ShantanuT01/DACTYL-Pretraining huggingface dataset:
Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then prove that adiabatic quantum computing can realize the ground states of Hamiltonians with certain random interactions, as well as the ground states of one, two, and three-dimensional fermionic interaction lattices, in polynomial time. Finally, we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. A direct consequence is that the one-dimensional cluster state can be found in polynomial time using adiabatic quantum computing.
This review-style article presents an overview of recent progress in constructing and studying critical Gaussian multiplicative chaos. A proof that the critical measure in any dimension can be obtained as a limit of subcritical measures is given.
High entropy alloys (HEAs) are considered as a novel class of materials with a large number of components available in nearly equatomic proportions. One of the characteristic properties of HEAs was believed to be so-called "sluggish" diffusion. The faith on this myth instead of rigorous experimental analysis played such a dominant role that the first set of data on interdiffusion, in fact based on an improper analysis, were cited in hundreds of articles to state the presence of sluggishness of diffusion rates in high entropy alloys. In this review, the recent data on atomic diffusion in HEAs are critically discussed. The discussion is focused on tracer diffusion which is already measured dominantly for polycrystalline, but in some cases for single crystalline high-entropy alloys. Alternatively, a rigorous analysis of the interdiffuson experiments, which provide the diffusion rates of chemical species, too, becomes more and more sophisticated for three and more elements in an alloy and it is challenging to derive physically sound quantities from a general multicomponent diffusion experiment. Most promising in this case is the diffusion couple technique, especially the so-called pseudo-binary approach. This approach is analyzed with a focus on the applicability and the possible errors induced if up-hill diffusion appears. It is shown that atomic diffusion in HEAs cannot a priori be considered as sluggish and both atomic interactions as well as correlation effects are responsible for the observed trends. Even if estimated on the same homologous scale, the diffusion retardation induced by a "high entropy" in FCC crystals is not simply proportional to the number of alloying components and it is shown to be similar to that induced by the L12 ordering in a binary system. Furthermore, the importance of cross-correlations in diffusion of different species in HEAs is highlighted.
In this letter the nontopological scalar solitons are investigated in an anti de Sitter spacetime. We find analytically that the solitons obeying the necessary conditions $m=\frac{2}{\sqrt{3}}|\Lambda|^{{1/2}}$ or $m=\sqrt{\frac{2(n+3)(2n+3)}{3}}|\Lambda|^{{1/2}}$ can exist in the background by means of the series expansion.
A set $S$ of vertices of graph $G$ is a \textit{defensive alliance} of $G$ if for every $v \in S$, it holds $|N[v] \cap S| \geq |N[v]-S|$. An alliance $S$ is called $global$ if it is also a dominating set. In this paper, we determine the exact values of the global defensive alliance number of lexicographic products of path and cycles.
Discovering new electrodes for sodium-ion battery requires clear understanding of the material process during battery operation. Using first-principles calculations, we identify mechanisms of ionic diffusion and electronic transfer in newly developed cathode material, eldfellite Na$_x$Fe(SO$_4$)$_2$, reproducing the electrochemical properties in good agreement with experiment. The inserted sodium atom is suggested to diffuse along the two-dimensional pathway with preceding movement of the host sodium atom, and the activation energy is calculated to be reasonable for fast insertion. We calculate the electronic properties, showing the band insulating at low composition of inserted sodium, for which the electron polaron formation and hoping are also suggested. Our results may contribute to opening a new way of developing innovative cathode materials based on iron and sulfate ion.
