ShantanuT01/DACTYL-Pretraining huggingface dataset:
The ground-state properties of the spin-1 pyrochlore antiferromagnet are studied by applying the VBS-like tetrahedron-unit decomposition to the original spin system. The symmetrization required on every vertex is taken into account by introducing a ferromagnetic coupling. The pairwise effective Hamiltonian between the adjacent tetrahedrons is obtained by considering the next nearest neighbor and the third neighbor exchange interactions. We find that the transverse component of the spin chirality exhibits a long-range order, breaking the parity symmetry of the tetrahedral group, while the chirality itself is not broken.
A new Nijmegen soft-core OBE potential model is presented for the low-energy YN interactions. Besides the results for the fit to the scattering data, which largely defines the model, we also present some applications to hypernuclear systems using the G-matrix method. An important innovation with respect to the original soft-core potential is the assignment of the cut-off masses for the baryon-baryon-meson (BBM) vertices in accordance with broken SU(3)$_F$, which serves to connect the NN and the YN channels. As a novel feature, we allow for medium strong breaking of the coupling constants, using the $^3P_0$ model with a Gell-Mann--Okubo hypercharge breaking for the BBM coupling. We present six hyperon-nucleon potentials which describe the available YN cross section data equally well, but which exhibit some differences on a more detailed level. The differences are constructed such that the models encompass a range of scattering lengths in the $\Sigma N$ and $\Lambda N$ channels. For the scalar-meson mixing angle we obtained values $\theta_S=37$ to 40 degrees, which points to almost ideal mixing angles for the scalar $q\bar{q}$ states. The G-matrix results indicate that the remarkably different spin-spin terms of the six potentials appear specifically in the energy spectra of $\Lambda$ hypernuclei.
The discoveries of Dirac and Weyl semimetal states in spin-orbit compounds led to the realizations of elementary particle analogs in table-top experiments. In this paper, we propose the concept of a three-dimensional type-II Dirac fermion and identify a new topological semimetal state in the large family of transition-metal icosagenides, MA3 (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl3 family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node consists of four type-II Weyl nodes with chiral charge +/-1 via symmetry breaking. Furthermore, we predict the Landau level spectrum arising from the type-II Dirac fermions in VAl3 that is distinct from that of known Dirac semimetals. We also show a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions. The new type-II Dirac fermions, their novel magneto-transport response, the topological tunability and the large number of compounds make VAl3 an exciting platform to explore the wide-ranging topological phenomena associated with Lorentz-violating Dirac fermions in electrical and optical transport, spectroscopic and device-based experiments.
For graphs $F_n$ and $G_n$ of order $n$, if $R(F_n, G_n)=(\chi(G_n)-1)(n-1)+\sigma(G_n)$, then $F_n$ is said to be $G_n$-good, where $\sigma(G_n)$ is the minimum size of a color class among all proper vertex-colorings of $G_n$ with $\chi(G_n)$ colors. Given $\Delta(G_n)\le \Delta$, it is shown that $P_n$ is asymptotically $G_n$-good if $\alpha(G_n)\le\frac{n}{4}$.
We investigate the observational constraints on the modified gravity, which combines the $R^{2-q}$ inflation with the power-law (exponential) type of the viable $f(R)$ dark energy models. We discuss the difference between the combined model and $R^{2-q}$ gravity in the inflationary epoch and obtain the constraints on the deviation power $q$ as well as the parameters in $f(R)$ by using the CosmoMC package. The allowed ranges of the spectral index and tensor-to-scalar ratio from the Planck data are highly restricted, resulting in $q < 2.66 \times 10^{-2}$ and $2.17 \times 10^{-2}$ for the power-law and exponential types of $f(R)$ gravity, respectively.
