ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present an analytical expression for the static many-body local field factor $G_{-}(q)$ of a homogeneous two-dimensional electron gas, which reproduces Diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number $q$. This allows us to also provide a closed-form expression for the spin-antisymmetric exchange and correlation kernel $K^{-}_{xc}(r)$ which represents a key input for spin-density functional studies of inhomogeneous electronic systems.
We present a comparison between ionized gas and stellar kinematics for a sample of 5 early-to-intermediate disk galaxies. We measured the major axis V and velocity dispersion radial profiles for both gas and stars, and the h_3 and h_4 radial profiles of the stars. We also derived from the R-band surface photometry of each galaxy the light contribution of their bulges and disks.   In order to investigate the differences in the velocity fields of our sample galaxies we adopted the self-consistent dynamical model by Pignatelli & Galletta (1998), which takes into account the asymmetric drift effects, the projection effects along the line-of-sight and the non-Gaussian shape of the line profiles due to the presence of different components with distinct dynamical behavior.
In the paper, we have introduced the notion of mild bounded ancient solutions to the Navier-Stokes equations in a half space. They play a certain role in understanding whether or not solutions to the initial boundary value problem for the Navier-Stokes system with non-slip boundary conditions have blowups of Type I.
Autoencoders are commonly trained using element-wise loss. However, element-wise loss disregards high-level structures in the image which can lead to embeddings that disregard them as well. A recent improvement to autoencoders that helps alleviate this problem is the use of perceptual loss. This work investigates perceptual loss from the perspective of encoder embeddings themselves. Autoencoders are trained to embed images from three different computer vision datasets using perceptual loss based on a pretrained model as well as pixel-wise loss. A host of different predictors are trained to perform object positioning and classification on the datasets given the embedded images as input. The two kinds of losses are evaluated by comparing how the predictors performed with embeddings from the differently trained autoencoders. The results show that, in the image domain, the embeddings generated by autoencoders trained with perceptual loss enable more accurate predictions than those trained with element-wise loss. Furthermore, the results show that, on the task of object positioning of a small-scale feature, perceptual loss can improve the results by a factor 10. The experimental setup is available online: https://github.com/guspih/Perceptual-Autoencoders
We consider the deformations of a supersymmetric quantum field theory by adding spacetime-dependent terms to the action. We propose to describe the renormalization of such deformations in terms of some cohomological invariants, a class of solutions of a Maurer-Cartan equation. We consider the strongly coupled limit of $N=4$ supersymmetric Yang-Mills theory. In the context of AdS/CFT correspondence, we explain what corresponds to our invariants in classical supergravity. There is a leg amputation procedure, which constructs a solution of the Maurer-Cartan equation from tree diagramms of SUGRA. We consider a particular example of the beta-deformation. It is known that the leading term of the beta-function is cubic in the parameter of the beta-deformation. We give a cohomological interpretation of this leading term. We conjecture that it is actually encoded in some simpler cohomology class, which is quadratic in the parameter of the beta-deformation.
In this article, we prove that any Q-Calabi-Yau 3-fold with only ordinary terminal singularities and any Q-Fano 3-fold of Fano index 1 with only terminal singularities have Q-smoothings.
One of the major obstacles to realizing spintronic devices such as MESO logic devices is the small signal magnitude used for magnetization readout, making it important to find materials with high spin-to-charge conversion efficiency. Although intermixing at the junction of two materials is a widely occurring phenomenon, its influence on material characterization and the estimation of spin-to-charge conversion efficiencies is easily neglected or underestimated. Here, we demonstrate all electrical spin-to-charge conversion in Bi$_x$Se$_{1-x}$ nanodevices and show how the conversion efficiency can be overestimated by tens of times depending on the adjacent metal used as a contact. We attribute this to the intermixing-induced compositional change and the properties of a polycrystal that lead to drastic changes in resistivity and spin Hall angle. Strategies to improve the spin-to-charge conversion signal in similar structures for functional devices are discussed.
The static and dynamic properties of V^{4+} spins (S = 1/2) in the frustrated square lattice compound Pb2(VO)(PO4)2 were investigated by means of magnetic susceptibility chi and 31P nuclear magnetic resonance (NMR) shift (K) and 31P nuclear spin-lattice relaxation rate 1/T1 measurements on a single crystal. This compound exhibits long-range antiferromagnetic order below TN \simeq 3.65 K. NMR spectra above TN show two distinct lines corresponding to two inequivalent P sites present in the crystal structure. The observed asymmetry in hyperfine coupling constant for the in-plane (P1) P site directly points towards a distortion in the square lattice at the microscopic level, consistent with the monoclinic crystal structure. The nearest- and next-nearest-neighbor exchange couplings were estimated to be J1/kB = (-5.4 \pm 0.5) K (ferromagnetic) and J2/kB = (9.3 \pm 0.6) K (antiferromagnetic), respectively. 1/(T1 T chi) is almost T-independent at high temperatures due to random fluctuation of spin moments. Below 20 K, the compound shows an enhancement of 1/(T1 T chi) which arises from a growth of antiferromagnetic spin correlations above TN. Below TN and for the field applied along the c-axis, the NMR spectrum for the P1 site splits into two satellites and the spacing between them increases monotonically with decreasing T which is a direct evidence of a columnar antiferromagnetic ordering with spins lying in the ab-plane. This type of magnetic ordering is consistent with expectation from the J2/J1 \simeq -1.72 ratio. The critical exponent beta = 0.25 \pm 0.02 estimated from the temperature dependence of sublattice magnetization as measured by 31P NMR at 11.13 MHz is close to the value (0.231) predicted for the two-dimensional XY model.
