ShantanuT01/DACTYL-Pretraining huggingface dataset:
Magnetic skyrmions are mesmerizing spin textures with peculiar topological and dynamical properties, typically the product of competing interactions in ferromagnets, and with great technological potential [1-5]. Researchers have long wondered whether analogous electric skyrmions might exist in ferroelectrics, maybe featuring novel behaviors and possibilities for electric and mechanical control. The results thus far are modest, though: an electric equivalent of the most typical magnetic skyrmion (which would rely on a counterpart of the Dzyaloshinskii-Moriya interaction) seems all but impossible; further, the exotic ferroelectric orders observed or predicted to date [6-8] rely on very specific nano-structures (composites, superlattices), which limits the generality and properties (e.g., mobility) of the possible associated skyrmions. Here we propose an original approach to write electric skyrmions in simple ferroelectric lattices in a customary manner. Our second-principles simulations [9] of columnar ferroelectric nano-domains, in prototype compound PbTiO3 , show that it is possible to harness the Bloch-type internal structure of the domain wall [10] and hence create a genuine skyrmion. We check that the object thus obtained displays the usual skyrmion-defining features; further, it also presents unusual ones, including a symmetry-breaking skyrmion-skyrmion transition driven by strain, various types of topological transformations induced by external fields and temperature, and potentially very small sizes. Our results suggest countless possibilities for creating and manipulating electric textures with non-trivial topologies, using standard experimental tools and materials, effectively inaugurating the field of electric skyrmions.
Interfaced single-photon sources and quantum memories for photons together form a foundational component of quantum technology. Achieving compatibility between heterogeneous, state-of-the-art devices is a long-standing challenge. We built and successfully interfaced a heralded single-photon source based on cavity-enhanced spontaneous parametric down-conversion in ppKTP and a matched memory based on electromagnetically induced transparency in warm $^{87}$Rb vapor. The bandwidth of the photons emitted by the source is 370 MHz, placing its speed in the technologically relevant regime while remaining well within the acceptance bandwidth of the memory. Simultaneously, the experimental complexity is kept low, with all components operating at or above room temperature. Read-out noise of the memory is considerably reduced by exploiting polarization selection rules in the hyperfine structure of spin-polarized atoms. For the first time, we demonstrate single-photon storage and retrieval in a ground-state vapor cell memory, with $g_{c,\text{ret}}^{(2)}=0.177(23)$ demonstrating the single-photon character of the retrieved light. Our platform of single-photon source and atomic memory is attractive for future experiments on room-temperature quantum networks operating at high bandwidth.
Let $G$ be an $n$-vertex graph with adjacency matrix $A$, and $W=[e,Ae,\ldots,A^{n-1}e]$ be the walk matrix of $G$, where $e$ is the all-one vector. In Wang [J. Combin. Theory, Ser. B, 122 (2017): 438-451], the author showed that any graph $G$ is uniquely determined by its generalized spectrum (DGS) whenever $2^{-\lfloor n/2 \rfloor}\det W$ is odd and square-free. In this paper, we introduce a large family of graphs $\mathcal{F}_n=\{$ $n$-vertex graphs $G\colon\, 2^{-\lfloor n/2 \rfloor}\det W =p^2b$ and rank$W=n-1$ over $\mathbb{Z}/p\mathbb{Z}\},$ where $b$ is odd and square-free, $p$ is an odd prime and $p\nmid b$. We prove that any graph in $\mathcal{F}_n$ either is DGS or has exactly one generalized cospectral mate up to isomorphism. Moreover, we show that the problem of finding the generalized cospectral mate for a graph in $\mathcal{F}_n$ is equivalent to that of generating an appropriate rational orthogonal matrix from a given integral vector. This equivalence essentially depends on an amazing property of graphs in terms of generalized spectra, which states that any symmetric integral matrix generalized cospectral with the adjacency matrix of some graph must be an adjacency matrix. Based on this equivalence, we develop an efficient algorithm to decide whether a given graph in $\mathcal{F}_n$ is DGS and further to find the unique generalized cospectral mate when it is not. We give some experimental results on graphs with at most 20 vertices, which suggest that $\mathcal{F}_n$ may have a positive density (nearly $3\%$) and possibly almost all graphs in $\mathcal{F}_n$ are DGS as $n\rightarrow \infty$. This gives a supporting evidence for Haemers' conjecture that almost all graphs are determined by their spectra.
