ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a general derivation the three-body spectator (Gross) equations and the corresponding electromagnetic currents. As in previous paper on two-body systems, the wave equations and currents are derived from those for Bethe-Salpeter equation with the help of algebraic method using a concise matrix notation. The three-body interactions and currents introduced by the transition to the spectator approach are isolated and the matrix elements of the e.m. current are presented in detail for system of three indistinguishable particles, namely for elastic scattering and for two and three body break-up. The general expressions are reduced to the one-boson-exchange approximation to make contact with previous work. The method is general in that it does not rely on introduction of the electromagnetic interaction with the help of the minimal replacement. It would therefore work also for other external fields.
We investigate the magnetic excitations of the hyperhoneycomb Kitaev magnet $\beta$-$\text{Li}_2\text{IrO}_3$ by means of inelastic Raman scattering. The spectra exhibits a coexistence of a broad scattering continuum and two sharp low-energy peaks at 2.5 meV and 3 meV, with a distinctive polarization dependence. While the continuum is suggestive of fractional quasi-particles emerging from a proximate quantum spin liquid phase, the sharp peaks provide the first experimental signature of the `non-Loudon-Fleury' one-magnon scattering processes proposed recently [Phys. Rev. B 104, 144412 (2021)]. The corresponding microscopic mechanism is similar to the one leading to the symmetric off-diagonal exchange interaction $\Gamma$ (as it involves a combination of both direct and ligand-mediated exchange paths), but is otherwise completely unexpected within the traditional Loudon-Fleury theory of Raman scattering. The present experimental verification therefore calls for a drastic reevaluation of Raman scattering in similar systems with strong spin orbit coupling and multiple exchange paths.
We prove a nonsmooth implicit function theorem applicable to the zero set of the difference of convex functions. This theorem is explicit and global: it gives a formula representing this zero set as a difference of convex functions which holds throughout the entire domain of the original functions. As applications, we prove results on the stability of singularities of envelopes of semi-convex functions, and solutions to optimal transport problems under appropriate perturbations, along with global structure theorems on certain discontinuities arising in optimal transport maps for Ma-Trudinger-Wang costs. For targets whose components satisfy additional convexity, separation, multiplicity and affine independence assumptions we show these discontinuities occur on submanifolds of the appropriate codimension which are parameterized locally as differences of convex functions (DC, hence $C^2$ rectifiable), and --- depending on the precise assumptions --- $C^{1,\alpha}$ smooth. In this case the highest codimension submanifolds consists of isolated points, each uniquely identified by the (affinely independent) components of the target to which it is transported.
The moduli space of stable curves of Deligne and Mumford is a compactification of the moduli space of smooth curves of genus >=2 that parametrizes certain nodal curves. It is a powerful tool for the study of algebraic curves. Higher-dimensional analogues were constructed by Koll\'ar, Shepherd-Barron and Alexeev in dimension 2, and by Viehweg in the case of smooth varieties. We will explain the recent ideas allowing for the construction of these moduli spaces in general, including the stable reduction theorem in higher dimension, which reflects their compactness.   L'espace de modules des courbes stables de Deligne et Mumford est une compactification de l'espace de modules des courbes lisses de genre >=2, param\'etrant certaines courbes nodales. C'est un outil puissant pour l'\'etude des courbes alg\'ebriques. Des analogues en dimension sup\'erieure ont \'et\'e construits par Koll\'ar, Shepherd-Barron et Alexeev en dimension 2, et par Viehweg dans le cas des vari\'et\'es lisses. Nous expliquerons les id\'ees r\'ecentes ayant permis la construction de ces espaces de modules en g\'en\'eral, notamment le th\'eor\`eme de r\'eduction stable en dimension sup\'erieure, qui refl\`ete leur compacit\'e.
Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one, it is well-known that the set of probability measures with a given mean is a lattice w.r.t. the convex order. Our main result is that, contrary to the minimum and maximum in the convex order, the Wasserstein projections are Lipschitz continuity w.r.t. the Wasserstein distance in dimension one. Moreover, we provide examples that show sharpness of the obtained bounds for the 1-Wasserstein distance.
We determine the surface reconstruction of SrTiO3 used to achieve superconducting FeSe films in experiments, which is different from the 1x1 TiO2 terminated SrTiO3 assumed by most previous theoretical studies. In particular, we identify the existence of a double TiO2 layer at the SrTiO3-FeSe interface that plays two important roles. First, it facilitates the epitaxial growth of FeSe. Second, ab initio calculations reveal a strong tendency for electrons to transfer from an oxygen deficient SrTiO3 surface to FeSe when the double TiO2 layer is present. As a better electron donor than previously proposed interfacial structures, the double layer helps to remove the hole pocket in the FeSe at the {\Gamma} point of the Brillouin zone and leads to a band structure characteristic of superconducting samples. The characterization of the interface structure presented here is a key step towards the resolution of many open questions about this novel superconductor.
This paper deals with the set of $\alpha\in{\mathbb{R}}$ such that $\alpha \zeta^{n} \bmod 1$ tends to $0$ for a fixed $\zeta\in{\mathbb{R}}$, which we call $\mathscr{M}_{\zeta}$. Predominately the case of Pisot numbers $\zeta$ is studied. In this case the inclusions $\mathcal{O}_{\mathbb{Q}(\zeta)}\subset\mathscr{M}_{\zeta}\subset\mathbb{Q}(\zeta)$ are known. We will show the properties of $\mathscr{M}_{\zeta}$ are connected to the module structure of the ring of integers $\mathcal{O}_{\mathbb{Q}(\zeta)}$. We will describe the module structure of $\mathscr{M}_{\zeta}$ and how much $\mathscr{M}_{\zeta}$ differs from $\mathcal{O}_{\mathbb{Q}(\zeta)}$. The results besides allow to give some information on the shape of integral bases of real number fields.
The problem of non-rigid point set registration is a key problem for many computer vision tasks. In many cases the nature of the data or capabilities of the point detection algorithms can give us some prior information on point sets distribution. In non-rigid case this information is able to drastically improve registration results by limiting number of possible solutions. In this paper we explore use of prior information about point sets clustering, such information can be obtained with preliminary segmentation. We extend existing probabilistic framework for fitting two level Gaussian mixture model and derive closed form solution for maximization step of the EM algorithm. This enables us to improve method accuracy with almost no performance loss. We evaluate our approach and compare the Cluster Coherent Point Drift with other existing non-rigid point set registration methods and show it's advantages for digital medicine tasks, especially for heart template model personalization using patient's medical data.
The canonical quantization of homogeneous cosmologies is considered in the high anisotropic limit. Exact wavefunctions are found in this limit when the momentum constraints are reduced at the classical level. Lorentzian solutions that represent tunnelling from classically forbidden regimes are identified. Solutions to the modified Wheeler-DeWitt equation are also found for the vacuum Bianchi IX model when a quantum reduction of the momentum constraints is considered.
In the paper stochastic Volterra equations with noise terms driven by series of independent scalar Wiener processes are considered. In our study we use the resolvent approach to the equations under consideration. We give sufficient condition for the existence of strong solution to the class of stochastic Volterra equations of convolution type. We provide regularity of stochastic convolution, as well.
We prove that every toric quiver flag variety $Y$ is isomorphic to a fine moduli space of cyclic modules over the algebra $\text{End}(T)$ for some tilting bundle $T$ on $Y$. This generalises the well known fact that $\mathbb{P}^n$ can be recovered from the endomorphism algebra of $\bigoplus_{0\leq i\leq n} \mathcal{O}_{\mathbb{P}^n}(i)$.
