ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Robertson -- Schr\"{o}dinger, Heisenberg -- Robertson and Trifonov uncertainty relations for arbitrary two functions $f_{1}$ and $f_{2}$ depending on the quantum phase and the number of photons respectively, are given. Intelligent states and states which minimize locally the product of uncertainties $(\Delta f_{1})^{2}\cdot (\Delta f_{2})^{2}$ or the sum $(\Delta f_{1})^{2}+(\Delta f_{2})^{2}$ are investigated for the cases $f_{1}=\phi,\exp{(i\phi)}, \exp{(-i\phi)}, \cos{\phi}, \sin{\phi}$ and $f_{2}=n$.
We briefly survey recent results related to linear series on curves that are general in various moduli spaces, highlighting the interplay between algebraic geometry on a general curve and the combinatorics of its degenerations. Breakthroughs include the proof of the Maximal Rank Theorem, which determines the Hilbert function of the general linear series of given degree and rank on the general curve in M_g, and complete analogs of the standard Brill-Noether theorems for curves that are general in Hurwitz spaces. Other advances include partial results in a similar direction for linear series in the Prym locus of a general unramified double cover of a general k-gonal curve and instances of the Strong Maximal Rank Conjecture.
We obtain an asymptotic representation formula for harmonic functions with respect to a linear anisotropic nonlocal operator. Furthermore we get a Bourgain-Brezis-Mironescu type limit formula for a related class of anisotropic nonlocal norms.
We study Ruan's \textit{cohomological crepant resolution conjecture} for orbifolds with transversal ADE singularities. In the $A_n$-case we compute both the Chen-Ruan cohomology ring $H^*_{\rm CR}([Y])$ and the quantum corrected cohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the later up to some additional, technical assumptions. We construct an explicit isomorphism between $H^*_{\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case, verifying Ruan's conjecture. In the $A_n$-case, the family $H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that the conjecture should be slightly modified. We propose a new conjecture in the $A_n$-case which we prove in the $A_2$-case by constructing an explicit isomorphism.
We discuss the application of the deformation quantization approach to perturbative quantum field theory. We show that the various forms of Wick's theorem are a direct consequence of the structure of the star products. We derive the scattering function for a free scalar field in interaction with a spacetime-dependent source. We show that the translation to operator formalism reproduces the known relations which lead to the derivation of the Feynman rules.
We utilize variable-temperature, variable-frequency magneto-optical transverse magnetic susceptibility technique to study the static and dynamical magnetic properties of a thin-film CoO/Permalloy bilayer. Our measurements demonstrate that in the studied system, the directional asymmetry of the hysteresis loop is associated mainly with the difference in the reversal mechanisms between the two reversed states of magnetization stabilized by the exchange-induced uniaxial anisotropy. The latter is found to be much larger than the exchange-induced unidirectional anisotropy of the ferromagnet. We also observe an abrupt variation of the frequency-dependent imaginary part of ac susceptibility near the exchange bias blocking temperature, consistent with the magnetic freezing transition inferred from the previous time-domain studies of magnetic aging in similar systems. The developed measurement approach enables precise characterization of the dynamical and static characteristics of thin-film magnetic heterostructures that can find applications in reconfigurable magnonic and neuromorphic circuits.
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with one coin and two walkers whose purpose is to generate entanglement between walkers. We provide several classical computer simulations of our quantum algorithm in which we show that, although the asymptotical amount of entanglement generated between walkers does not reach the highest degree of entanglement possible at each step for either coin measurement outcome, the entanglement ratio (entanglement generated/highest value of entanglement possible, for each step) tends to converge, and the actual convergence value depends on the coin initial state and on the coin measurement outcome. Furthermore, our numerical simulations show that, for the quantum walks used in our algorithm, the value towards which entanglement ratio converges also depends on the position probability distribution symmetry of a quantum walk computed with one single walker and the same coin initial state employed in the corresponding quantum walk with two walkers.