Let $f$ be a non-negative square-integrable function on a finite volume hyperbolic surface $\Gamma\backslash\mathbb{H}$, and assume that $f$ is non-autocorrelated, that is, perpendicular to its image under the operator of averaging over the circle of a fixed radius $r$. We show that in this case the support of $f$ is small, namely, it satisfies $\mu(supp{f}) \leq (r+1)e^{-\frac{r}{2}} \mu(\Gamma\backslash\mathbb{H})$.   As a corollary, we prove a lower bound for the measurable chromatic number of the graph, whose vertices are the points of $\Gamma\backslash\mathbb{H}$, and two points are connected by an edge if there is a geodesic of length $r$ between them. We show that for any finite covolume $\Gamma$ the measurable chromatic number is at least $e^{\frac{r}{2}}(r+1)^{-1}$.
Given a smooth non-hyperelliptic curve C of genus 3 and a maximal isotropic subgroup (w.r.t. the Weil pairing) L in Jac(C)[2], there exists a smooth curve C' s.t. Jac(C')=Jac(C)/L. This construction is symmetric. i.e. if we start with C' and the dual flag on it, we get C. A previous less explicit approach was taken by Donagi and Livne. The advantage of our construction is that it is explicit enough to describe the isomorphism H^0(C,K_C)=H^0(C',K_C').
Low-energy dipole (LED) excitations in $^{18}$O were investigated using a combination of the variation after $K$-projection in the framework of antisymmetrized molecular dynamics with $\beta$-constraint with the generator coordinate method. We obtained two LED states, namely, the $1_1^-$ state with a dominant shell-model structure and the $1_2^-$ state with a large $^{14}\textrm{C}+\alpha$ cluster component. Both these states had significant toroidal dipole (TD) and compressive dipole (CD) strengths, indicating that the TD and CD modes are not separated but mixed in the LED excitations of $^{18}$O. This is unlike the CD and TD modes for well-deformed nuclei such as $^{10}$Be, where the CD and TD modes are generated as $K^{\pi}=0^-$ and $K^{\pi}=1^-$ excitations, respectively, in a largely deformed state.
We present a strong lensing modeling technique based on versatile basis sets for the lens and source planes. Our method uses high performance Monte Carlo algorithms, allows for an adaptive build up of complexity and bridges the gap between parametric and pixel based reconstruction methods. We apply our method to a HST image of the strong lens system RXJ1131-1231 and show that our method finds a reliable solution and is able to detect substructure in the lens and source planes simultaneously. Using mock data we show that our method is sensitive to sub-clumps with masses four orders of magnitude smaller than the main lens, which corresponds to about $10^8 M_{\odot}$, without prior knowledge on the position and mass of the sub-clump. The modelling approach is flexible and maximises automation to facilitate the analysis of the large number of strong lensing systems expected in upcoming wide field surveys. The resulting search for dark sub-clumps in these systems, without mass-to-light priors, offers promise for probing physics beyond the standard model in the dark matter sector.
This paper deals with the semiclassical radiation spectrum of static and circularly symmetric 3D charged dilaton black holes with cosmological constant {\Lambda} in non-asymptotically flat spacetimes. We first review the 3D charged dilaton black holes which are solution to low-energy string action. The wave equation of a massless scalar field is shown to be exactly solvable in terms of hypergeometric functions. Thus, the radiation spectrum and its corresponding temperature are obtained, precisely. Computations at high frequency regime show that the radiation spectrum yields the Hawking temperature of the black hole with no charge. Unlike the chargeless case, the Hawking temperature of the charged dilaton black holes is derived from the radiation spectrum at the low frequencies. The utmost importance of the {\Lambda} in the latter result is highlighted.
We analyze the electromagnetic scattering of massive particles with and without spin wherein one particle (or both) is electrically neutral. Using the techniques of effective field theory, we isolate the leading long distance effects, both classical and quantum mechanical. For spinless systems results are identical to those obtained earlier via more elaborate dispersive methods. However, we also find new results if either or both particles carry apin.