Bi5(GaCl4)3 sample has been synthesized through the oxidation of Bi metal by gallium chloride (GaCl3) salt. Powder X-ray diffraction as well as micro-Raman scattering results revealed that, in addition to crystalline Bi5(GaCl4)3 in the product, amorphous phase containing [GaCl4]- and [Ga2Cl7]- units also exist. The thorough comparison of steady-state and time-resolved photoluminescent behaviors between Bi5(GaCl4)3 product and Bi5(AlCl4)3 crystal leads us to conclude that Bi53+ is the dominant emitter in the product, which gives rise to the ultrabroad emission ranging from 1 to 2.7 micrometer. Detailed quantum chemistry calculation helps us assign the observed excitations to some electronic transitions of Bi53+ polycation, especially at shorter wavelengths. It is believed that our work shown here not only is helpful to solve the confusions on the luminescent origin of bismuth in other material systems, but also serves to develop novel broadband tunable laser materials.
We study the connected component of the automorphism group of a cubic hypersurface over complex numbers. When the cubic hypersurface has nonzero Hessian, this group is usually small. But there are examples with unusually large automorphism groups: the secants of Severi varieties. Can we characterize them by the property of having unusually large automorphism groups? We study this question from the viewpoint of prolongations of the Lie algebras. Our result characterizes the secants of Severi varieties, among cubic hypersurfaces with nonzero Hessian and smooth singular locus, in terms of prolongations of certain type.
We assess the future directions for the search for supersymmetry at the Large Hadron Collider in view of the new precision results on the muon anomaly by the Fermilab Collaboration. The existence of a deviation of size 4.1$\sigma$ from the Standard Model prediction points to light sleptons and light weakinos in the mass range of few hundred GeV while the observation of the Higgs boson mass at $\sim 125$ GeV points to squark masses lying in the few TeV range. Thus a split sparticle spectrum is indicated. We discuss the possibility of such a split sparticle spectrum in the supergravity unified model and show that a splitting of the sfermion spectrum into light sleptons and heavy squarks naturally arises within radiative breaking of the electroweak symmetry driven by heavy gluinos ($\tilde g$SUGRA). We discuss the possible avenues for the discovery of supersymmetry at the LHC within this framework under the further constraint of the recent muon anomaly result from the Fermilab Collaboration. We show that the most likely candidates for early discovery of a sparticle at the LHC are the chargino, the stau, the smuon and the selectron. We present a set of benchmarks and discuss future directions for further work. Specifically, we point to the most promising channels for SUSY discovery and estimate the integrated luminosity needed for the discovery of these benchmarks at the High Luminosity LHC and also at the High Energy LHC.
Line-intensity mapping (LIM) provides a promising way to probe cosmology, reionization and galaxy evolution. However, its sensitivity to cosmology and astrophysics at the same time is also a nuisance. Here we develop a comprehensive framework for modelling the LIM power spectrum, which includes redshift space distortions and the Alcock-Paczynski effect. We then identify and isolate degeneracies with astrophysics so that they can be marginalized over. We study the gains of using the multipole expansion of the anisotropic power spectrum, providing an accurate analytic expression for their covariance, and find a 10%-60% increase in the precision of the baryon acoustic oscillation scale measurements when including the hexadecapole in the analysis. We discuss different observational strategies when targeting other cosmological parameters, such as the sum of neutrino masses or primordial non-Gaussianity, finding that fewer and wider bins are typically more optimal. Overall, our formalism facilitates an optimal extraction of cosmological constraints robust to astrophysics.
