ShantanuT01/DACTYL-Pretraining huggingface dataset:
In order to test for non-Gaussianities with respect to scale-dependencies we use so-called surrogate maps, in which possible phase correlations of the Fourier phases of the original WMAP data and simulations, respectively, are destroyed by applying a shuffling scheme to the maps. A statistical comparison of the original maps with the surrogate maps then allows to test for the existence of higher order correlations in the original maps, also and especially on well-defined Fourier modes. Using Minkowski functionals as an image analysis technique we calculate the deviation between the original data and 500 surrogates for different hemispheres in the sky and find ecliptic hemispherical asymmetries between northern and southern ecliptic sky. We find strong deviations from Gaussianity in the WMAP data when considering the low-l range with l = [2,20]. The analysis technique of the scaling indices leads to a slightly lower deviation. Although the underlying foreground reduction methods of the maps differ from each other, we find similar results for the WMAP 7yr ILC map and the WMAP 7yr (needlet-based) NILC map in the low-l range. Our results point once more to a cosmological nature of the signal. For a higher l range with l = [120,300] the results differ between the two image analysis techniques and between the two maps which makes an intrinsic nature of the signal on this l range less likely. When we decrease the size of the analysed sky regions for the low-l study, we do not find signatures of NG in the northern sky. In the south we find individual spots which show deviations from Gaussianity. In addition, we investigate non-Gaussian CMB simulations that depend on the f_NL parameter of the local type. These simulations cannot account for the detected signatures on the low-l range.
A width difference of the order of 20\% has previously been predicted for the two mass eigenstates of the $B_s$ meson. The dominant contributor to the width difference is the $b\rightarrow c\bar c s$ transition, with final states common to both $B_s$ and $\overline{B}_s$. All current experimental analyses fit the time-dependences of flavor-specific $B_s$-modes to a single exponential, which essentially determines the average $B_s$ lifetime. We stress that the same data sample allows even the measurement of the width difference. To see that, this note reviews the time-dependent formulae for tagged $B_s$ decays, which involve rapid oscillatory terms depending on $\Delta mt$. In untagged data samples the rapid oscillatory terms cancel. Their time-evolutions depend only on the much more slowly varying exponential falloffs. We discuss in detail the extraction of the two widths, and identify the large (small) CP-even (-odd) rate with that of the light (heavy) $B_s$ mass eigenstate. It is demonstrated that decay length distributions of some \underline{untagged} $B_s$ modes, such as $\rho^0 K_S, \; D_s^{(*)\pm}K^{(*)\mp}$, can be used to extract the notoriously difficult CKM unitarity triangle angle $\gamma$. Sizable CP violating effects may be seen with such untagged $B_s$ data samples. Listing $\Delta\Gamma$ as an observable allows for additional important standard model constraints. Within the CKM model, the ratio $\Delta\Gamma/ \Delta m$ involves no CKM parameters, only a QCD uncertainty. Thus a measurement of $\Delta\Gamma \;(\Delta m)$ would predict $\Delta m \;(\Delta\Gamma )$, up to the QCD uncertainty. A large width difference would automatically solve the puzzle of the number of charmed hadrons per $B$ decay in favor of theory. We also derive an upper limit of $(| \Delta\Gamma | / \Gamma)_{B_s} <~ 0.3$. Further, we must abandon the notion of branching fractions of $B_s\rightarrow f$, and instead consider $ B(B^0_{L(H)}\rightarrow f)$, in analogy to the neutral kaons.
Supernova remnants (SNRs) have long been considered as one of the most promising sources of Galactic cosmic rays. In the SNR paradigm, petaelectronvolt (PeV) proton acceleration may only be feasible at the early evolution stage, lasting a few hundred years, when the SNR shock speed is high. While evidence supporting the acceleration of PeV protons in young SNRs has yet to be discovered, X-ray synchrotron emission is an important indicator of fast shock. We here report the first discovery of X-ray synchrotron emission from the possibly middle-aged SNR G106.3+2.7, implying that this SNR is still an energetic particle accelerator despite its age. This discovery, along with the ambient environmental information, multiwavelength observation, and theoretical arguments, supports SNR G106.3+2.7 as a likely powerful PeV proton accelerator.
