a vector-valued blow-up solution with values in $\mathbb{R}^m$ for the semilinear wave equation with power nonlinearity in one space dimension (this is a system of PDEs). We first characterize all the solutions of the associated stationary problem as an m-parameter family. Then, we show that the solution in self-similar variables approaches some particular stationary one in the energy norm, in the non-characteristic cases. Our analysis is not just a simple adaptation of the already handled real or complex case. In particular, there is a new structure of the set a stationary solutions.
We present a new exact treatment of $T\bar{T}$ deformed 2D CFT in terms of the worldsheet theory of a non-critical string. The transverse dimensions of the non-critical string are represented by the undeformed CFT, while the two longitudinal light-cone directions are described by two scalar fields $X^+$ and $X^-$ with free field OPE's but with a modified stress tensor, arranged so that the total central charge adds up to 26. The relation between our $X^\pm$ field variables and 2D dilaton gravity is indicated. We compute the physical spectrum and the partition function and find a match with known results. We describe how to compute general correlation functions and present an integral expression for the three point function, which can be viewed as an exact formula for the OPE coefficients of the $T\bar{T}$ deformed theory. We comment on the relationship with other proposed definitions of local operators.
We calculate the physical mass and the width of the sigma meson by considering that it couples in vacuum to two virtual pions. The mass is calculated by using the spectral function, and we find that it is about 600MeV. In addition, we obtained the value of 250MeV for the width of its spectral function. The value obtained for the mass, is in an excellent agreement with that reported in the Particle data Book for the sigma meson, which is also named f0(600). This result also shows that the sigma meson can be considered as a two pion resonance.
We investigate two sympathetic filament eruptions observed by the New Vacuum Solar Telescope (NVST) on 2015 October 15. The full picture of the eruptions is obtained from the corresponding SDO/AIA observations. The two filaments start from active region NOAA 12434 in the north and end in one large quiescent filament channel in the south. The left filament erupts firstly, followed by the right filament eruption about 10 minutes later. Clear twist structure and rotating motion are observed in both filaments during the eruption. Both eruptions are failed, since the filaments firstly rise up, then flow towards the south and merge into the southern large quiescent filament. We also observe repeating activations of mini filaments below the right filament after its eruption. Using magnetic field models constructed based on SDO/HMI magnetograms by flux rope insertion method, we find that the left filament eruption is likely to be triggered by kink instability, while weakening of overlying magnetic fields due to magnetic reconnection at an X-point between the two filament systems might play an important role in the onset of the right filament eruption.
Recent detections of GeV photons in a few GRBs by Fermi-LAT imply huge bulk Lorentz factors to avoid a large gamma gamma optical depth at high energy. Estimates can be as high as Gamma ~ 1000 in the most extreme cases. This puts severe constraints on models of the central engine and the jet acceleration in GRBs. These estimates are however obtained from a simplified single zone model. We present here a more realistic calculation which takes into account the time, space and direction dependent photon field existing in an outflow with several relativistically moving emitting zones. The formalism is general and can be applied to many models of the prompt GRB emission. We present results obtained for a numerical implementation in the framework of the internal shock model. We show that (i) the minimum Lorentz factor Gamma_min in bright LAT GRBs is reduced by a factor ~ 2-3 compared to previous estimates if the GeV and MeV emission are produced in the same region, and by an additional factor ~ 2-8 if the GeV emission is produced at larger radii. We provide an improved approximate formula for Gamma_min which is in good agreement with our numerical results and can be directly applied to LAT GRB data; (ii) a delayed GeV onset can be due to the time evolution of the opacity. As an illustration of these two first results, we present a synthetic GRB that reproduces most features of GRB 080916C with a mean Lorentz factor of ~ 340, an optically thin regime for gamma gamma opacity at 3GeV in bin 'b', a variability timescale of 0.5s in the MeV lightcurve and a delayed onset of ~ 5s of the GeV emission; (iii) the gamma gamma opacity can smooth the short timescale variability in the GeV lightcurve. This last result implies that the observed variability at high energy is not necessarily a good test to distinguish between an internal and an external origin for the GeV emission in GRBs. [abridged]
We adapt our previous results for the ``partition function'' of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{-\alpha H}, where H is the associated hamiltonian. The spontaneous magnetization M_r can be expressed in terms of particular matrix elements of e^{-\alpha H} S^r_1 \e^{-\beta H}, where S_1 is a diagonal matrix.We present a conjecture for these matrix elements as an m by m determinant, where m is proportional to the width of the lattice. The author has previously derived the spontaneous magnetization of the chiral Potts model by analytic means, but hopes that this work will facilitate a more algebraic derivation, similar to that of Yang for the Ising model.