In this paper, we propose $\text{HF}^2$-VAD, a Hybrid framework that integrates Flow reconstruction and Frame prediction seamlessly to handle Video Anomaly Detection. Firstly, we design the network of ML-MemAE-SC (Multi-Level Memory modules in an Autoencoder with Skip Connections) to memorize normal patterns for optical flow reconstruction so that abnormal events can be sensitively identified with larger flow reconstruction errors. More importantly, conditioned on the reconstructed flows, we then employ a Conditional Variational Autoencoder (CVAE), which captures the high correlation between video frame and optical flow, to predict the next frame given several previous frames. By CVAE, the quality of flow reconstruction essentially influences that of frame prediction. Therefore, poorly reconstructed optical flows of abnormal events further deteriorate the quality of the final predicted future frame, making the anomalies more detectable. Experimental results demonstrate the effectiveness of the proposed method. Code is available at \href{https://github.com/LiUzHiAn/hf2vad}{https://github.com/LiUzHiAn/hf2vad}.
This note briefly reviews the {\it Mirror Principle} as developed in the series of papers \LLYI\LLYII\LLYIII\LLYIV\LCHY. We illustrate this theory with a few new examples. One of them gives an intriguing connection to a problem of counting holomorphic disks and annuli. This note has been submitted for the proceedings of the Workshop on Strings, Duality and Geometry the C.R.M. in Montreal of March 2000.
We construct a notion of teleparallelization for Newton-Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is consistent with teleparallelization in general relativity, and can be obtained by null-reducing the teleparallel equivalent of a five-dimensional gravitational wave solution. This work thus strengthens substantially the connections between four theories: Newton-Cartan theory, Newtonian gravitation theory, general relativity, and teleparallel gravity.
By means of extensive first-principles calculations we studied the ferroelectric phase transition and the associated isotope effect in KH2PO4 (KDP)
We report a resonant inelastic x-ray scattering study of electronic excitations in Li_2CuO_2, an insulating compound comprised of ribbons of edge-sharing copper-oxygen chains. Three excitations, which show little dependence on momentum transfer, are observed in our measurements. The lowest energy excitation at ~2.1 eV is dispersionless and is attributed to a localized d-d orbital excitation. We also observe two excitations at ~5.4 eV and ~7.6 eV which we assign to charge-transfer excitations. These high-energy excitations are also dispersionless along the copper-oxygen chain direction. However, in each case we observe a small energy dispersion along the direction perpendicular to the copper-oxygen ribbons, suggesting a significant interchain coupling in this system. We also discuss the possible implications of ferromagnetic nearest-neighbor intrachain coupling on the charge excitation spectra.
We define Hilbert-Siegel modular forms and Hecke "operators" acting on them. As with Hilbert modular forms, these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo natural identifications we can make between certain spaces. With Hilbert-Siegel forms we identify several families of natural identifications between certain spaces of modular forms. We associate the Fourier coefficients of a form in our product space to even integral lattices, independent of a basis and choice of coefficient rings. We then determine the action of the Hecke operators on these Fourier coefficients, paralleling the result of Hafner and Walling for Siegel modular forms (where the number field is the field of rationals).
We explore the significance of bars in triggering central star formation (SF) and AGN activity for spiral galaxy evolution using a volume-limited sample with $0.020<z<0.055$, $M_{\rm r}<-19.5$, and $\sigma>70\rm km s^{-1}$ selected from SDSS DR7. On a central SF rate-$\sigma$ plane, we measure the fraction of galaxies with strong bars in our sample and also the AGN fractions for barred and non-barred galaxies, respectively. The comparison between the bar and AGN fractions reveals a causal connection between the two phenomena of SF quenching and AGN activity. A massive BH and abundant gas fuels are sufficient conditions to trigger AGNs. We infer that the AGNs triggered by satisfying the two conditions drive the strong AGN feedback, suddenly suppressing the central SF and leaving the SF sequence. We find that in galaxies where either of the two conditions is not sufficient, bars are a great help for the AGN triggering, accelerating the entire process of evolution, which is particularly evident in pseudo-bulge galaxies. All of our findings are obtained only when plotted in terms of their central velocity dispersion and central SFR (not galactic scale SFR), indicating that the AGN-driven SF quenching is confined in the central kpc region.