We consider spherically symmetric supercritical focusing wave equations outside a ball. Using mixed analytical and numerical methods, we show that the threshold for blowup is given by a codimension-one stable manifold of the unique static solution with exactly one unstable direction. We analyze in detail the convergence to this critical solution for initial data fine-tuned to the threshold.
Three-body Faddeev equations are considered as a spectral problem for nonsymmetrical matrix operator. Invariant subspaces related to physical and spurious solutions to Faddeev equations and its adjoint are described. Respective eigenvectors corresponding to invariant subspaces are constructed for Faddeev operator and its adjoint. Extensions of the formalism on CCA equations are discussed.
We report the Fermi Large Area Telescope (LAT) detection of a $\gamma$-ray source at the position of SAX J1808.4$-$3658. This transient low-mass X-ray binary contains an accreting millisecond puslar, which is only seen during its month-long outbursts and likely switches to be rotation powered during its quiescent state. Emission from the $\gamma$-ray source can be described by a power law with an exponential cutoff, the characteristic form for pulsar emission. Folding the source's 2.0--300 GeV photons at the binary orbital period, a weak modulation is seen (with an H-test value of $\sim$17). In addition, three sets of archival XMM-Newton data for the source field are analyzed, and we find only one X-ray source with 3--4$\sigma$ flux variations in the 2$\sigma$ error circle of the $\gamma$-ray source. However based on the X-ray properties, this X-ray source is not likely a background AGN, the major class of Fermi sources detected by LAT. These results support the possible association between the $\gamma$-ray source and SAX J1808.4$-$3658 and thus the scenario that the millisecond pulsar is rotation powered in the quiescent state. Considering a source distance of 3.5 kpc for SAX J1808.4$-$3658, the 0.1--300 GeV luminosity is 5.7$\times 10^{33}$ erg s$^{-1}$, implying a $\gamma$-ray conversion efficiency of 63\% for the pulsar in this binary.
We report a comprehensive specific heat and inelastic neutron scattering study to explore the possible origin of multiferroicity in HoCrO$_3$. We have performed specific heat measurements in the temperature range 100 mK - 290 K and inelastic neutron scattering measurements were performed in the temperature range 1.5 - 200 K. From the specific heat data we determined hyperfine splitting at 22.5(2) $\mu$eV and crystal field transitions at 1.379(5) meV, 10.37(4) meV, 15.49(9) meV and 23.44(9) meV, indicating the existence of strong hyperfine and crystal field interactions in HoCrO$_3$. Further, an effective hyperfine field is determined to be 600(3) T. The quasielastic scattering observed in the inelastic scattering data and a large linear term $\gamma=6.3(8)$ mJmol$^{-1}$K$^{-2}$ in the specific heat is attributed to the presence of short range exchange interactions, which is understood to be contributing to the observed ferroelectricity. Further the nuclear and magnetic entropies were computed to be, $\sim$$17.2$ Jmol$^{-1}$K$^{-1}$ and $\sim$34 Jmol$^{-1}$K$^{-1}$, respectively. The entropy values are in excellent agreement with the limiting theoretical values. An anomaly is observed in peak position of the temperature dependent crystal field spectra around 60 K, at the same temperature an anomaly in the pyroelectric current is reported. From this we could elucidate a direct correlation between the crystal electric field excitations of Ho$^{3+}$ and ferroelectricity in HoCrO$_3$. Our present study along with recent reports confirm that HoCrO$_3$, and $R$CrO$_3$ ($R=$ Rare earth) in general, possess more than one driving force for the ferroelectricity and multiferroicity.