We have conducted a kinematic study of 165 young M dwarfs with ages of <300 Myr. Our sample is composed of stars and brown dwarfs with spectral types ranging from K7 to L0, detected by ROSAT and with photometric distances of <25 pc assuming the stars are single and on the main-sequence. In order to find stars kinematically linked to known young moving groups (YMGs), we measured radial velocities for the complete sample with Keck and CFHT optical spectroscopy and trigonometric parallaxes for 75 of the M dwarfs with the CAPSCam instrument on the du Pont 2.5-m Telescope. Due to their youthful overluminosity and unresolved binarity, the original photometric distances for our sample underestimated the distances by 70% on average, excluding two extremely young (<3 Myr) objects found to have distances beyond a few hundred parsecs. We searched for kinematic matches to 14 reported YMGs and identified 9 new members of the AB Dor YMG and 2 of the Ursa Majoris group. Additional possible candidates include 6 Castor, 4 Ursa Majoris, 2 AB Dor members, and 1 member each of the Her-Lyr and beta Pic groups. Our sample also contains 27 young low-mass stars and 4 brown dwarfs with ages <150 Myr which are not associated with any known YMG. We identified an additional 15 stars which are kinematic matches to one of the YMGs, but the ages from spectroscopic diagnostics and/or the positions on the sky do not match. These warn against grouping stars together based only on kinematics and that a confluence of evidence is required to claim that a group of stars originated from the same star-forming event.
The main conjectures in Iwasawa theory predict the relationship between the Iwasawa modules and the $p$-adic $L$-functions. Using a certain proved formulation of the main conjecture, Greither and Kurihara described explicitly the (initial) Fitting ideals of the Iwasawa modules for the cyclotomic $\mathbb{Z}_p$-extensions of finite abelian extensions of totally real fields. In this paper, we generalize the algebraic theory behind their work by developing the theory of ``shifts of Fitting invariants.'' As applications to Iwasawa theory, we obtain a noncommutative version and a two-variable version of the work of Greither and Kurihara.
[Abridged] We present the results of new near-IR spectroscopic observations of passive galaxies at z>1.4 in a concentration of BzK-selected galaxies in the COSMOS field. The observations have been conducted with Subaru/MOIRCS, and have resulted in absorption lines and/or continuum detection for 18 out of 34 objects. This allows us to measure spectroscopic redshifts for a sample almost complete to K(AB)=21. COSMOS photometric redshifts are found in fair agreement overall with the spectroscopic redshifts, with a standard deviation of ~0.05; however, ~30% of objects have photometric redshifts systematically underestimated by up to ~25%. We show that these systematic offsets in photometric redshifts can be removed by using these objects as a training set. All galaxies fall in four distinct redshift spikes at z=1.43, 1.53, 1.67 and 1.82, with this latter one including 7 galaxies. SED fits to broad-band fluxes indicate stellar masses in the range of ~4-40x10^10Msun and that star formation was quenched ~1 Gyr before the cosmic epoch at which they are observed. The spectra of several individual galaxies have allowed us to measure their Hdelta_F and Dn4000 indices, which confirms their identification as passive galaxies, as does a composite spectrum resulting from the coaddition of 17 individual spectra. The effective radii of the galaxies have been measured on the HST/ACS F814W image, confirming the coexistence at these redshifts of passive galaxies which are substantially more compact than their local counterparts with others that follow the local size-stellar mass relation. For the galaxy with best S/N spectrum we were able to measure a velocity dispersion of 270+/-105 km/s, indicating that this galaxy lies closely on the virial relation given its stellar mass and effective radius.
This letter presents a study of the inclusive production of X$\rightarrow b\bar{b}$ plus a recoil, using simulated samples of $pp$ collisions at $\sqrt{s}=14$ TeV for an integrated luminosity in the range between 30 fb$^{-1}$ to 3 ab$^{-1}$. The case for experiments to include un-prescaled $b$-tag multijet triggers for this topology is made and the ideal jet thresholds are discussed. The sensitivity to Standard Model Higgs with a transverse momentum of at least 200 GeV is evaluated with respect to a continuous background, dominated by multijet processes. The mass of $b$-jet-pairs is analysed, quoting sensitivity to cross-sections in the range of 1 to 2 pb, for 100 fb$^{-1}$, covering the Higgs production cross section of 1.8 pb. The trigger strategy presented in this letter is compared to triggers already in use, showing an increase on the signal efficiency for masses below 200 GeV and a performance comparable to a logic OR of all the currently available akin triggers for higher masses. The robustness of the expected sensitivity against systematic uncertainties is estimated by considering various typical sources, such as those on the fitting parameters of the continuous background, shape uncertainties affecting the signal acceptance and the background modelling. The accuracy of a Higgs production cross section measurements is also discussed, quoting sensitivity to deviations of 50% for 100 fb$^{-1}$ and 10% for 3 ab$^{-1}$.