In this work we describe a construction of semistable fibrations over an elliptic curve with one unique singular fibre and we give effective examples using monodromy of curves.
We study the effect of electron-electron interactions on the charge and spin structures of a Quantum Hall strip in a triangularly confined potential. We find that the strip undergoes a spin-unpolarized to spin-polarized transition as a function of magnetic field perpendicular to the strip. For sharp confinements the spin-polarization transition is spontaneous and first develops at the softer side of the triangular potential which shows up as an "eye-structure" in the electron dispersion. For sufficiently weak confinements this spin-polarization transition is preceded by a charge reconstruction of a single spin species, which creates a spin-polarized strip of electrons with a width of the order of the magnetic length detached from the rest of the system. Relevance of our findings to the recent momentum resolved tunneling experiments is also discussed.
Everett's Relative State Interpretation has gained increasing interest due to the progress of understanding the role of decoherence. In order to fulfill its promise as a realistic description of the physical world, two postulates are formulated. In short they are 1) for a system with continuous coordinates $\vec{x}$, discrete variable $j$, and state $\psi_j(\vec{x})$, the density $\rho_j(\vec{x})=|\psi_j(\vec{x})|^2$ gives the distribution of the location of the system with the respect to the variables $\vec{x}$ and $j$; 2) an equation of motion for the state $i\hbar \partial_t \psi = H\psi$. The first postulate connects the mathematical description to the physical reality, which has been missing in previous versions. The contents of the standard (Copenhagen) postulates are derived, including the appearance of Hilbert space and the Born rule. The approach to probabilities earlier proposed by Greaves replaces the classical probability concept in the Born rule. The new quantum probability concept, earlier advocated by Deutsch and Wallace, is void of the requirement of uncertainty.
A class of boundary conditions for canonical general relativity are proposed and studied at the quasi-local level. It is shown that for untrapped or marginal surfaces, fixing the area element on the 2-surface (rather than the induced 2-metric) and the angular momentum surface density is enough to have a functionally differentiable Hamiltonian, thus providing definition of conserved quantities for the quasi-local regions. If on the boundary the evolution vector normal to the 2-surface is chosen to be proportional to the dual expansion vector, we obtain a generalization of the Hawking energy associated with a generalized Kodama vector. This vector plays the role for the stationary untrapped boundary conditions which the stationary Killing vector plays for stationary black holes. When the dual expansion vector is null, the boundary conditions reduce to the ones given by the non-expanding horizons and the null trapping horizons.
The ability to manipulate plasmons is driving new developments in electronics, optics, sensing, energy, and medicine. Despite the massive momentum of experimental research in this direction, a predictive quantum-mechanical framework for describing electron-plasmon interactions in real materials is still missing. Here, starting from a many-body Green's function approach, we develop an ab initio approach for investigating electron-plasmon coupling in solids. As a first demonstration of this methodology, we show that electron-plasmon scattering is the primary mechanism for the cooling of hot carriers in doped silicon, it is key to explain measured electron mobilities at high doping, and it leads to a quantum zero-point renormalization of the band gap in agreement with experiment.