This paper proposes an automatic spatially-aware concept discovery approach using weakly labeled image-text data from shopping websites. We first fine-tune GoogleNet by jointly modeling clothing images and their corresponding descriptions in a visual-semantic embedding space. Then, for each attribute (word), we generate its spatially-aware representation by combining its semantic word vector representation with its spatial representation derived from the convolutional maps of the fine-tuned network. The resulting spatially-aware representations are further used to cluster attributes into multiple groups to form spatially-aware concepts (e.g., the neckline concept might consist of attributes like v-neck, round-neck, etc). Finally, we decompose the visual-semantic embedding space into multiple concept-specific subspaces, which facilitates structured browsing and attribute-feedback product retrieval by exploiting multimodal linguistic regularities. We conducted extensive experiments on our newly collected Fashion200K dataset, and results on clustering quality evaluation and attribute-feedback product retrieval task demonstrate the effectiveness of our automatically discovered spatially-aware concepts.
We study smoothings of Fano threefolds. We prove that the Picard number remains constant in the case of terminal Gorenstein singularities.
Large-scale, wave-like disturbances in extreme-ultraviolet (EUV) and type II radio bursts are often associated with coronal mass ejections (CMEs). Both phenomena may signify shock waves driven by CMEs. Taking EUV full-disk images at an unprecedented cadence, the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory has observed the so-called EIT waves or large-scale coronal propagating fronts (LCPFs) from their early evolution, which coincides with the period when most metric type II bursts occur. This article discusses the relation of LCPFs as captured by AIA with metric type II bursts. We show examples of type II bursts without a clear LCPF and fast LCPFs without a type II burst. Part of the disconnect between the two phenomena may be due to the difficulty in identifying them objectively. Furthermore, it is possible that the individual LCPFs and type II bursts may reflect different physical processes and external factors. In particular, the type II bursts that start at low frequencies and high altitudes tend to accompany an extended arc- shaped feature, which probably represents the 3D structure of the CME and the shock wave around it, rather than its near-surface track, which has usually been identified with EIT waves. This feature expands and propagates toward and beyond the limb. These events may be characterized by stretching of field lines in the radial direction, and be distinct from other LCPFs, which may be explained in terms of sudden lateral expansion of the coronal volume. Neither LCPFs nor type II bursts by themselves serve as necessary conditions for coronal shock waves, but these phenomena may provide useful information on the early evolution of the shock waves in 3D when both are clearly identified in eruptive events.
Atomic forces formulation based on the Dirac-Kohn-Sham equation and flexible (APW+lo/LAPW)+LO basis set is presented. The formulation was implemented in the code FlapwMBPT and allows a user to easily switch between different basis functions of the augmentation type (APW or LAPW) and between different kind of local orbitals. Similar to the work (Phys.Rev.B 91 (2015) 035105), the implementation takes into account small discontinuities of the wave functions, density, and potential at the muffin-tin sphere boundaries. Applications to the materials with strong relativistic effects, such as $\alpha$-Uranium, PuCoGa$_{5}$, and FePt, demonstrate robustness of the method. Comparison of the calculated forces with the ones obtained by numerical differentiation of the free energy shows close agreement with deviations about 0.1\% or less.
Understanding the process of electron tunneling in chirality-induced single-molecule junctions is imperative for the development of nanoscale switching and artificial nanomotors. Based on the combined non-equilibrium Green functions formalism and the ground-state density functional theory, we present here the charge transport behavior of chiral gold (7,3) nanowires (NWs) in comparison with various other chiral and achiral 1D gold nanostructures as the principal leads to form stable single-molecule junctions. For sigma-saturated alkane chains, we find that the contact potential barriers vary widely with the achiral leads but not with the chiral ones, although a close resemblance exists in the tunneling constants. Lower energy gaps for single-molecule junctions with Au(7,3)NWs ensure better electronic conductance even after allowing for the low thermal loss, due mainly to the close-packed arrangements of atoms with minimum wire tension. Our first-principles quantum transport analysis further suggests that chiral Au(7,3)NWs render higher electronic conductance than chiral gold (5,3) nanotubes (NTs), once bridged by either sigma-saturated or pi-conjugated molecular moieties. It, however, turns out that asymmetricity in the characteristics of channel formation at the lead-molecule contact remains often associated with chiral Au(7,3)NWs only.