BIMA CO 1-0 observations are presented of the spiral galaxies NGC 5394 and NGC 5395 that have undergone a recent, grazing encounter. In NGC 5394, 80% of the CO emission detected by BIMA is concentrated in the central 800 pc (FWHM) starburst region.In an encounter simulation that reproduces some of the main features of this galaxy pair, a considerable amount of gas in NGC 5394 falls into the central region early in the collision. The observed total gas distribution in the disk of NGC 5394 is lopsided, with more HI, CO, and H-alpha emission coming from the western or southwestern side. The innermost western arm of NGC 5394 is seen in CO and H-alpha emission, but the eastern inner-disk arm, which is very bright in the optical continuum, is not detected in CO or H-alpha emission. From a comparison of the radio continuum, H-alpha, 60 micron, and CO luminosities, we estimate that the average visual extinction of the starburst is 3 - 4 mag and the conversion factor N(H2)/I(CO) in the starburst is a factor of 3 - 4 below the standard value. Comparison of NGC 5394 with two other systems previously studied suggests that in prograde grazing encounters a central starburst may not develop until near the end of the ocular phase. Very little of the CO emission from NGC 5395 found in previous single-dish observations is detected by BIMA.
An unspecified strong dynamics may give rise to composite vectors sufficiently light that their interactions, among themselves or with the electroweak gauge bosons, be approximately described by an effective Lagrangian invariant under $SU(2)_L\times SU(2)_R/ SU(2)_{L+R}$. We study the production at the LHC of two such states by vector boson fusion or by the Drell--Yan process in this general framework and we compare it with the case of gauge vectors from a $SU(2)_L\times SU(2)_R\times SU(2)^N$ gauge model spontaneously broken to the diagonal SU(2) subgroup by a generic $\sigma$-model. Special attention is payed to the asymptotic behaviour of the different amplitudes in both cases. The expected rates of multi-lepton events from the decay of the composite vectors are also given. A thorough phenomenological analysis and the evaluation of the backgrounds to such signals, aiming at assessing the visibility of composite-vector pairs at the LHC, is instead deferred to future work.
Semantic segmentation is a fundamental task in computer vision, which can be considered as a per-pixel classification problem. Recently, although fully convolutional neural network (FCN) based approaches have made remarkable progress in such task, aggregating local and contextual information in convolutional feature maps is still a challenging problem. In this paper, we argue that, when predicting the category of a given pixel, the regions close to the target are more important than those far from it. To tackle this problem, we then propose an effective yet efficient approach named Vortex Pooling to effectively utilize contextual information. Empirical studies are also provided to validate the effectiveness of the proposed method. To be specific, our approach outperforms the previous state-of-the-art model named DeepLab v3 by 1.5% on the PASCAL VOC 2012 val set and 0.6% on the test set by replacing the Atrous Spatial Pyramid Pooling (ASPP) module in DeepLab v3 with the proposed Vortex Pooling. Moreover, our model (10.13FPS) shares similar computation cost with DeepLab v3 (10.37 FPS).
Given an $r$-edge-coloured complete graph $K_n$, how many monochromatic connected components does one need in order to cover its vertex set? This natural question is a well-known essentially equivalent formulation of the classical Ryser's conjecture which, despite a lot of attention over the last 50 years, still remains open. A number of recent papers consider a sparse random analogue of this question, asking for the minimum number of monochromatic components needed to cover the vertex set of an $r$-edge-coloured random graph $\mathcal{G}(n,p)$.   Recently, Buci\'{c}, Kor\'{a}ndi and Sudakov established a connection between this problem and a certain Helly-type local to global question for hypergraphs raised about 30 years ago by Erd\H{o}s, Hajnal and Tuza. We identify a modified version of the hypergraph problem which controls the answer to the problem of covering random graphs with monochromatic components more precisely. To showcase the power of our approach, we essentially resolve the $3$-colour case by showing that $(\log n / n)^{1/4}$ is a threshold at which point three monochromatic components are needed to cover all vertices of a $3$-edge-coloured random graph, answering a question posed by Kohayakawa, Mendon\c{c}a, Mota and Sch\"ulke. Our approach also allows us to determine the answer in the general $r$-edge coloured instance of the problem, up to lower order terms, around the point when it first becomes bounded, answering a question of Buci\'c, Kor\'andi and Sudakov.