Context. The [CII] 158 {\mu}m far-infrared (FIR) fine-structure line is one of the most important cooling lines of the star-forming interstellar medium (ISM). High spectral resolution observations have shown complex structures in the line profiles of the [CII] emission. Aims. Our aim is to determine whether the complex profiles observed in [^{12}CII] are due to individual velocity components along the line-of-sight or to self-absorption based on a comparison of the [^{12}CII] and isotopic [^{13}CII] line profiles. Methods. Deep integrations with the SOFIA/upGREAT 7-pixel array receiver in M43, Horsehead~PDR, Monoceros~R2, and M17~SW allow for the detection of optically thin [^{13}CII] emission lines, along with the [^{12}CII] emission lines, with a high signal-to-noise ratio. We first derived the [^{12}CII] optical depth and the [CII] column density from a single component model. However, the complex line profiles observed require a double layer model with an emitting background and an absorbing foreground. A multi-component velocity fit allows us to derive the physical conditions of the [CII] gas: column density and excitation temperature. Results. We find moderate to high [^{12}CII] optical depths in all four sources and self-absorption of [^{12}CII] in Mon R2 and M17 SW. The high column density of the warm background emission corresponds to an equivalent Av of up to 41 mag. The foreground absorption requires substantial column densities of cold and dense [CII] gas, with an equivalent Av ranging up to about 13 mag. Conclusions. The column density of the warm background material requires multiple photon-dominated region (PDR) surfaces stacked along the line of sight and in velocity. The substantial column density of dense and cold foreground [CII] gas detected in absorption cannot be explained with any known scenario and we can only speculate on its origins
In this work we review some features of topological defects in field theory models for real scalar fields. We investigate topological defects in models involving one and two or more real scalar fields. In models involving a single field we examine two different subclasses of models, which support one or more topological defects. In models involving two or more real scalar fields, we explore the presence of defects that live inside topological defects, and junctions and networks of defects. In the case of junctions of defects we investigte structures that simulate nanotubes and fulerenes. Our investigations may also be used to describe nonlinear properties of polymers, Langmuir films and optical solitons in fibers.
Permanental sequences with non-symmetric kernels that are generalization of the potentials of a Markov chain with state space $\{0,1/2, \ldots, 1/n,\ldots\}$ that was introduced by Kolmogorov, are studied. Depending on a parameter in the kernels we obtain an exact rate of divergence of the sequence at $0$, an exact local modulus of continuity of the sequence at $0$, or a precise bounded discontinuity for the sequence at $0$.
A Bayesian statistical formalism is developed to quantify the level at which the mass function slope (alpha) and the projected cumulative mass fraction (f) of (CDM) substructure in strong gravitational-lens galaxies, with arcs or Einstein rings, can be recovered as function of the lens-survey parameters and the detection threshold of the substructure mass. The method is applied to different sets of mock data to explore a range of observational limits: (i) the number of lens galaxies in the survey, (ii) the mass threshold, Mlow, for the detection of substructures and (iii) the uncertainty of the measured substructure masses. We explore two different priors on the mass function slope: a uniform prior and a Gaussian prior with alpha = 1.90+-0.1. With a substructure detection threshold Mlow=3x10^8 Msun, the number of lenses available now (n_l=30), a true dark-matter mass fraction in (CDM) substructure <=1.0% and a prior of alpha = 1.90+-0.1, we find that the upper limit of f can be constrained down to a level <=1.0% (95% CL). In the case of a Gaussian prior on alpha, it is always possible to set stringent constraints on both parameters. We also find that lowering the detection threshold has the largest impact on the ability to recover alpha, because of the (expected) steep mass-function slope. In the future, thanks to new surveys with telescopes, such as SKA, LSST and JDEM and follow-up telescopes with high-fidelity data, a significant increase in the number of known lenses will allow us to recover the satellite population in its completeness. For example, a sample of 200 lenses, equivalent in data-quality to the Sloan Lens ACS Survey and a detection threshold of 10^8 Msun, allows one to determine f=0.5+-0.1% (68% CL) and alpha=1.90+-0.2 (68% CL).
How is the universe organized on large scales? How did this structure evolve from the unknown initial conditions of a rather smooth early universe to the present time? The answers to these questions will shed light on the cosmology we live in, the amount, composition and distribution of matter in the universe, the initial spectrum of density fluctuations that gave rise to this structure, and the formation and evolution of galaxies, clusters of galaxies, and larger scale structures. To address these fundamental questions, large and accurate sky surveys are needed---in various wavelengths and to various depths. In this presentation I review current observational studies of large scale structure, present the constraints these observations place on cosmological models and on the amount of dark matter in the universe, and highlight some of the main unsolved problems in the field of large-scale structure that could be solved over the next decade with the aid of current and future surveys. I briefly discuss some of
We present an approach to generate machine-learned force fields (MLFF) with beyond density functional theory (DFT) accuracy. Our approach combines on-the-fly active learning and $\Delta$-machine learning in order to generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on-the-fly during DFT based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces and stress tensors. Thanks to the relatively smooth nature of the differences, the expensive RPA calculations are performed only on a small number of representative structures of small unit cells. These structures are determined by a singular value decomposition rank compression of the kernel matrix with low spatial resolution. This dramatically reduces the computational cost and allows us to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia.
We analyze 4\,050 wide binary star systems involving a white dwarf (WD) and usually a main sequence (MS) star, drawn from the large sample assembled by \citet[][hereafter, T20]{Tian_2020}. Using the modeling code BASE-9, we determine the system's ages, the WD progenitors' ZAMS masses, the extinction values ($A_V$), and the distance moduli. Discarding the cases with poor age convergences, we obtain ages for 3\,551 WDs, with a median age precision of $\sigma_{\tau}/\tau = 20$\%, and system ages typically in the range of 1-6 Gyr. We validated these ages against the very few known clusters and through cross-validation of 236 WD-WD binaries. Under the assumption that the components are co-eval in a binary system, this provides precise age constraints on the usually low-mass MS companions, mostly inaccessible by any other means.
