ShantanuT01/DACTYL-Pretraining huggingface dataset:
We perform a perturbative QCD analysis of the gravitational form factors (GFFs) of nucleon at large momentum transfer. We derive the explicit factorization formula of the GFFs in terms of twist-3 and twist-4 light-cone distribution amplitudes of nucleon. Power behaviors for these GFFs are obtained from the leading order calculations. Numeric results of the quark and gluon contributions to various GFFs are presented with model assumptions for the distribution amplitudes in the literature. We also present the perturbative calculations of the scalar form factor $\langle P'|F^2| P\rangle$ for pion and proton at large momentum transfer.
A theta is a graph consisting of two non-adjacent vertices and three internally disjoint paths between them, each of length at least two. For a family $\mathcal{H}$ of graphs, we say a graph $G$ is $\mathcal{H}$-free if no induced subgraph of $G$ is isomorphic to a member of $\mathcal{H}$. We prove a conjecture of Sintiari and Trotignon, that there exists an absolute constant $c$ for which every (theta, triangle)-free graph $G$ has treewidth at most $c\log (|V(G)|)$. A construction by Sintiari and Trotignon shows that this bound is asymptotically best possible, and (theta, triangle)-free graphs comprise the first known hereditary class of graphs with arbitrarily large yet logarithmic treewidth.   Our main result is in fact a generalization of the above conjecture, that treewidth is at most logarithmic in $|V(G)|$ for every graph $G$ excluding the so-called three-path-configurations as well as a fixed complete graph. It follows that several NP-hard problems such as Stable Set, Vertex Cover, Dominating Set and Coloring admit polynomial time algorithms in graphs excluding the three-path-configurations and a fixed complete graph.
Multiple spatial zero formations for Stokes and Navier-Stokes equations in three dimensions are shown to occur according to nodal sets of solenoidal Hermite polynomials. Extensions to well-posed Burnett equations with the bi-harmonic viscosity operator are also discussed.
Experimental results of E2 transition probabilities or B(E2) values for the known first 2$^{+}$ states in 447 even-even nuclei have been compiled and evaluated. The evaluation policies for the analysis of experimental data have been described and new results are discussed. The recommended B(E2) values have been compared with comprehensive shell model calculations for a selected set of nuclei, where such theoretical procedures are amenable. The present work was motivated by a rapid increase in the number of new B(E2) measurements for the first 2$^{+}$ states since the previous evaluation of such data by S. Raman {\it et al.} published in 2001. Future plans to investigate the systematics of B(E2)$\uparrow$ values, and intercomparison of different experimental techniques to obtain these data are outlined.
Lithium niobate photonic circuits have the salutary property of permitting the generation, transmission, and processing of photons to be accommodated on a single chip. Compact photonic circuits such as these, with multiple components integrated on a single chip, are crucial for efficiently implementing quantum information processing schemes. We present a set of basic transformations that are useful for manipulating modal qubits in Ti:LiNbO$_3$ photonic quantum circuits. These include the mode analyzer, a device that separates the even and odd components of a state into two separate spatial paths; the mode rotator, which rotates the state by an angle in mode space; and modal Pauli spin operators that effect related operations. We also describe the design of a deterministic, two-qubit, single-photon, CNOT gate, a key element in certain sets of universal quantum logic gates. It is implemented as a Ti:LiNbO$_3$ photonic quantum circuit in which the polarization and mode number of a single photon serve as the control and target qubits, respectively. It is shown that the effects of dispersion in the CNOT circuit can be mitigated by augmenting it with an additional path. The performance of all of these components are confirmed by numerical simulations. The implementation of these transformations relies on selective and controllable power coupling among single- and two-mode waveguides, as well as the polarization sensitivity of the Pockels coefficients in LiNbO$_3$.