The correct use of energy-dependent single-particle level (s.p.l.) densities within particle-hole state densities based on the equidistant spacing model (ESM) is analysed. First, an analytical expression is obtained following the convolution of energy-dependent excited-particle and hole densities. Next, a comparison is made with results of the ESM formula using average s.p.l. densities for the excited particles and holes, respectively. The Fermi-gas model (FGM) s.p.l. densities calculated at the corresponding average excitation energies are used in both cases. The analysis concerns also the density of particle-hole bound states. The pairing correlations are taken into account while the comparison of various effects includes the exact correction for the Pauli exclusion principle. Quantum-mechanical s.p.l. densities and the continuum effect can also match a corresponding FGM formula, suitable for use within the average energy-dependent partial state density in multistep reaction models.
In the present work, a set of ZrO2 thin films have been deposited at 82 degree angle of deposition at several substrate rotation speeds and at 0 degree. The effect of substrate rotation on optical, structural, morphological properties and residual stress has been studies thoroughly. Refractive index estimated from ellipsometric measurement and suitable modeling depicts an interesting decreasing behavior with substrate rotation and has been explained in the light of varying columnar structure with substrate rotation. Refractive index of GLAD ZrO2 films varies between and 1.901 to 2.011. Normally deposited film exhibits refractive index value of 2.178 which is substantially greater than that of GLAD films. Lowering in refractive index of glancing angle deposited films is the attribute of dominant atomic shadowing at glancing angles. Further, correlation length which is the representative of surface grain size was obtained from suitable modeling of atomic force microscopy data and it exhibits a decreasing trend with substrate rotation. The trend has also been attributed to the varying columnar microstructure with substrate rotation. All the glancing angle deposited ZrO2 films possess root mean square roughness between 4.6 and 5.1 nm whereas normally deposited film depicts 1.0 nm rms roughness. Dominant atomic shadowing is responsible for high roughness of GLAD films. Both glancing angle and normally deposited films exhibit preferential growth of monoclinic phase oriented in different directions. GLAD films also depict a tetragonal peak which has been attributed to the fine nano-crystallite size (~13 nm). Residual stress depicts a great switching from large compressive to small tensile as the deposition angle switches from normal to glancing angle
We summarize the current status of our understanding of nuclear forces based upon chiral symmetry--an idea that was advocated by Gerry Brown already several decades ago.
Why should we trust the detections of deep neural networks for manipulated faces? Understanding the reasons is important for users in improving the fairness, reliability, privacy and trust of the detection models. In this work, we propose an interpretable face manipulation detection approach to achieve the trustworthy and accurate inference. The approach could make the face manipulation detection process transparent by embedding the feature whitening module. This module aims to whiten the internal working mechanism of deep networks through feature decorrelation and feature constraint. The experimental results demonstrate that our proposed approach can strike a balance between the detection accuracy and the model interpretability.
The success of the "Cluster Variation Method" (CVM) in reproducing quite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of errors: We show that the CVM produces correlation functions that are too close to zero, which leads to an overestimation of the exact energy, E, and at the same time, to an underestimation of -TS, so the free energy F=E-TS is more accurate than either of its parts. This insight explains a problem with "hybrid methods" using MC correlation functions in the CVM entropy expression: They give exact energies E and do not give significantly improved -TS relative to CVM, so they do not benefit from the above noted cancellation of errors. Additionally, "hybrid methods" suffer from the difficulty of adequately accounting for both ordered and disordered phases in a consistent way. A different technique, the "Entropic Monte Carlo" (EMC), is shown here to provide a means for critically evaluating the CVM entropy. Inspired by EMC results, we find a universal and simple correction to the CVM entropy which produces individual components of the free energy with MC accuracy, but is computationally much less expensive than either MC thermodynamic integration or EMC.