Studies of MHD turbulence often investigate the Fourier power spectrum to provide information on the nature of the turbulence cascade. However, the Fourier power spectrum only contains the Fourier amplitudes and rejects all information regarding the Fourier phases. Here we investigate the utility of two statistical diagnostics for recovering information on Fourier phases in ISM density data: the averaged amplitudes of the bispectrum and the phase coherence index (PCI), a new phase technique for the ISM. We create 3D density and 2D column density maps using a set of simulations of isothermal ideal MHD turbulence with a wide range of sonic and Alfv\'enic Mach numbers. We find that the bispectrum averaged along different angles with respect to either the $k_1$ or $k_2$ axis is primarily sensitive to the sonic Mach number while averaging the bispectral amplitudes over different annuli is sensitive to both the sonic and Alfv\'enic Mach numbers. The PCI of density suggests that the most correlated phases occur in supersonic sub-Alfv\'enic turbulence and also near the numerical dissipation regime. This suggests that non-linear interactions with correlated phases are strongest in shock dominated regions, in agreement with findings from the solar wind. Additionally, our results are particularly encouraging as they suggests the phase information contained in the bispectrum and PCI can be used to find parameters of turbulence in column density maps.
We extract atom-atom potentials from the effective spherical potentials that suc cessfully model Hugoniot experiments on molecular fluids, e.g., $O_2$ and $N_2$. In the case of $O_2$ the resulting potentials compare very well with the atom-atom potentials used in studies of solid-state propertie s, while for $N_2$ they are considerably softer at short distances. Ground state (T=0K) and room temperatu re calculations performed with the new $N-N$ potential resolve the previous discrepancy between experimental and theoretical results.
Boron is an element of fascinating chemical complexity. Controversies have shrouded this element since its discovery was announced in 1808: the new 'element' turned out to be a compound containing less than 60-70 percent of boron, and it was not until 1909 that 99-percent pure boron was obtained. And although we now know of at least 16 polymorphs, the stable phase of boron is not yet experimentally established even at ambient conditions. Boron's complexities arise from frustration: situated between metals and insulators in the periodic table, boron has only three valence electrons, which would favour metallicity, but they are sufficiently localized that insulating states emerge. However, this subtle balance between metallic and insulating states is easily shifted by pressure, temperature and impurities. Here we report the results of high-pressure experiments and ab initio evolutionary crystal structure predictions that explore the structural stability of boron under pressure and, strikingly, reveal a partially ionic high-pressure boron phase. This new phase is stable between 19 and 89 GPa, can be quenched to ambient conditions, and has a hitherto unknown structure (space group Pnnm, 28 atoms in the unit cell) consisting of icosahedral B12 clusters and B2 pairs in a NaCl-type arrangement. We find that the ionicity of the phase affects its electronic bandgap, infrared adsorption and dielectric constants, and that it arises from the different electronic properties of the B2 pairs and B12 clusters and the resultant charge transfer between them.
We have performed detailed first-principles calculations to determine the eigenvectors of the zone-center modes of hexagonal BaTiO3 and shown that the experimentally relevant low-energy modes (including the non-polar instability) can be represented as suitable combinations of basic local polar distortions associated with the instability of the cubic perovskite phase. The hexagonal structure provides a testing ground for the analysis of the influence of the stacking of TiO6 octahedra: the occurrence of relatively high-energy chains of dipoles highlights the importance of local effects related to the coherent hybridization enhancement between Ti and O ions. Our results provide simple heuristic rules that could be useful for the analysis of related compounds.