Theoretical calculations, based on hybrid exchange density functional theory, are used to show that in graphene a periodic array of defects generates a ferromagnetic ground state at room temperature for unexpectedly large defect separations. This is demonstrated for defects that consist of a carbon vacancy in which two of the dangling bonds are saturated with H atoms. The magnetic coupling mechanism is analysed and found to be due to an instability in the $\pi$ electron system with respect to a long-range spin polarisation characterised by alternation in the spin direction between adjacent carbon atoms. The disruption of the $\pi$-bonding opens a semiconducting gap at the Fermi edge. The size of the energy gap and the magnetic coupling strength are strong functions of the defect separation and can thus be controlled by varying the defect concentration. The position of the semiconducting energy gap and the electron effective mass are strongly spin-dependent and this is expected to result in a spin asymmetry in the transport properties of the system. A defective graphene sheet is therefore a very promising material with an in-built mechanism for tailoring the properties of the spintronic devices of the future.
The infinite dimensional half-filled Hubbard model can be mapped exactly with no additional constraint onto a model of free fermions coupled in a $Z_2$ gauge-invariant manner to auxiliary Ising spins in a transverse field. In this slave-spin representation, the zero-temperature insulator-to-metal transition translates into spontaneous breaking of the local $Z_2$ gauge symmetry, which is not forbidden in infinite dimensions, thus endowing the Mott transition of an order parameter that is otherwise elusive in the original fermion representation. We demonstrate this interesting scenario by exactly solving the effective spin-fermion model by dynamical mean-field theory both at zero and at finite temperature.
We study the distribution of particle number in extended subsystems of a one-dimensional non-interacting Fermi gas confined in a potential well at zero temperature. Universal features are identified in the scaled bulk and edge regions of the trapped gas where the full counting statistics are given by the corresponding limits of the eigenvalue statistics in Gaussian unitary random matrix ensembles. The universal limiting behavior is confirmed by the bulk and edge scaling of the particle number fluctuations and the entanglement entropy.
We present near-IR observations of the 2010 outburst of U Sco. JHK photometry is presented on ten consecutive days starting from 0.59 days after outburst. Such photometry can gainfully be integrated into a larger database of other multi-wavelength data which aim to comprehensively study the evolution of U Sco. Early near-IR spectra, starting from 0.56 days after outburst, are presented and their general characteristics discussed. Early in the eruption, we see very broad wings in several spectral lines, with tails extending up to ~10000km/s along the line of sight; it is unexpected to have a nova with ejection velocities equal to those usually thought to be exclusive to supernovae. From recombination analysis, we estimate an upper limit of 10^-4.64[+0.92.-0.74]Msun for the ejected mass.
Significant progress has been made recently in our understanding of the structure of stellar magnetic fields, thanks to advances in detection methods such as Zeeman-Doppler Imaging. The extrapolation of this surface magnetic field into the corona has provided 3D models of the coronal magnetic field and plasma. This method is sensitive mainly to the magnetic field in the bright regions of the stellar surface. The dark (spotted) regions are censored because the Zeeman signature there is suppressed. By modelling the magnetic field that might have been contained in these spots, we have studied the effect that this loss of information might have on our understanding of the coronal structure. As examples, we have chosen two stars (V374 peg and AB Dor) that have very different magnetograms and patterns of spot coverage. We find that the effect of the spot field depends not only on the relative amount of flux in the spots, but also its distribution across the stellar surface. For a star such as AB Dor with a high spot coverage and a large polar spot, at its greatest effect the spot field may almost double the fraction of the flux that is open (hence decreasing the spindown time) while at the same time increasing the X-ray emission measure by two orders of magnitude and significantly affecting the X-ray rotational modulation.