We discuss a class of supersymmetric type II non-relativistic solutions with exact or asymptotic scale invariance. As already emerged from previous investigations, we find a clear correspondence between anisotropic d-dimensional vacua and relativistic solutions in (d + 1)-dimensions. We will show that supersymmetric four-dimensional Poincare' invariant backgrounds in type IIB can descend to analogous solutions with anisotropic scaling in t and (x, y). This result can be applied to scale invariant theories, domain walls interpolating between four-dimensional Lifshitz vacua and more general solutions with only asymptotic or approximate scaling behaviour.
Before we have determined that giant radio structure is typical for steep-spectrum sources detected with Ukrainian T-shaped Radio Telescope of model 2 (UTR-2). To estimate the jet propagation velocity and environment density of giant radio sources we consider the sample of galaxies and quasars with steep radio spectrum compiled from two regions of UTR-2 catalogue. The value of velocity of jet propagation is obtained from our estimates of linear size of radio structure and characteristic age of a source. We use the obtained values of jet propagation velocity for the estimates of density of jet environment, that is, density of environment at galaxies and quasars outskirts. We have derived that values of jet propagation velocities of examined sources are ~10e9 cm/s. The positive correlation of jet velocity and redshift of sources is displayed in our sample. On the assumption of equality of jet luminosity and corresponding kinetic luminosity we estimate the density of jet environment (radio structure environment) for galaxies (10e-26 gcm-3 to 10e-27 gcm-3) and quasars (10e-28 gcm-3). Considered steep-spectrum galaxies and quasars display strong evolution of jet propagation velocity and jet environment density. Properties of giant steep-spectrum sources are in accordance with conception of long evolution of powerful sources. The steep low-frequency spectra may be as markers of giant radio structures of galaxies and quasars.
Effects of temperature (6--225 K) and magnetic field (0--7 T) on the low-energy (1.2--5 meV) electrodynamics of the electromagnon, the magnetic resonance driven by the light electric field, have been investigated for a hexaferrite magnet Ba$_2$Mg$_2$Fe$_{12}$O$_{22}$ by using terahertz time-domain spectroscopy. We find the gigantic terahertz magnetochromism via electromagnons; the magnetochromic change, as defined by the difference of the absorption intensity with and without magnetic field, exceeds 500% even at 0.6 T. The results arise from the fact that the spectral intensity of the electromagnon critically depends on the magnetic structure. With changing the conical spin structures in terms of the conical angle $\theta$ from the proper screw ($\theta=0^\circ$) to the ferrimagnetic ($\theta=90^\circ$) through the conical spin-ordered phases ($0^\circ<\theta<90^\circ$) by external magnetic fields, we identify the maximal magnetochromism around $\theta\approx45^\circ$. On the contrary, there is no remarkable signature of the electromagnon in the proper screw and spin-collinear (ferrimagnetic) phases, clearly indicating the important role of the conical spin order to produce the magnetically-controllable electromagnons. The possible origin of this electromagnon is argued in terms of the exchange-striction mechanism.
Measurements of the hardness of a new high-pressure boron phase, orthorhombic {\gamma}-B28, are reported. According to the data obtained, {\gamma}-B28 has the highest hardness (~50 GPa) of all known crystalline modifications of boron.