An interesting aspect of multipartite entanglement is that for perfect teleportation and superdense coding, not the maximally entangled W states but a special class of non-maximally entangled W-like states are required. Therefore, efficient preparation of such W-like states is of great importance in quantum communications, which has not been studied as much as the preparation of W states. In this letter, we propose a simple optical scheme for efficient preparation of large-scale polarization based entangled W-like states by fusing two W-like states or expanding a W-like state with an ancilla photon. Our scheme can also generate large-scale W states by fusing or expanding W or even W-like states. The cost analysis show that in generating large scale W states, the fusion mechanism achieves a higher efficiency with non-maximally entangled W-like states than maximally entangled W states. Our scheme can also start fusion or expansion with Bell states, and it is composed of a polarization dependent beam splitter, two polarizing beam splitters and photon detectors. Requiring no ancilla photons or controlled gates to operate, our scheme can be realized with the current photonics technology and we believe it enables advances in quantum teleportation and superdense coding in multipartite settings.
We have studied the probability distribution of the perimeter and the area of the k-th largest erased-loop in loop-erased random walks in two-dimensions for k = 1 to 3. For a random walk of N steps, for large N, the average value of the k-th largest perimeter and area scales as N^{5/8} and N respectively. The behavior of the scaled distribution functions is determined for very large and very small arguments. We have used exact enumeration for N <= 20 to determine the probability that no loop of size greater than l (ell) is erased. We show that correlations between loops have to be taken into account to describe the average size of the k-th largest erased-loops. We propose a one-dimensional Levy walk model which takes care of these correlations. The simulations of this simpler model compare very well with the simulations of the original problem.
We consider a continuous coercive Hamiltonian $H$ on the cotangent bundle of the compact connected manifold $M$ which is convex in the momentum. If $u_\lambda:M\to\mathbb R$ is the viscosity solution of the discounted equation $$   \lambda u_\lambda(x)+H(x,d_x u_\lambda)=c(H), $$ where $c(H)$ is the critical value, we prove that $u_\lambda$ converges uniformly, as $\lambda\to 0$, to a specific solution $u_0:M\to\mathbb R$ of the critical equation $$ H(x,d_x u)=c(H). $$ We characterize $u_0$ in terms of Peierls barrier and projected Mather measures.
To solve the ancient problem of fluids, i.e., of states in which there is no difference between gas and liquid (the so-called supercritical states), it is necessary to abandon several "rules of the game", which are customary to physicists and to refine them by using rigorous mathematical theorems.
We establish the validity of the Euler$+$Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only near the boundary, and Sobolev smooth away from the boundary. Our proof does not require higher order correctors, and works directly by estimating an $L^{1}$-type norm for the vorticity of the error term in the expansion Navier-Stokes$-($Euler$+$Prandtl$)$. An important ingredient in the proof is the propagation of local analyticity for the Euler equation, a result of independent interest.
In this paper we numerically research the solutions of the phase field system for the spherically symmetric Stefan-Gibbs-Thomson problem in the case of interaction of the free boundaries. We analyze the effect of the soliton type disturbance of the temperature in the point of the contact of the free boundaries.
The model considered is that of ``signal plus white noise.'' Known connections between the noncausal filtering error and mutual information are combined with new ones involving the causal estimation error, in a general abstract setup. The results are shown to be invariant under a wide class of causality patterns; they are applied to the derivation of the causal estimation error of a Gaussian nonstationary filtering problem and to a multidimensional extension of the Yovits--Jackson formula.