We are studying possible interaction of damping coefficients in the subprincipal part of the linear 3D wave equation and their impact on the critical exponent of the corresponding nonlinear Cauchy problem with small initial data. The main new phenomena is that certain relation between these coefficients may cause very strong jump of the critical Strauss exponent in 3D to the critical 5D Strauss exponent for the wave equation without damping coefficients.
Video Visual Relation Detection (VidVRD), has received significant attention of our community over recent years. In this paper, we apply the state-of-the-art video object tracklet detection pipeline MEGA and deepSORT to generate tracklet proposals. Then we perform VidVRD in a tracklet-based manner without any pre-cutting operations. Specifically, we design a tracklet-based visual Transformer. It contains a temporal-aware decoder which performs feature interactions between the tracklets and learnable predicate query embeddings, and finally predicts the relations. Experimental results strongly demonstrate the superiority of our method, which outperforms other methods by a large margin on the Video Relation Understanding (VRU) Grand Challenge in ACM Multimedia 2021. Codes are released at https://github.com/Dawn-LX/VidVRD-tracklets.
The band structure of N=Z nuclei is constructed from intrinsic states defined in terms of quartets. The simplest of these states is a condensate of collective quartets with isospin T=0. The other intrinsic states are built by promoting one quartet of the condensate to an excited T=0 configuration. From these intrinsic states, by angular momentum projection, band structures are generated that approximate well the experimental ones. The projected states also reproduce to a very good extent the spectra resulting from configuration interaction calculations based on the same quartets forming the intrinsic states. These results show that the quartet-based intrinsic states provide the appropriate framework to understand in a simple and intuitive manner the emergence of band-like structures in N=Z nuclei.
The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.
The periodic standing wave approach to binary inspiral assumes rigid rotation of gravitational fields and hence helically symmetric solutions. To exploit the symmetry, numerical computations must solve for ``helical scalars,'' fields that are functions only of corotating coordinates, the labels on the helical Killing trajectories. Here we present the formalism for describing linearized general relativity in terms of helical scalars and we present solutions to the mixed partial differential equations of the linearized gravity problem (and to a toy nonlinear problem) using the adapted coordinates and numerical techniques previously developed for scalar periodic standing wave computations. We argue that the formalism developed may suffice for periodic standing wave computations for post-Minkowskian computations and for full general relativity.
Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy$_2$ spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as a bowl, a cup, or any surface of revolution? To give an answer to this, we report here extensive numerical analyses of several one-dimensional KPZ models on substrates whose size enlarges as $\langle L(t) \rangle = L_0+\omega t^{\gamma}$, while their mean height $\langle h \rangle$ increases as usual [$\langle h \rangle\sim t$]. We show that the competition between the $L$ enlargement and the correlation length ($\xi \simeq c t^{1/z}$) plays a key role in the asymptotic statistics of the interfaces. While systems with $\gamma>1/z$ have HDs given by GUE and the interface width increasing as $w \sim t^{\beta}$, for $\gamma<1/z$ the HDs are Gaussian, in a correlated regime where $w \sim t^{\alpha \gamma}$. For the special case $\gamma=1/z$, a continuous class of distributions exists, which interpolate between Gaussian (for small $\omega/c$) and GUE (for $\omega/c \gg 1$). Interestingly, the HD seems to agree with the Gaussian symplectic ensemble (GSE) TW distribution for $\omega/c \approx 10$. Despite the GUE HDs for $\gamma>1/z$, the spatial covariances present a strong dependence on the parameters $\omega$ and $\gamma$, agreeing with Airy$_2$ only for $\omega \gg 1$, for a given $\gamma$, or when $\gamma=1$, for a fixed $\omega$. These results considerably generalize our knowledge on the 1D KPZ systems, unveiling the importance of the background space in their statistics.