We study the different phases of field theories of compact antisymmetric tensors of rank $h-1$ in arbitrary space-time dimensions $D=d+1$. Starting in a `Coulomb' phase, topological defects of dimension $d-h-1$ ($(d-h-1)$-branes) may condense leading to a generalized `confinement' phase. If the dual theory is also compact the model may also have a third, generalized `Higgs' phase, driven by the condensation of the dual $(h-2)$-branes. Developing on the work of Julia and Toulouse for ordered solid-state media, we obtain the low energy effective action for these phases. Each phase has two dual descriptions in terms of antisymmetric tensors of different ranks, which are massless for the Coulomb phase but massive for the Higgs and confinement phases. We illustrate our prescription in detail for compact QED in 4D. Compact QED and $O(2)$ models in 3D, as well as a periodic scalar field in 2D (strings on a circle), are also discussed. In this last case we show how $T$-duality is maintained if one considers both worldsheet instantons and their duals. We also unify various approaches to the problem of the axion mass in 4D string models. Finally we discuss possible implications of our results for non-perturbative issues in string theory.
Humans perform co-saliency detection by first summarizing the consensus knowledge in the whole group and then searching corresponding objects in each image. Previous methods usually lack robustness, scalability, or stability for the first process and simply fuse consensus features with image features for the second process. In this paper, we propose a novel consensus-aware dynamic convolution model to explicitly and effectively perform the "summarize and search" process. To summarize consensus image features, we first summarize robust features for every single image using an effective pooling method and then aggregate cross-image consensus cues via the self-attention mechanism. By doing this, our model meets the scalability and stability requirements. Next, we generate dynamic kernels from consensus features to encode the summarized consensus knowledge. Two kinds of kernels are generated in a supplementary way to summarize fine-grained image-specific consensus object cues and the coarse group-wise common knowledge, respectively. Then, we can effectively perform object searching by employing dynamic convolution at multiple scales. Besides, a novel and effective data synthesis method is also proposed to train our network. Experimental results on four benchmark datasets verify the effectiveness of our proposed method. Our code and saliency maps are available at \url{https://github.com/nnizhang/CADC}.
Because many classical Be stars may owe their nature to mass and angular-momentum transfer in a close binary, the present masses, temperatures, and radii of their components are of high interest for comparison to stellar evolution models. Kappa Dra is a 61.5-day single-lined binary with a B6 IIIe primary. With the CHARA Array instruments MIRC/MIRC-X and MYSTIC, we detected the secondary at (approximately photospheric) flux ratios of 1.49 +- 0.10% and 1.63 +- 0.09% in the H and K band, respectively. From a large and diverse optical spectroscopic database only the radial velocity curve of the Be star could be extracted. However, employing the parallaxes from Hipparcos and Gaia, which agree within their nominal 1-sigma errors, we could derive the total mass and found component masses of 3.65 +- 0.48 Msun and 0.426 +- 0.043 Msun for the Be star and the companion, respectively. Previous cross-correlation of the observed far-UV spectrum with sdO spectral model templates had not detected a companion belonging to the hot O-type subdwarf (sdO) population known from ~20 earlier-type Be stars. Guided by our full 3D orbital solution, we found a strong cross-correlation signal for a stripped subdwarf B-type companion (far-UV flux ratio of 2.3 +- 0.5%), enabling the first firm characterization of such a star, and making kappa Dra the first mid- to late-type Be star with a directly-observed subdwarf companion.
In this paper, we study the stellar structure in terms of alternative theory of gravity specially by f (R;T) gravity theory. Here, we consider the function f (R;T) = R+2VT where R is the Ricci scalar, T is the stress-energy momentum and V is the coupling constant. Using it we developed a stellar model that briefly explains the isotropic matter distribution within the compact object filled with perfect fluid. The stability of the model is shown by several physical and stability conditions. With the accecptibility of our theory, we were able to collect data for compact stars like PSR-B0943+10, CEN X-3, SMC X-4, Her X-1 and 4U1538-52 with great accuracy.