An affine algebraic variety $X$ is rigid if the algebra of regular functions ${\mathbb K}[X]$ admits no nonzero locally nilpotent derivation. We prove that a factorial trinomial hypersurface is rigid if and only if every exponent in the trinomial is at least 2.
This paper is focused on the functional renormalization group applied to the $T_5^6$ tensor model on the Abelian group $U(1)$ with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.
We compute the branching ratio of inclusive $B \to \eta' X_s$ decay based upon the QCD anomaly mechanism: $b\to s+g^*\to s+g+\eta'$. To obtain a reliable $B \to \eta' X_s$ branching ratio, we calculate the $b\to s+g^*$ form factors up to the next-to-leading-logarithmic(NLL) approximation. We point out that the Standard Model prediction for $B\to \eta' X_s$ is consistent with the CLEO data, in contrast to the claims of some previous works.
The available minima timings of 14 selected eclipsing binaries (V1297 Cas, HD 24105, KU Aur, GU CMa, GH Mon, AZ Vel, DI Lyn, DK Her, GQ Dra, V624 Her, V1134 Her, KIC 6187893, V1928 Aql, V2486 Cyg) were collected and analyzed. Using the automatic telescopes, surveys, and satellite data, we derived more than 2500 times of eclipses, accompanied with our own ground-based observations. These data were used to detect the period variations in these multiple systems. The eclipse timing variations were described using the third-body hypothesis and the light-time effect. Their respective periods were derived as 2.5, 16.2, 27, 20, 64, 5.6, 22, 115, 27, 42, 6.9, 11.2, 4.1, and 8.4 years for these systems, respectively. The predicted minimal mass of the third body was calculated for each of the systems, and we discuss here their prospective detectability. The light curves of HD 24105, GH Mon, DK Her, V1134 Her, KIC 6187893, V1928 Aql, and V2486 Cyg were analyzed using the PHOEBE program, resulting in physical parameters of the components. Significant fractions of the third light were detected during the light-curve analysis, supporting our hypothesis of the triple-star nature of all these systems. The majority of these systems (nine out of 14) were already known as visual doubles. Our study shifts them to possible quadruples, what makes them even more interesting.
In the hierarchical view of star formation, giant molecular gas clouds (GMCs) undergo fragmentation to form small-scale structures made up of stars and star clusters. Here we study the connection between young star clusters and cold gas across a range of extragalactic environments by combining the high resolution (1") PHANGS-ALMA catalogue of GMCs with the star cluster catalogues from PHANGS-HST. The star clusters are spatially matched with the GMCs across a sample of 11 nearby star-forming galaxies with a range of galactic environments (centres, bars, spiral arms, etc.). We find that after 4-6 Myr the star clusters are no longer associated with any gas clouds. Additionally, we measure the autocorrelation of the star clusters and GMCs as well as their cross-correlation to quantify the fractal nature of hierarchical star formation. Young ($\leq$ 10 Myr) star clusters are more strongly autocorrelated on kpc and smaller spatial scales than the >10 Myr stellar populations, indicating that the hierarchical structure dissolves over time.
We report the first study of OH(1720 MHz) masers in the LMC in order to probe regions where supernova remnants interact with adjacent molecular clouds. Using the ATCA, we observed four sources in the LMC and detected a single OH(1720 MHz) maser with a flux density of 377 mJy toward 30 Doradus. No main line emission at 1665 or 1667 MHz was detected. The observed OH(1720 MHz) maser emission from 30 Dor shows characteristics similar to the well-known collisionally-pumped supernova remnant masers found in the Galaxy, though 30 Dor is known as a star forming region. It is possible that shocks driven by a nearby supernova remnant or by strong stellar winds from young stars are responsible for production of OH(1720 MHz) maser in 30 Dor. Future studies are required to distinguish between collisional and radiative pumping mechanisms for the 30 Dor OH (1720 MHz) maser.