Hydrogen-poor superluminous supernovae (SLSN-I) are a class of rare and energetic explosions discovered in untargeted transient surveys in the past decade. The progenitor stars and the physical mechanism behind their large radiated energies ($\sim10^{51}$ erg) are both debated, with one class of models primarily requiring a large rotational energy, while the other requires very massive progenitors to either convert kinetic energy into radiation via interaction with circumstellar material (CSM), or engender a pair-instability explosion. Observing the structure of the CSM around SLSN-I offers a powerful test of some scenarios, though direct observations are scarce. Here, we present a series of spectroscopic observations of the SLSN-I iPTF16eh, which reveal both absorption and time- and frequency-variable emission in the Mg II resonance doublet. We show that these observations are naturally explained as a resonance scattering light echo from a circumstellar shell. Modeling the evolution of the emission, we find a shell radius of 0.1 pc and velocity of 3300 km s$^{-1}$, implying the shell was ejected three decades prior to the supernova explosion. These properties match theoretical predictions of pulsational pair-instability shell ejections, and imply the progenitor had a He core mass of $\sim 50-55~{\rm M}_{\odot}$, corresponding to an initial mass of $\sim 115~{\rm M}_{\odot}$.
The new challenges posed by the need of finding strong rare-earth free magnets demand methods that can predict magnetization and magnetocrystalline anisotropy energy (MAE). We argue that correlated electron effects, which are normally underestimated in band structure calculations, play a crucial role in the development of the orbital component of the magnetic moments. Because magnetic anisotropy arises from this orbital component, the ability to include correlation effects has profound consequences on our predictive power of the MAE of strong magnets. Here we show that incorporating the local effects of electronic correlations with dynamical mean-field theory provides reliable estimates of the orbital moment, the mass enhancement and the MAE of YCo5.
A solar active region (AR) is a three-dimensional magnetic structure formed in the convection zone, whose property is fundamentally important for determining the coronal structure and solar activity when emerged. However, our knowledge on the detailed 3-D structure prior to its emergence is rather poor, largely limited by the low cadence and sensitivity of previous instruments. Here, using the 45-second high-cadence observations from the Helioseismic and Magnetic Imager (\emph{HMI}) onboard the Solar Dynamics Observatory (\emph{SDO}), we are able for the first time to reconstruct a 3-D datacube and infer the detailed subsurface magnetic structure of NOAA AR 11158 and to characterize its magnetic connectivity and topology. This task is accomplished with the aid of the image-stacking method and advanced 3-D visualization. We find that the AR consists of two major bipoles, or four major polarities. Each polarity in 3-D shows interesting tree-like structure, i.e. while the root of the polarity appears as a single tree-trunk-like tube, the top of the polarity has multiple branches consisting of smaller and thinner flux-tubes which connect to the branches of the opposite polarity that is similarly fragmented. The roots of the four polarities align well along a straight line, while the top branches are slightly non-coplanar. Our observations suggest that an active region, even appearing highly complicated on the surface, may originate from a simple straight flux-tube that undergoes both horizontal and vertical bifurcation processes during its rise through the convection zone.
The two-mode relative phase associated with Gaussian states plays an important role in quantum information processes in optical, atomic and electronic systems. In this work, the origin and structure of the two-mode relative phase in pure Gaussian states is studied in terms of its dependences on the quadratures of the modes. This is done by constructing local canonical transformations to an associated two-mode squeezed state. The results are illustrated by studying the time dependence of the phase under a nonlocal unitary model evolution containing correlations between the modes. In a more general context, this approach may allow the two-mode phase to be studied in situations sensitive to different physical parameters within experimental configurations relevant to quantum information processing tasks.