The maximum oriented $k$-forcing number of a simple graph $G$, written $\MOF_k(G)$, is the maximum directed $k$-forcing number among all orientations of $G$. This invariant was recently introduced by Caro, Davila and Pepper in [CaroDavilaPepper], and in the current paper we study the special case where $G$ is the complete graph with order $n$, denoted $K_n$. While $\MOF_k(G)$ is an invariant for the underlying simple graph $G$, $\MOF_k(K_n)$ can also be interpreted as an interesting property for tournaments. Our main results further focus on the case when $k=1$. These include a lower bound on $\MOF(K_n)$ of roughly $\frac{3}{4}n$, and for $n\ge 2$, a lower bound of $n - \frac{2n}{\log_2(n)}$. Along the way, we also consider various lower bounds on the maximum oriented $k$-forcing number for the closely related complete $q$-partite graphs.
The electronic anomalous Hall effect (AHE), where charge carriers acquire a velocity component orthogonal to an applied electric field, is one of the most fundamental and widely studied phenomena in physics. There are several different AHE mechanisms known, and material examples are highly sought after, however in the highly conductive (skew scattering) regime the focus has centered around ferromagnetic metals. Here we report the observation of a giant extrinsic AHE in KV$_3$Sb$_5$, an exfoliable, Dirac semimetal with a Kagome layer of Vanadium atoms. Although there has been no reports of magnetic ordering down to 0.25 K, the anomalous Hall conductivity (AHC) reaches $\approx$ 15,507 $\Omega^{-1}$cm$^{-1}$ with an anomalous Hall ratio (AHR) of $\approx$ 1.8$ \%$; an order of magnitude larger than Fe. Defying expectations from skew scattering theory, KV$_3$Sb$_5$ shows an enhanced skew scattering effect that scales quadratically, not linearly, with the longitudinal conductivity ($\sigma_{xx}$), opening the possibility of reaching an anomalous Hall angle (AHA) of 90$^{\circ}$ in metals; an effect thought reserved for quantum anomalous Hall insulators. This observation raises fundamental questions about the AHE and opens a new frontier for AHE (and correspondingly SHE) exploration, stimulating investigation in a new direction of materials, including metallic geometrically frustrated magnets, spin-liquid candidates, and cluster magnets.
A well-known high-school problem asking the final temperature of two spheres that are given the same amount of heat, one lying on a table and the other hanging from a thread, is re-examined. The conventional solution states that the sphere on the table ends up colder, since thermal expansion raises its center of mass. It is found that this solution violates the second law of thermodynamics and is therefore incorrect. Two different new solutions are proposed. The first uses statistical mechanics, while the second is based on purely classical thermodynamical arguments. It is found that gravity produces a counterintuitive effect on the heat capacity, and the new answer to the problem goes in the opposite direction of what traditionally thought.
This article studies the decoherence induced on a system of two qubits by local interactions with a spin chain with nontrivial internal dynamics (governed by an XY Hamiltonian). Special attention is payed to the transition between two limits: one in which both qubits interact with the same site of the chain and another one where they interact with distant sites. The two cases exhibit different behaviours in the weak and strong coupling regimes: when the coupling is weak it is found that decoherence tends to decrease with distance, while for strong coupling the result is the opposite. Also, in the weak coupling case, the long distance limit is rapidly reached, while for strong coupling there is clear evidence of an expected effect: environment-induced interactions between the qubits of the system. A consequence of this is the appearance of quasiperiodic events that can be interpreted as ``sudden deaths'' and ``sudden revivals'' of the entanglement between the qubits, with a time scale related to the distance between them.
We present an explicit basis for orders of arbitrary level N>1 in definite rational quaternion algebras. These orders have applications to computations of spaces of elliptic and quaternionic modular forms.