The dark halo substructures predicted by current cold dark matter simulations may in principle be detectable through strong-lensing image splitting of quasars on small angular scales (0.01 arcseconds or below). Here, we estimate the overall probabilities for lensing by substructures in a host halo closely aligned to the line of sight to a background quasar. Under the assumption that the quasar can be approximated as a point source, the optical depth for strong gravitational lensing by subhalos typically turns out to be very small (tau < 0.01), contrary to previous claims. We therefore conclude that it is currently not feasible to use this strategy to put the simulation predictions for the dark matter subhalo population to the test. However, if one assumes the source to be spatially extended, as is the case for a quasar observed at radio wavelengths, there is a reasonable probability for witnessing substructure lensing effects even at rather large projected distances from the host galaxy, provided that the angular resolution is sufficient. While multiply-imaged, radio-loud quasars would be the best targets for unambiguously detecting dark matter subhalos, even singly-imaged radio quasars might be useful for setting upper limits on the abundance and central surface mass density of subhalos.
We show that the Kazhdan-Lusztig basis elements $C_w$ of the Hecke algebra of the symmetric group, when $w \in S_n$ corresponds to a Schubert subvariety of a Grassmann variety, can be written as a product of factors of the form $T_i+f_j(v)$, where $f_j$ are rational functions.
This is a continuation of the first author's development of the theory of elliptic differential operators with edge degeneracies. That first paper treated basic mapping theory, focusing on semi-Fredholm properties on weighted Sobolev and H\"older spaces and regularity in the form of asymptotic expansions of solutions. The present paper builds on this through the formulation of boundary conditions and the construction of parametrices for the associated boundary problems. As before, the emphasis is on the geometric microlocal structure of the Schwartz kernels of parametrices and generalized inverses.
Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the restrictions to D of Sol M and Sol End M are local systems. By contrast to the very different natures of these loci (the first one is defined via algebra, the second one is defined via analysis), the proof of their coincidence is geometric. It relies on the moduli of Stokes torsors.
These are the notes accompanying three lectures given by the second author at the Motivic Geometry program at CAS, which aim to give an introduction and an overview of some recent developments in the field of reciprocity sheaves.
We investigate the changes to a single photon state caused by the non-maximal entanglement in continuous variable quantum teleportation. It is shown that the teleportation measurement introduces field coherence in the output.
WMAP data when combined with ancillary data on free-free, synchrotron and dust allow an improved understanding of the spectrum of emission from each of these components. Here we examine the sky variation at intermediate and high latitudes using a cross-correlation technique. In particular, we compare the observed emission in several large partitions of the sky plus 33 selected sky regions to three "standard" templates. The regions are selected using a criterion based on the morphology of these template maps. The synchrotron emission shows evidence of steepening between GHz frequencies and the \emph{WMAP} bands. There are indications of spectral index variations across the sky but the current data are not precise enough to accurately quantify this from region-to-region. The emission correlated with the $H_{\alpha}$ template shows clear evidence of deviation from a free-free spectrum. The emission can be decomposed into a contribution from both free-free and spinning dust in the warm ionised medium of the Galaxy. The derived free-free emissivity corresponds to a mean electron temperature of $\sim 6000$ K, although the value depends critically on the impact of dust absorption on the $H_{\alpha}$ intensity. The WIM spinning dust emission has a peak emission in intensity in the range 40--50 GHz. The anomalous microwave emission associated with dust is detected at high significance in most of the 33 fields studied. The anomalous emission correlates well with the Finkbeiner et al. (1999) model 8 predictions (FDS8) at 94 GHz, and is well described globally by a power-law emission model with an effective spectral index between 20 and 60 GHz of $\beta \approx -2.7$. It is clear that attempts to explain the emission by spinning dust models require multiple components, which presumably relates to a complex mix of emission regions along a given line-of-sight.
We have studied the electric and thermal response of two-dimensional Dirac-fermions in a quantizing magnetic field in the presence of localized disorder. The electric and heat current operators in the presence of magnetic field are derived. The self-energy due to impurities is calculated self-consistently, and depends strongly on the frequency and field strength, resulting in asymmetric peaks in the density of states at the Landau level energies, and small islands connecting them. The Shubnikov-de Haas oscillations remain periodic in 1/B, in spite of the distinct quantization of quasiparticle orbits compared to normal metals. The Seebeck coefficient depends strongly on the field strength and orientation. For finite field and chemical potential, the Wiedemann-Franz law can be violated.