Camera and 3D LiDAR sensors have become indispensable devices in modern autonomous driving vehicles, where the camera provides the fine-grained texture, color information in 2D space and LiDAR captures more precise and farther-away distance measurements of the surrounding environments. The complementary information from these two sensors makes the two-modality fusion be a desired option. However, two major issues of the fusion between camera and LiDAR hinder its performance, \ie, how to effectively fuse these two modalities and how to precisely align them (suffering from the weak spatiotemporal synchronization problem). In this paper, we propose a coarse-to-fine LiDAR and camera fusion-based network (termed as LIF-Seg) for LiDAR segmentation. For the first issue, unlike these previous works fusing the point cloud and image information in a one-to-one manner, the proposed method fully utilizes the contextual information of images and introduces a simple but effective early-fusion strategy. Second, due to the weak spatiotemporal synchronization problem, an offset rectification approach is designed to align these two-modality features. The cooperation of these two components leads to the success of the effective camera-LiDAR fusion. Experimental results on the nuScenes dataset show the superiority of the proposed LIF-Seg over existing methods with a large margin. Ablation studies and analyses demonstrate that our proposed LIF-Seg can effectively tackle the weak spatiotemporal synchronization problem.
In this paper we discuss some results concerning the abundance discrepancy problem in the context of H II regions. We discuss the behavior of the abundance discrepancy factor (ADF) for different objects and ions. There are evidences that stellar abundances seem to agree better with the nebular ones derived from recombination lines in high-metallicity environments and from collisionally excited lines in the low-metallicity regime. Recent data point out that the ADF seems to be correlated with the metallicity and the electron temperature of the objects. These results open new ways for investigating the origin of the abundance discrepancy problem in H II regions and in ionized nebulae in general.
We present detailed results for the model-independent low momentum nucleon-nucleon interaction V_{low k}. By introducing a cutoff in momentum space, we separate the Hilbert space into a low momentum and a high momentum part. The renormalization group is used to construct the effective interaction V_{low k} in the low momentum space, starting from various high precision potential models commonly used in nuclear many-body calculations. With a cutoff in the range of $\Lambda ~ 2.1 fm^{-1}$, the new potential V_{low k} is independent of the input model, and reproduces the experimental phase shift data for corresponding laboratory energies below $E_{lab} ~ 350 MeV$, as well as the deuteron binding energy with similar accuracy as the realistic input potentials. The model independence of V_{low k} demonstrates that the physics of nucleons interacting at low momenta does not depend on details of the high momentum dynamics assumed in conventional potential models. V_{low k} does not have momentum components larger than the cutoff, and as a consequence is considerably softer than the high precision potentials. Therefore, when V_{low k} is used as microscopic input in the many-body problem, the high momentum effects in the particle-particle channel do not have to be addressed by performing a Brueckner ladder resummation or short-range correlation methods. By varying the cutoff, we study how the model independence of V_{low k} is reached in different partial waves. This provides numerical evidence for the separation of scales in the nuclear problem, and physical insight into the nature of the low momentum interaction.
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are investigated. Exact as well as asymptotic results are provided for the probability density function of (a) the front-position, (b) the maximum of the front-positions, and (c) the first-passage time to a given position. The asymptotic laws for the front-position and the maximum front-position are found to be governed by the Fisher-Tippett-Gumbel extreme value statistics. The asymptotic properties of the first-passage time is dominated by a stretched-exponential tail in the distribution. The farness of the front with the rest of the system is investigated by considering (i) the gap from the front to the closest particle, and (ii) the density profile with respect to the front-position, and analytical results are provided for late time behaviors.