In this paper, we study the annealed ferromagnetic Ising model on the configuration model. In an annealed system, we take the average on both sides of the ratio {defining the Boltzmann-Gibbs measure of the Ising model}. In the configuration model, the degrees are specified. Remarkably, when the degrees are deterministic, the critical value of the annealed Ising model is the same as that for the quenched Ising model. For independent and identically distributed (i.i.d.) degrees, instead, the annealed critical value is strictly smaller than that of the quenched Ising model. This identifies the degree structure of the underlying graph as the main driver for the critical value. Furthermore, in both contexts (deterministic or random degrees), we provide the variational expression for the annealed pressure. Interestingly, our rigorous results establish that only part of the heuristic conjectures in the physics literature were correct.
In the framework of the Relativistic Mean Field Approach a pseudospin dependence of the residual forces in nuclei is considered. It is shown that this dependence is relatively weak. As a consequence, a pseudospin dependence of the particle--core coupling is weak as well. This leads to a small splitting of the pseudospin doublets produced by a vector coupling of an odd particle pseudospin and a pseudo--orbital momentum of the core. Some possibilities for experimental investigations of the manifestations of the pseudospin symmetry in the spectra of odd nuclei with $Z\ge$ 100 are indicated.
A survey of pairing properties of nucleonic matter is presented that includes the off-shell propagation associated with short-range and tensor correlations. For this purpose, the gap equation has been solved in its most general form employing the complete energy and momentum dependence of the normal self-energy contributions. The latter correlations include the self-consistent calculation of the nucleon self-energy that is generated by the summation of ladder diagrams. This treatment preserves the conservation of particle number unlike approaches in which the self-energy is based on the Brueckner-Hartree-Fock approximation. A huge reduction in the strength as well as temperature and density range of ${}^3S_1$-${}^3D_1$ pairing is obtained for nuclear matter as compared to the standard BCS treatment. Similar dramatic results pertain to ${}^1S_0$ pairing of neutrons in neutron matter.
The measurement of baryon acoustic oscillations (BAO) from a galaxy redshift survey provides one of the most promising methods for probing dark energy. In this paper, we clarify the assumptions that go into the forecasts of dark energy constraints from BAO. We show that assuming a constant nP_{0.2}/G^2(z) (where P_{0.2} is the real space galaxy power spectrum at k=0.2h/Mpc and redshift z) gives a good approximation of the observed galaxy number density expected from a realistic flux-limited galaxy redshift survey. We find that assuming nP_{0.2}/G^2(z)=10 gives very similar dark energy constraints to assuming nP_{0.2}=3, but the latter corresponds to a galaxy number density larger by ~70% at z=2. We show how the Figure-of-Merit (FoM) for constraining dark energy depends on the assumed galaxy number density, redshift accuracy, redshift range, survey area, and the systematic errors due to calibration and uncertainties in the theory of nonlinear evolution and galaxy biasing. We find that an additive systematic noise of up to 0.4-0.5% per dz=0.1 redshift slice does not lead to significant decrease in the BAO FoM.
We perform a deductive study of accelerating Universe and focus on the importance of variable time-dependent $\Lambda$ in the Einstein's field equations under the phenomenological assumption, $\Lambda =\alpha H^2$ for the full physical range of $\alpha$. The relevance of variable $\Lambda$ with regard to various key issues like dark matter, dark energy, geometry of the field, age of the Universe, deceleration parameter and barotropic equation of state has been trivially addressed. The deceleration parameter and the barotropic equation of state parameter obey a straight line relationship for a flat Universe described by Friedmann and Raychaudhuri equations. Both the parameters are found identical for $\alpha = 1$.
This talk is a rather sceptical review of our knowledge and understanding of deep inelastic scattering at low x (high energy). We show that the well known success of the DGLAP evolution equations in describing of experimental HERA data brought more problems and puzzles than answers. We advocate that more systematic theoretical and experimental investigations of the nonperturbative QCD are needed to clarify physics of DIS at high energy.