Galaxy clusters grow by mergers with other clusters and galaxy groups. These mergers create shock waves within the intracluster medium (ICM) that can accelerate particles to extreme energies. In the presence of magnetic fields, relativistic electrons form large regions emitting synchrotron radiation, so-called radio relics. Behind the shock front, synchrotron and inverse Compton (IC) losses cause the radio spectral index to steepen away from the shock front. An example of such a cluster is CIZA J2242.8+5301, where very clear spectral steepening in the downstream region is observed. Here we present hydrodynamical simulations of idealized binary cluster mergers with the aim of constraining the merger scenario for this cluster. From our simulations, we find that CIZA J2242.8+5301 is probably undergoing a merger in the plane of the sky (less then 10 deg from edge-on) with a mass ratio of about 2:1, and an impact parameter < 400 kpc. We find that the core passage of the clusters happened about 1 Gyr ago. We conclude that double relics relics can set constraints on the mass ratios, impact parameters, timescales, and viewing geometry of binary cluster mergers, which is particularly useful when detailed X-ray observations are not available. In addition, the presence of large radio relics can be used to constrain the degree of clumping in the outskirts of the ICM, which is important to constrain the baryon fraction, density and entropy profiles, around the virial radius and beyond. We find that the amplitude of density fluctuations, with sizes of < 200 kpc, in the relic in CIZA J2242.8+5301 is not larger than 30%. [abridged]
We investigate the nef cone spanned by the diagonal and the fibre classes of second symmetric product of a curve of genus $g$. This 2-dimensional nef cone gives a characterization of double covers of curves of genus $\le \frac{g-1}{8}$. This is a generalization of a result by Debarre.
We consider a model in which positive and negative particles diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counterclockwise and oppositely-charged adjacent particles may swap positions. Monte-Carlo simulations and analytic calculations suggest that the model has three phases; a "pure" phase in which one has three pinned blocks of only positive, negative particles and vacancies, and in which translational invariance is spontaneously broken, a "mixed" phase with a non-vanishing current in which the three blocks are positive, negative and neutral, and a disordered phase without blocks.
We study quenching dynamics of a one-dimensional transverse Ising chain with nearest neighbor antiferromagentic interactions in the presence of a longitudinal field which renders the model non-integrable. The dynamics of the spin chain is studied following a slow (characterized by a rate) or sudden quenches of the longitudinal field; the residual energy, as obtained numerically using a t-DMRG scheme, is found to satisfy analytically predicted scaling relations in both the cases. However, analyzing the temporal evolution of the Loschmidt overlap, we find different possibilities of the presence (or absence) of dynamical phase transitions (DPTs) manifested in the non-analyticities of the rate function. Even though the model is non-integrable, there are {periodic} occurrences of DPTs when the system is slowly ramped across the quantum critical point (QCP) as opposed to the ferromagnetic (FM) version of the model; this numerical finding is qualitatively explained by mapping the original model to an effective integrable spin model which is appropriate for describing such slow quenches. Furthermore, concerning the sudden quenches, our numerical results show that in some cases, DPTs can be present even when the spin chain is quenched within the same phase or even to the QCP while in some other situations they completely disappear even after quenching across the QCP. These observations lead us to the conclusion that it is the change in the nature of the ground state that determines the presence of DPTs following a sudden quench.
The interpretation of the new effect of the superfluidity in reactions with small number of particles is discussed in a simple model where the exact solution is accessible. It is find that the fluctuations of observable with the gauge angle reproduce well the exact fluctuations. Then a method of projection is proposed and tested to determine the transfer probabilities between two superfluid systems.
We investigate the effect of Rashba spin-orbit coupling and of a tunnel barrier on the zero conduc- tance resonances appearing in a one-dimensional conducting Aharonov-Bohm (AB) ring symmet- rically coupled to two leads. The transmission function of the corresponding one-electron problem is derived within the scattering matrix approach and analyzed in the complex energy plane with focus on the role of the tunnel barrier strength on the zero-pole structure characteristic of trans- mission (anti)resonances. The lifting of the real conductance zeros is related to the breaking of the spin-reversal symmetry and time-reversal symmetry of Aharonov-Casher (AC)and AB rings, as well as to rotational symmetry breaking in presence of a tunnel barrier. We show that the polarization direction of transmitted electrons can be controlled via the tunnel barrier strength and discuss a novel spin-filtering design in one-dimensional rings with tunable spin-orbit interaction.