High-precision sensing of vectorial forces has broad impact on both fundamental research and technological applications such as the examination of vacuum fluctuations \cite{casimir09rmp} and the detection of surface roughness of nanostructures \cite{RevModPhys.89.035002}. Recent years have witnessed much progress on sensing alternating electromagnetic forces for the rapidly advancing quantum technology -- orders-of-magnitude improvement has been accomplished on the detection sensitivity with atomic sensors \cite{Schreppler1486,Shaniv2017,Gilmore673}, whereas precision measurement of static {electromagnetic} forces lags far behind with the corresponding long-term stability rarely demonstrated. Here, based on quantum atomic matter waves confined by an optical lattice, we perform precision measurement of static {electromagnetic} forces by imaging coherent wave mechanics in the reciprocal space. We achieve a state-of-the-art measurement sensitivity of $ 2.30(8)\times 10^{-26}$ N/$\sqrt{\rm \bf Hz}$. Long-term stabilities on the order of $10^{-28}$ N are observed in the two spatial components of a force, which allows probing atomic Van der Waals forces at a millimeter distance \cite{NatureNanoScanning}. As a further illustrative application, we use our atomic sensor to calibrate the control precision of an alternating electromagnetic force applied in the experiment. Future developments of our method hold promise for delivering unprecedented atom-based quantum force sensing technologies.
In this article, we study the order of vanishing and a quantitative form of Landis' conjecture in the plane for solutions to second-order elliptic equations with variable coefficients and singular lower order terms. Precisely, we let $A$ be real-valued, bounded and elliptic, but not necessary symmetric or continuous, and we assume that $V$ and $W_i$ are real-valued and belong to $L^p$ and $L^{q_i}$, respectively. We prove that if $u$ is a real-valued, bounded and normalized solution to an equation of the form $-\nabla \cdot (A \nabla u + W_1 u) + W_2 \cdot \nabla u + V u = 0$ in $B_d$, then under suitable conditions on the lower order terms, for any $r$ sufficiently small, the following order of vanishing estimate holds $$\|u\|_{L^\infty(B_r)} \ge r^{C M},$$ where $M$ depends on the Lebesgue norms of the lower order terms. In a number of settings, a scaling argument gives rise to a quantitative form of Landis' conjecture, \[ \inf_{|z_0| = R} \|u\|_{L^\infty(B_1(z_0))} \ge \exp(- C R^\beta \log R), \] where $\beta$ depends on $p$, $q_1$, and $q_2$. The integrability assumptions that we impose on $V$ and $W_i$ are nearly optimal in view of a scaling argument. We use the theory of elliptic boundary value problems to establish the existence of positive multipliers associated to the elliptic equation. Then the proofs rely on transforming the equations to Beltrami systems and applying a generalization of Hadamard's three-circle theorem.
We show that at second order, ensemble averages of observables and directional averages do not commute due to gravitational lensing -- observing the same thing in many directions over the sky is not the same as taking an ensemble average. In principle this non-commutativity is significant for a variety of quantities that we often use as observables and can lead to a bias in parameter estimation. We derive the relation between the ensemble average and the directional average of an observable, at second order in perturbation theory. We discuss the relevance of these two types of averages for making predictions of cosmological observables, focusing on observables related to distances and magnitudes. In particular, we show that the ensemble average of the distance in a given observed direction is increased by gravitational lensing, whereas the directional average of the distance is decreased. For a generic observable, there exists a particular function of the observable that is not affected by second-order lensing perturbations. We also show that standard areas have an advantage over standard rulers, and we discuss the subtleties involved in averaging in the case of supernova observations.