We discuss the phenomenology of a light U(1) gauge boson, $\gamma_B$, that couples only to baryon number. We assume that the new U(1) gauge symmetry is spontaneously broken and that the $\gamma_B$ mass is smaller than $m_Z$. Nevertheless, we show that the model survives the current experimental constraints. In addition, we argue that evidence for the existence of such a particle could be hidden in existing LEP and Tevatron data. We determine the allowed regions of the $m_B$-$\alpha_B$ plane, where $m_B$ is the $\gamma_B$ mass, and where $4 \pi \alpha_B$ is the squared gauge coupling. We point out that in some parts of the allowed parameter space our model can account for rapidity gap events in proton-antiproton scattering seen at the Fermilab Tevatron.
A positive, non-saturating and dominantly linear magnetoresistance is demonstrated to occur in the surface state of a topological insulator having a wavevector-linear energy dispersion together with a finite positive Zeeman energy splitting. This linear magnetoresistance shows up within quite wide magnetic-field range in a spatially homogenous system of high carrier density and low mobility in which the conduction electrons are in extended states and spread over many smeared Landau levels, and is robust against increasing temperature, in agreement with recent experimental findings in Bi$_2$Se$_3$ nanoribbons.
Document layout analysis is crucial for understanding document structures. On this task, vision and semantics of documents, and relations between layout components contribute to the understanding process. Though many works have been proposed to exploit the above information, they show unsatisfactory results. NLP-based methods model layout analysis as a sequence labeling task and show insufficient capabilities in layout modeling. CV-based methods model layout analysis as a detection or segmentation task, but bear limitations of inefficient modality fusion and lack of relation modeling between layout components. To address the above limitations, we propose a unified framework VSR for document layout analysis, combining vision, semantics and relations. VSR supports both NLP-based and CV-based methods. Specifically, we first introduce vision through document image and semantics through text embedding maps. Then, modality-specific visual and semantic features are extracted using a two-stream network, which are adaptively fused to make full use of complementary information. Finally, given component candidates, a relation module based on graph neural network is incorported to model relations between components and output final results. On three popular benchmarks, VSR outperforms previous models by large margins. Code will be released soon.
We present an integral representation formula for a Dirichlet series whose coefficients are the values of the Liouville's arithmetic function.
We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero-Sutherland model is suggested.
In this paper we prove strong unique continuation principle and unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the Caffarelli-Silvestre extension method combined with an Almgren type monotonicity formula. The corresponding extended problem is formulated as a systems of two second order equations with singular or degenerate weights in a half-space, for which asymptotics estimates are derived by a blow-up analysis.
Abdus Salam was known for his `grand views', grand views of science as well as grand views of society. In this talk the grand view of theoretical physics is put in perspective.
We prove the following theorem. Suppose that $F=(f_1, f_2)$ is a 2-dimensional vector-valued modular form on $SL_2(Z)$ whose component functions $f_1, f_2$ have rational Fourier coefficients with bounded denominators. Then $f_1$ and $f_2$ are classical modular forms on a congruence subgroup of the modular group.
We present a method to determine the spin temperature $T_{\rm S}$ and volume density $n$ of HI gas simultaneously along the tangent-point circle of galactic rotation in the Milky Way by using the least-$\chi^2$ method. The best-fit $T_{\rm S}$ is shown to range either in $T_{\rm S}=100-120$ K or in $1000-3000$ K, indicating that the gas is either in cold HI phase with high density and large optical depth, or in warm HI with low density and small optical depth. Averaged values at $3\le R \le 8$ kpc are obtained to be $T_{\rm S}=106.7 \pm 16.0$ K and $n=1.53\pm 0.86$ H cm$^{-3}$ for cold HI, and $1720 \pm 1060$ K and $0.38 \pm 0.10$ H cm$^{-3}$ for warm HI, where $R=8\ |\sin \ l|$ kpc is the galacto-centric distance along the tangent-point circle. The cold HI appears in spiral arms and rings, whereas warm HI in the inter-arm regions. The cold HI is denser by a factor of $\sim 4$ than warm HI. The present analysis has revealed the hidden HI mass in cold and optically thick phase in the galactic disk. The total HI mass inside the solar circle is shown to be greater by a factor of $2 - 2.5$ than the current estimation by optically thin assumption.