We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions. We also establish a Chung-type law of the iterated logarithm. The results can be applied to the Brownian sheet, fractional Brownian sheets whose Hurst indices are the same in all directions, and systems of linear stochastic wave equations in one spatial dimension driven by space-time white noise or colored noise.
We present an ab-initio calculation of the longitudinal electron scattering response function off 4He with two- and three-nucleon forces and compare to experimental data. The full four-body continuum dynamics is considered via the Lorentz integral transform method. The importance of the final state interaction is shown at various energies and momentum transfers q. The three-nucleon force reduces the quasi-elastic peak by 10% for q between 300 and 500 MeV/c. Its effect increases significantly at lower q, up to about 40% at q=100 MeV/c. At very low q, however, data are missing.
We investigate the production of direct photons in central Au-Au collisions at the relativistic Heavy-Ion Collider (RHIC) at 200 GeV per nucleon, considering all possible sources. We treat thermal photons emitted from a quark-gluon plasma and from a hadron gas, based on a realistic thermodynamic expansion. Hard photons from elementary nucleon-nucleon scatterings are included: primordial elementary scatterings are certainly dominant at large transverse momenta, but also secondary photons from jet fragmentation and jet-photon conversion cannot be ignored. In both cases we study the effect of energy loss, and we also consider photons emitted from bremsstrahlung gluons via fragmentation.
We demonstrate charge pumping in semiconducting carbon nanotubes by a traveling potential wave. From the observation of pumping in the nanotube insulating state we deduce that transport occurs by packets of charge being carried along by the wave. By tuning the potential of a side gate, transport of either electron or hole packets can be realized. Prospects for the realization of nanotube based single-electron pumps are discussed.
We report controlled formation of sub-100 nm-thin electron channels in SrTiO$_3$ by doping with oxygen vacancies induced by Ar$^+$-ion irradiation. The conducting channels exhibit a consistent high electron mobility (~15,000 cm$^2$V$^{-1}$s$^{-1}$), which enables clear observation of magnetic quantum oscillations, and gate-tunable linear magnetoresistance. Near the onset of electrical conduction, the metal-insulator transition is induced by the mobility suppression. With the high electron mobility and the ease of controlled channel formation, this ion-irradiation doping method may provide an excellent basis for developing oxide electronics.
We prove that the periodic initial value problem for the modified Hunter-Saxton equation is locally well-posed for continuously differentiable initial data. We also study the analytic regularity of this problem and prove a Cauchy-Kowalevski type theorem.
In this Letter we show that the time reversal asymmetry of a stationary time series provides information about the entropy production of the physical mechanism generating the series, even if one ignores any detail of that mechanism. We develop estimators for the entropy production which can detect non-equilibrium processes even when there are no measurable flows in the time series.
The two-time correlation function of the displacement of a free quantum Brownian particle with respect to its position at a given time is calculated analytically in the framework of the Caldeira and Leggett ohmic dissipation model (linear coupling of the particle with a thermal bath with a continuum of modes, proportional to the frequency at low frequency). As a result, at any temperature, the displacement correlation function exhibits aging, i.e. it depends explicitly on both times involved and not only on their difference, even in the limit of large age (or waiting time), in contrast with a dynamic variable in equilibrium such as the particle velocity. The equilibrium quantum fluctuation-dissipation theorem (QFDT) has to be modified in order to relate the displacement response and correlation functions, since this latter quantity takes into account even those fluctuations of the displacement which take place during the waiting time. We describe the deviation from the equilibrium QFDT in terms of an effective temperature which depends both on the time difference and of the waiting time. The definition of this quantity heavily relies on the time-dependent diffusion coefficient. The behavior of the effective temperature as a function of the time difference for given values of the bath temperature and of the waiting time is analyzed.