Total derivative terms play an important role in the integration of conformal anomaly. In four dimensional space $4D$ there is only one such term, namely $\,{\square}R$. In the case of six dimensions $6D$ the structure of surface terms is more complicated, and it is useful to construct a basis of linear independent total derivative terms. We briefly review the general scheme of integrating anomaly and present the reduction of the minimal set of the surface terms in $6D$ from eight to seven.
Direct transitions, driven by disorder, from several integral quantum Hall states to an insulator have been observed in experiment. This finding is enigmatic in light of a theoretical phase diagram, based on rather general considerations, that predicts a sequence of transitions in which the integer $n$ characterizing the Hall conductivity is reduced successively by unity, eventually going from $n=1$ into an insulator. In this work, we suggest that the direct transition occurs because, in certain parameter regime, the edge states of different Landau levels are strongly coupled and behave as a single edge state. It is indicated under what conditions successive transitions may be seen.
The conformal transformation of the Misner-Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner-Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar-tensor theories of gravity is also examined.
We study the quantization of chiral QED by means of an extended Slavnov-Taylor (ST) identity under which an external source and the ghost field form a doublet. This ST identity incorporates the Adler-Bardeen anomaly. We prove that the cohomology classes of the extended classical linearized ST operator ${\cal S}'_0$ are modified with respect to the ones of the classical BRST differential in the FP neutral sector (physical observables). This provides a counterexample showing that the introduction of a doublet can modify the cohomology of the model, as a consequence of the fact that the counting operator for the doublet does not commute with ${\cal S}'_0$.
Simple formulas for the number of different cyclic and dihedral necklaces containing $n_j$ beads of the $j$-th color, $j\leq m$ and $\sum_{j=1}^mn_j=N$, are derived.
We combine the Herschel Space Observatory PACS and SPIRE photometry with archival WISE photometry to construct the spectral energy distributions (SED) for over 300 local ($z < 0.05$), ultra-hard X-ray (14 - 195 keV) selected active galactic nuclei (AGN) from the Swift Burst Alert Telescope (BAT) 58 month catalogue. Using a simple analytical model that combines an exponentially cut-off powerlaw with a single temperature modified blackbody, we decompose the SEDs into a host-galaxy and AGN component. We calculate dust masses, dust temperatures, and star-formation rates (SFR) for our entire sample and compare them to a stellar mass-matched sample of local non-AGN galaxies. We find AGN host galaxies have systematically higher dust masses, dust temperatures, and SFRs due to the higher prevalence of late-type galaxies to host an AGN, in agreement with previous studies of the Swift/BAT AGN. We provide a scaling to convert X-ray luminosities into 8 - 1000 $\mu$m AGN luminosities, as well as determine the best mid-to-far IR colors for identifying AGN dominated galaxies in the IR regime. We find that for nearly 30 per cent of our sample, the 70 $\mu$m emission contains a significant contribution from the AGN ($> 0.5$), especially at higher luminosities ($L_{14-195\,\rm{keV}} > 10^{42.5}$ ergs s$^{-1}$). Finally, we measure the local SFR-AGN luminosity relationship, finding a slope of 0.18, large scatter (0.37 dex), and no evidence for an upturn at high AGN luminosity. We conclude with a discussion on the implications of our results within the context of galaxy evolution with and without AGN feedback.
Using an elementary identity, we prove that for infinitely many polynomials $P(x)\in \mathbb{Z}[X]$ of fourth degree, the equation $\prod\limits_{k=1}^{n}P(k)=y^2$ has finitely many solutions in $\mathbb{Z}$. We also give an example of a quartic polynomial for which the product of it's first consecutive values is infinitely often a perfect square.
In this paper, we extend the maximum modulus estimate of the solutions of the nonstationary Stokes equations in the bounded $C^2$ cylinders for the space variables in \cite{CC} to time estimate. We show that if the boundary data is $L^\infty$ and the normal part of the boundary data has log-Dini continuity with respect to time, then the velocity is bounded. We emphasize that there is no continuity assumption on space variables in the new maximum modulus estimate. This completes the maximum modulus estimate.