In the present work, we discuss the Wheeler-DeWitt quantization scheme for an n-dimensional anisotropic cosmological model with a perfect fluid in presence of a massless scalar field. We identify the time parameter using the generalization of Schutz formalism and find the wavepacket of the universe following standard Wheeler-DeWitt methodology of quantum cosmology. We also calculate the expectation values of scale factors and volume element. We show that quantized model escapes the singularity and supports bouncing universe solutions.
The low energy systems of three or four neutrons are treated within the adiabatic hyperspherical framework, yielding an understanding of the low energy quantum states in terms of an adiabatic potential energy curve. The dominant low energy potential curve for each system, computed here using widely accepted nucleon-nucleon interactions with and without the inclusion of a three-nucleon force, shows no sign of a low energy resonance. However, both systems exhibit a low energy enhancement of the density of states, or of the Wigner-Smith time-delay, which derives from long-range universal physics analogous to the Efimov effect. That enhancement could be relevant to understanding the low energy excess of correlated 4-neutron ejection events observed experimentally in a nuclear reaction by Kisamori et al.
The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of solutions with corrector terms) for gradients, diffusion fluxes and time-derivatives without assumptions for smoothness of coefficients. Proofs of the main results are based on the space-time version of the unfolding method, which is deeply concerned with the strong two-scale convergence theory.
Modifications of the Cont-Bouchaud percolation model for price fluctuations give an asymmetry for time-reversal, an asymmetry between high and low prices, volatility clustering, effective multifractality, correlations between volatility and traded volume, and a power law tail with exponent near 3 for the cumulative distribution of price changes. Combining them together still gives the same power law. Using Ising-correlated percolation does not change these results. Different modifications give log-periodic oscillations before a crash, arising from nonlinear feedback between random fluctuations.
We have recently developed an extended merger-tree model that efficiently follows hierarchical evolution of galaxy clusters and provides a quantitative description of both their dark matter and gas properties. We employed this diagnostic tool to calculate the thermal SZ power spectrum and cluster number counts, accounting explicitly for uncertainties in the relevant statistical and intrinsic cluster properties, such as the halo mass function and the gas equation of state. Results of these calculations are compared with those obtained from a direct analytic treatment and from hydrodynamical simulations. We show that under certain assumptions on the gas mass fraction our results are consistent with the latest SPT measurement. Our approach can be particularly useful in predicting cluster number counts and their dependence on cluster and cosmological parameters.
Spatially structured light fields applied to semiconductor quantum dots yield fundamentally different absorption spectra than homogeneous beams. In this paper, we theoretically discuss the resulting spectra for different light beams using a cylindrical multipole expansion. For the description of the quantum dots we employ a model based on the effective mass approximation including Coulomb and valence band mixing. The combination of a single spatially structured light beam and state mixing allows all exciton states in the quantum dot to become optically addressable. Furthermore, we demonstrate that the beams can be tailored such that single states are selectively excited, without the need of spectral separation. Using this selectivity, we propose a method to measure the exciton wave function of the quantum dot eigenstate. The measurement goes beyond electron density measurements by revealing the spatial phase information of the exciton wave function. Thereby polarization sensitive measurements are generalized by including the infinitely large spatial degree of freedom.
If unitary evolution of a quantum system is interrupted by a sequence of measurements we call the dynamics as quantum Zeno dynamics. We show that under quantum Zeno dynamics not only the transition probability (leading to quantum Zeno effect) but also phases are affected. We call this new effect as quantum Zeno phase effect (QZPE) which says that under repeated measurements the geometric phase of a quantum system can be inhibited. Since geometric phase attributes a memory to a quatum system this result also proves that under quantum Zeno dynamics the memory of a system can be erased. We have proposed a neutron interference experiment where this prediction can be tested. We also beleive that with Itano's kind of set up for two-level systems this prediction can be tested. This will provide a new way of controlling phase shift in interference experiment by doing repeated measurements.