We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as the ratio v:=d/(2g-2) decreases. We prove that the first three values of v at which the GIT quotients change are given by v=4, 3.5, 2. We show that, for v>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5<v<4, the Hilbert semistable locus coincides with the Chow semistable locus and it maps to the moduli stack of weakly-pseudo-stable curves. If 2<v<3.5, the Hilbert and Chow semistable loci coincide and they map to the moduli stack of pseudo-stable curves. We also analyze in detail the critical values v=3.5 and v=4, where the Hilbert semistable locus is strictly smaller than the Chow semistable locus. As an application, we obtain three compactifications of the universal Jacobian over the moduli space of stable curves, weakly-pseudo-stable curves and pseudo-stable curves, respectively.
In this paper, we consider the dynamics of the solution to the mass critical focusing Hartree equation with inverse-square potential in the energy space $H^{1}(\mathbb{R}^d)$. The main difficulties are the equation is \emph{not} space-translation invariant and the nonlinearity is non-local. We first prove that if the mass of the initial data is less than that of ground states, then the solution will be global. Although we don't know whether the ground state is unique, we can verify all the ground states have the same, minimal mass threshold. Then at the minimal mass threshold, we can construct the finite-time blow up solution, which is a pseudo-conformal transformation of the ground state, up to the symmetries of the equation. Finally, we establish an mass concentration phenomenon of the finite-time blow up solution to the equation.
This paper would focus on the subject of the 2-D incompressible Navier-Stokes-Cahn-Hilliard (NS-CH) system with a singular free energy density. Due to lack of the maximum principle for the convective Cahn-Hilliard equation (as a fourth-order parabolic equation), we construct its approximate second-order parabolic equation, and use comparison principle and the basic energy estimates to separate the solution from the singular values of the singular free energy density, where the Orlicz embedding theorem plays a key role. Based on these, we prove the global well-posedness of the Cauchy problem of the 2-D NS-CH equations with periodic domains by using energy estimates and the Logarithmic Sobolev inequality.
We have measured the specific heat of the coupled spin-dimer antiferromagnet Ba$_3$Mn$_2$O$_8$ to 50 mK in temperature and to 29 T in the magnetic field. The experiment extends to the midpoint of the field region (25.9 T $\leq H \leq$ 32.3 T) of the magnetization plateau at 1/2 of the saturation magnetization, and reveals the presence of three ordered phases in the field region between that of the magnetization plateau and the low-field spin-liquid region. The exponent of the phase boundary with the thermally disordered region is smaller than the theoretical value based on the Bose-Einstein condensation of spin triplets. At zero field and 29 T, the specific-heat data show gapped behaviors characteristic of spin liquids. The zero-field data indicate that the gapped triplet excitations form two levels whose energies differ by nearly a factor of two. At least the lower level is well localized. The data at 29 T reveal that the low-lying excitations at the magnetization plateau are weakly delocalized.
We study the density X(t,x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P(0<X(t,x)<a) as a approaches 0, as well as the Hausdorff dimension of the boundary of the support of X(t). The answers are in terms of the lead eigenvalue of the Ornstein-Uhlenbeck generator with a particular killing term. This work is motivated in part by questions of pathwise uniqueness for associated stochastic partial differential equations.
Given a finite irreducible Coxeter group $W$ with a fixed Coxeter element $c$, we define the Coxeter pop-tsack torsing operator $\mathsf{Pop}_T:W\to W$ by $\mathsf{Pop}_T(w)=w\cdot\pi_T(w)^{-1}$, where $\pi_T(w)$ is the join in the noncrossing partition lattice $\mathrm{NC}(w,c)$ of the set of reflections lying weakly below $w$ in the absolute order. This definition serves as a "Bessis dual" version of the first author's notion of a Coxeter pop-stack sorting operator, which, in turn, generalizes the pop-stack-sorting map on symmetric groups. We show that if $W$ is coincidental or of type $D$, then the identity element of $W$ is the unique periodic point of $\mathsf{Pop}_T$ and the maximum size of a forward orbit of $\mathsf{Pop}_T$ is the Coxeter number $h$ of $W$. In each of these types, we obtain a natural lift from $W$ to the dual braid monoid of $W$. We also prove that $W$ is coincidental if and only if it has a unique forward orbit of size $h$. For arbitrary $W$, we show that the forward orbit of $c^{-1}$ under $\mathsf{Pop}_T$ has size $h$ and is isolated in the sense that none of the non-identity elements of the orbit have preimages lying outside of the orbit.