We study the X-ray emission of baryon fluid in the universe using the WIGEON cosmological hydrodynamic simulations. It has been revealed that cosmic baryon fluid in the nonlinear regime behaves like Burgers turbulence, i.e. the fluid field consists of shocks. Like turbulence in incompressible fluid, the Burgers turbulence plays an important role in converting the kinetic energy of the fluid to thermal energy and heats the gas. We show that the simulation sample of the $\Lambda$CDM model without adding extra heating sources can fit well the observed distributions of X-ray luminosity versus temperature ($L_{\rm x}$ vs. $T$) of galaxy groups and is also consistent with the distributions of X-ray luminosity versus velocity dispersion ($L_{\rm x}$ vs. $\sigma$). Because the baryonic gas is multiphase, the $L_{\rm x}-T$ and $L_{\rm x}-\sigma$ distributions are significantly scattered. If we describe the relationships by power laws $L_{\rm x}\propto T^{\alpha_{LT}}$ and $L_{\rm x}\propto \sigma^{\alpha_{LV}}$, we find $\alpha_{LT}>2.5$ and $\alpha_{LV}>2.1$. The X-ray background in the soft $0.5-2$ keV band emitted by the baryonic gas in the temperature range $10^5<T<10^7$ K has also been calculated. We show that of the total background, (1) no more than 2% comes from the region with temperature less than $10^{6.5}$ K, and (2) no more than 7% is from the region of dark matter with mass density $\rho_{\rm dm}<50 \bar{\rho}_{\rm dm}$. The region of $\rho_{\rm dm}>50\bar{\rho}_{\rm dm}$ is generally clustered and discretely distributed. Therefore, almost all of the soft X-ray background comes from clustered sources, and the contribution from truly diffuse gas is probably negligible. This point agrees with current X-ray observations.
Oriented matroids (often called order types) are combinatorial structures that generalize point configurations, vector configurations, hyperplane arrangements, polyhedra, linear programs, and directed graphs. Oriented matroids have played a key role in combinatorics, computational geometry, and optimization. This paper surveys prior work and presents an update on the search for bounds on the diameter of the cocircuit graph of an oriented matroid.   We review the diameter problem and show the diameter bounds of general oriented matroids reduce to those of uniform oriented matroids. We give the latest exact bounds for oriented matroids of low rank and low corank, and for all oriented matroids with up to nine elements (this part required a large computer-based proof). The motivation for our investigations is the complexity of the simplex method and the criss-cross method. For arbitrary oriented matroids, we present an improvement to a quadratic bound of Finschi. Our discussion highlights two very important conjectures related to the polynomial Hirsch conjecture for polytope diameters.
We prove asymptotic upper bounds for the $L^2$ Betti numbers of the locally symmetric spaces associated to a quasi-split $U(4)$. These manifolds are 8-dimensional, and we prove bounds in degrees 2 and 3, with the behaviour in the other degrees being well understood. In degree 3, we conjecture that these bounds are sharp. Our main tool is the endoscopic classification of automorphic representations of U(N) by Mok.
The essential annihilating-ideal graph $\mathcal{EG}(R)$ of a commutative unital ring $R$ is a simple graph whose vertices are non-zero ideals of $R$ with non-zero annihilator and there exists an edge between two distinct vertices $I,J$ if and only if $Ann(IJ)$ has a non-zero intersection with any non-zero ideal of $R$. In this paper, we show that $\mathcal{EG}(R)$ is weakly perfect, if $R$ is Noetherian and an explicit formula for the clique number of $\mathcal{EG}(R)$ is given. Moreover, the structures of all rings whose essential annihilating-ideal graphs have chromatic number $2$ are fully determined. Among other results, twin-free clique number and edge chromatic number of $\mathcal{EG}(R)$ are examined.
Using angle-resolved photoemission spectroscopy, we show that the recently-discovered surface state on SrTiO$_{3}$ consists of non-degenerate $t_{2g}$ states with different dimensional characters. While the $d_{xy}$ bands have quasi-2D dispersions with weak $k_{z}$ dependence, the lifted $d_{xz}$/$d_{yz}$ bands show 3D dispersions that differ significantly from bulk expectations and signal that electrons associated with those orbitals permeate the near-surface region. Like their more 2D counterparts, the size and character of the $d_{xz}$/$d_{yz}$ Fermi surface components are essentially the same for different sample preparations. Irradiating SrTiO$_{3}$ in ultrahigh vacuum is one method observed so far to induce the "universal" surface metallic state. We reveal that during this process, changes in the oxygen valence band spectral weight that coincide with the emergence of surface conductivity are disproportionate to any change in the total intensity of the O $1s$ core level spectrum. This signifies that the formation of the metallic surface goes beyond a straightforward chemical doping scenario and occurs in conjunction with profound changes in the initial states and/or spatial distribution of near-$E_{F}$ electrons in the surface region.