We present results from spectral and temporal analyses of Suzaku and RXTE observations of the high mass X-ray binary LMC X-4. Using the full 13 years of available RXTE/ASM data, we apply the ANOVA and Lomb normalized Periodogram methods to obtain an improved superorbital period measurement of 30.32 +/- 0.04 days. The phase-averaged X-ray spectra from Suzaku observations during the high state of the superorbital period can be modeled in the 0.6--50 keV band as the combination of a power-law with Gamma ~ 0.6 and a high-energy cutoff at ~ 25 keV, a blackbody with kT_BB ~ 0.18 keV, and emission lines from Fe K_alpha, O VIII, and Ne IX (X Lyalpha). Assuming a distance of 50 kpc, The source has luminosity L_X ~ 3 x 10^38 ergs s^-1 in the 2--50 keV band, and the luminosity of the soft (blackbody) component is L_BB ~ 1.5 x 10^37 ergs s^-1. The energy resolved pulse profiles show single-peaked soft (0.5-1 keV) and hard (6-10 keV) pulses but a more complex pattern of medium (2-10 keV) pulses; cross-correlation of the hard with the soft pulses shows a phase shift that varies between observations. We interpret these results in terms of a picture in which a precessing disk reprocesses the hard X-rays and produces the observed soft spectral component, as has been suggested for the similar sources Her X-1 and SMC X-1.
The spatial search problem on regular lattice structures in integer number of dimensions $d\geq2$ has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here we investigate the spatial search problem on fractals of non-integer dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (and not the fractal) dimension. Our numerical results have been obtained on the well-known Sierpinski gaskets in two and three dimensions.
Due to the advancement of Generative Adversarial Networks (GAN), Autoencoders, and other AI technologies, it has been much easier to create fake images such as "Deepfakes". More recent research has introduced few-shot learning, which uses a small amount of training data to produce fake images and videos more effectively. Therefore, the ease of generating manipulated images and the difficulty of distinguishing those images can cause a serious threat to our society, such as propagating fake information. However, detecting realistic fake images generated by the latest AI technology is challenging due to the reasons mentioned above. In this work, we propose Dual Attention Fake Detection Fine-tuning Network (DA-FDFtNet) to detect the manipulated fake face images from the real face data. Our DA-FDFtNet integrates the pre-trained model with Fine-Tune Transformer, MBblockV3, and a channel attention module to improve the performance and robustness across different types of fake images. In particular, Fine-Tune Transformer consists of multiple numbers of an image-based self-attention module and a down-sampling layer. The channel attention module is also connected with the pre-trained model to capture the fake images feature space. We experiment with our DA-FDFtNet with the FaceForensics++ dataset and various GAN-generated datasets, and we show that our approach outperforms the previous baseline models.
Let $\0$ be a nilpotent orbit in a semisimple complex Lie algebra $\g$. Denote by $G$ the simply connected Lie group with Lie algebra $\g$. For a $G$-homogeneous covering $M \to \0$, let $X$ be the normalization of $\bar{\0}$ in the function field of $M$. In this note, we study the existence of symplectic resolutions for such coverings $X$.
This is a chapter on Black-hole Scattering that was commissioned for an Encyclopaedia on Scattering edited by Pike and Sabatier, to be published by Academic Press. The chapter surveys wave propagation in black-hole spacetimes, diffraction effects in wave scattering, resonances, quasinormal modes and related topics.
The high-energy gamma-ray emission discovered using the H.E.S.S. telescopes from the binary system PSR B1259 -63, is modelled using an extension of the approach that successfully predicted it. We find that the simultaneous INTEGRAL and H.E.S.S. data permit both a model with dominant radiative losses, high pulsar wind Lorentz factor and modest efficiency as well as one with dominant adiabatic losses, a slower wind and higher efficiency. Additional, simultaneous, X-ray and TeV data sets are needed to lift this degeneracy.