We present observations of the 1.3 mm continuum emission toward hub-N and hub-S of the infrared dark cloud G14.225-0.506 carried out with the Submillimeter Array, together with observations of the dust emission at 870 and 350 microns obtained with APEX and CSO telescopes. The large scale dust emission of both hubs consists of a single peaked clump elongated in the direction of the associated filament. At small scales, the SMA images reveal that both hubs fragment into several dust condensations. The fragmentation level was assessed under the same conditions and we found that hub-N presents 4 fragments while hub-S is more fragmented, with 13 fragments identified. We studied the density structure by means of a simultaneous fit of the radial intensity profile at 870 and 350 microns and the spectral energy distribution adopting a Plummer-like function to describe the density structure. The parameters inferred from the model are remarkably similar in both hubs, suggesting that density structure could not be responsible in determining the fragmentation level. We estimated several physical parameters such as the level of turbulence and the magnetic field strength, and we found no significant differences between these hubs. The Jeans analysis indicates that the observed fragmentation is more consistent with thermal Jeans fragmentation compared with a scenario that turbulent support is included. The lower fragmentation level observed in hub-N could be explained in terms of stronger UV radiation effects from a nearby HII region, evolutionary effects, and/or stronger magnetic fields at small scales, a scenario that should be further investigated.
We present a compelling evidence for the opening of a bandgap in exfoliated bottom-gated bilayer graphene by fitting the gate-voltage modulated infrared reflectivity spectra in a large range of doping levels with a tight-binding model and the Kubo formula. A close quantitative agreement between the experimental and calculated spectra is achieved, allowing us to determine self-consistently the full set of Slonczewski-Weiss-McClure tight-binding parameters together with the gate-voltage dependent bandgap. The doping dependence of the bandgap shows a good agreement with the existing calculations that take the effects of self-screening into account. We also identify certain mismatches between the tight-binding model and the data, which can be related to electron-electron and electron-phonon interactions.
The estimation of cosmological parameters from a given data set requires a construction of a likelihood function which, in general, has a complicated functional form. We adopt a Gaussian copula and constructed a copula likelihood function for the convergence power spectrum from a weak lensing survey. We show that the parameter estimation based on the Gaussian likelihood erroneously introduces a systematic shift in the confidence region, in particular for a parameter of the dark energy equation of state w. Thus, the copula likelihood should be used in future cosmological observations.
Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement -- a highly non-classical correlation -- remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50\%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.
We consider a nonlocal version of the Nambu and Jona-Lasinio model. The nonlocality is contained in the quark-antiquark bilinears of the four-quark vertices as a form factor of the Gaussian type. The model has three parameters which can be fixed in favour of the values of the pion mass, the pion decay constant f_pi, and the current quark mass. The pi pi scattering amplitude is obtained by calculating the quark box and the sigma-pole diagrams, where sigma is the scalar isoscalar meson. It is shown that this amplitude satisfies the well-known Weinberg relation. We obtain the s, p, d wave scattering lengths in all isotopic channels and the s wave slope parameters. The results are in satisfactory agreement with both phenomenological data and the basic requirements of low-energy theorems, thus supporting to the form factor used.
The damping rate \gamma_t(p) of on-shell transverse gluons with ultrasoft momentum p is calculated in the context of next-to-leading-order hard-thermal-loop-summed perturbation of high-temperature QCD. It is obtained in an expansion to second order in p. The first coefficient is recovered but that of order p^2 is found divergent in the infrared. Divergences from light-like momenta do also occur but are circumvented. Our result and method are critically discussed, particularly regarding a Ward identity obtained in the literature. When enforcing the equality between \gamma_t(0) and \gamma_l(0), a rough estimate of the magnetic mass is obtained. Carrying a similar calculation in the context of scalar quantum electrodynamics shows that the early ultrasoft-momentum expansion we make has little to do with the infrared sensitivity of the result.