We study the implications of a pseudo-phase-space density power-law for the anisotropy profile of a Milky Way-like dark matter halo. Requiring that the anisotropy parameter does not take non-physical values within the virial radius places a maximum value on the local radial velocity dispersion. For a plausible range of halo parameters, it is possible to take a local total velocity dispersion of up to about $300\,\mathrm{km/s}$. Making this choice uniquely specifies the anisotropy and dispersion profiles. We introduce a way to model the local velocity distribution that incorporates this anisotropy and study the impact on direct detection.
The $so(2,1)$ Euclidean Connection formalism is used to calculate the $S$ matrix for the Hypergeometric Natanzon Potentials ($HNP$).
We classify smooth Fano weighted complete intersections of large codimension.
St\"uckelberg interferometry describes the interference of two strongly coupled modes during a double passage through an avoided energy level crossing. In this work, we experimentally investigate finite time effects in St\"uckelberg interference and provide an exact analytical solution of the St\"uckelberg problem. Approximating this solution in distinct limits reveals uncharted parameter regimes of St\"uckelberg interferometry. Experimentally, we study these regimes using a purely classical, strongly coupled nanomechanical two-mode system of high quality factor. The classical two-mode system consists of the in-plane and out-of-plane fundamental flexural mode of a high stress silicon nitride string resonator, coupled via electric gradient fields. The dielectric control and microwave cavity enhanced universal transduction of the nanoelectromechanical system allows for the experimental access to all theoretically predicted St\"uckelberg parameter regimes. We exploit our experimental and theoretical findings by studying the onset of St\"uckelberg interference in dependence of the characteristic system control parameters and obtain characteristic excitation oscillations between the two modes even without the explicit need of traversing the avoided crossing. The presented theory is not limited to classical mechanical two-mode systems but can be applied to every strongly coupled (quantum) two-level system, for example a spin-1/2 system or superconducting qubit.
Starting from a uniform d-wave superconducting phase we study the energy cost due to imposed unidirectional defects with a vanishing pairing amplitude. Both renormalized mean-field theory and variational Monte Carlo calculations within the t-J model yield that the energies of inhomogeneous and uniform phases are very close to each other. This suggests that small perturbations in the microscopic Hamiltonian, might lead to inhomogeneous superconducting phases in real materials as observed in recent scanning tunneling microscopy on Ca_{2-x}Na_xCuO_2Cl_2.
In the previous work, it was shown that the degrees of freedom on the horizon of BTZ black hole can be described by two chiral massless scalar fields with opposite chirality. In this paper, we continuous this research. It is found that the scalar field is actually a compact boson field on a circle. The compactness results in the quantization of the black hole radius. Then we quantize the two boson fields and get two abelian Kac-Moody algebras. From the boson field, one can construct the full $W_{1+\infty}$ algebra which was used to classify the BTZ black holes.
$\delta'$-function perturbations and Neumann boundary conditions are incorporated into the path integral formalism. The starting point is the consideration of the path integral representation for the one dimensional Dirac particle together with a relativistic point interaction. The non-relativistic limit yields either a usual $\delta$-function or a $\delta'$-function perturbation; making their strengths infinitely repulsive one obtains Dirichlet, respectively Neumann boundary conditions in the path integral.
Can a theory of flavour capable of describing the spectrum of fermion (including neutrino) masses and mixings also contain within it the seeds for a solution of the SUSY flavour and CP problems? We argue that supergravity together with a non-Abelian family symmetry can completely resolve the SUSY flavour and CP problems in a broad class of theories in which family symmetry and CP is spontaneously broken in the flavon sector. We show that a simple superpotential structure can suppresses the F-terms of the flavons and GUT scale Higgs fields and that, if this mechanism is implemented, the resulting flavour and CP violation is suppressed and comfortably within the experimental limits. For illustration, we study a specific model based on SU(3) family symmetry, but similar models based on non-Abelian (continuous or discrete) family symmetry will lead to similar results.