ShantanuT01/DACTYL-Pretraining huggingface dataset:
The energy levels of two and three anyons in a two-dimensional parabolic quantum dot and a perpendicular magnetic field are computed as power series in 1/|J|, where J is the angular momentum. The particles interact repulsively through a coulombic (1/r) potential. In the two-anyon problem, the reached accuracy is better than one part in 10^5. For three anyons, we study the combined effects of anyon statistics and coulomb repulsion in the ``linear'' anyonic states.
We interpret the lens transformation (a variant of the pseudoconformal transformation) as a pseudoconformal compactification of spacetime, which converts the nonlinear Schr\"odinger equation (NLS) without potential with a nonlinear Schr\"odinger equation with attractive harmonic potential. We then discuss how several existing results about NLS can be placed in this compactified setting, thus offering a new perspective to view this theory.
Sharpened dimensionality reduction (SDR), which belongs to the class of multidimensional projection techniques, has recently been introduced to tackle the challenges in the exploratory and visual analysis of high-dimensional data. SDR has been applied to various real-world datasets, such as human activity sensory data and astronomical datasets. However, manually labeling the samples from the generated projection are expensive. To address this problem, we propose here to use clustering methods such as k-means, Hierarchical Clustering, Density-Based Spatial Clustering of Applications with Noise (DBSCAN), and Spectral Clustering to easily label the 2D projections of high-dimensional data. We test our pipeline of SDR and the clustering methods on a range of synthetic and real-world datasets, including two different public human activity datasets extracted from smartphone accelerometer or gyroscope recordings of various movements. We apply clustering to assess the visual cluster separation of SDR, both qualitatively and quantitatively. We conclude that clustering SDR results yields better labeling results than clustering plain DR, and that k-means is the recommended clustering method for SDR in terms of clustering accuracy, ease-of-use, and computational scalability.
We consider the 2-D incompressible Euler equations in a bounded domain and show that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result $$u \in L_{\rm loc}^{2+\varepsilon}(\Omega_T) \implies {\rm regularity}$$ for weak solutions in the energy space $L_t^\infty L_x^2$ satisfying appropriate vorticity estimates. The argument is completely local in nature as the result follows from the structural properties of the equation alone, while completely avoiding all sorts of boundary conditions and related gradient estimates. To the best of our knowledge, the approach we follow is new in the context of Euler equations and provides an alternative look at interior regularity issues. We also show how our method can be used to give a modified proof of the classical Serrin condition for the regularity of the Navier-Stokes equations in any dimension.
The delafossite series of layered oxides include some of the highest conductivity metals ever discovered. Of these, PtCoO2, with a room temperature resistivity of 1.8 microOhmcm for in-plane transport, is the most conducting of all. The high conduction takes place in triangular lattice Pt layers, separated by layers of Co-O octahedra, and the electronic structure is determined by the interplay of the two types of layer. We present a detailed study of quantum oscillations in PtCoO2, at temperatures down to 35 mK and magnetic fields up to 30 T. As for PdCoO2 and PdRhO2, the Fermi surface consists of a single cylinder with mainly Pt character, and an effective mass close to the free electron value. Due to Fermi-surface warping, two close-lying high frequencies are observed. Additionally, a pronounced difference frequency appears. By analysing the detailed angular dependence of the quantum-oscillation frequencies, we establish the warping parameters of the Fermi surface. We compare these results to the predictions of first-principles electronic structure calculations including spin-orbit coupling on Pt and Co and on-site correlation U on Co, and hence demonstrate that electronic correlations in the Co-O layers play an important role in determining characteristic features of the electronic structure of PtCoO2.
Pairing correlations on generalized t-U-J two-leg ladders are reported. We find that the pairing correlations on the usual t-U Hubbard ladder are significantly enhanced by the addition of a nearest-neighbor exchange interaction J. Likewise, these correlations are also enhanced for the t-J model when the onsite Coulomb interaction is reduced from infinity. Moreover, the pairing correlations are larger on a t-U-J ladder than on a t-Jeff ladder in which Jeff has been adjusted so that the two models have the same spin gap at half-filling. This enhancement of the pairing correlations is associated with an increase in the pair-binding energy and the pair mobility in the t-U-J model and point to the importance of the charge transfer nature of the cuprate systems.
Following earlier insights by Livine and Terno, we develop a technique for describing quantum states of the gravitational field in terms of coarse grained spin networks. We show that the number of nodes and links and the values of the spin depend on the observables chosen for the description of the state. Hence the question in the title of this paper is ill posed, unless further information about what is been measured is given.
Define the sequence $\{b_n\}$ by $b_0=1,b_1=1, b_2=2,b_3=1$, and $$b_n=\begin{cases} \frac{b_{n-1}b_{n-3}-b_{n-2}^2}{b_{n-4}}&\textrm{if}~ n\not\equiv 0\pmod 3, \frac{b_{n-1}b_{n-3}-3b_{n-2}^2}{b_{n-4}}&\textrm{if}~ n\equiv 0\pmod 3. We relate this sequence $\{b_n\}$ to the coordinates of points on the elliptic curve $E:y^2+y=x^3-3x+4$. We use Galois representations attached to $E$ to prove that the density of primes dividing a term in this sequence is equal to $\frac{179}{336}$. Furthermore, we describe an infinite family of elliptic curves whose Galois images match that of $E$.
We report on an 105 ks Suzaku observation of the supernova remnant CTA 1 (G119.5+10.2). The Suzaku soft X-ray observation was carried out with both timing mode and imaging mode. A ~ 10' extended feature, which is interpreted as a bow-shock component of the pulsar wind nebula (PWN), is revealed in this deep observation for the first time. The nebular spectrum can be modelled by a power-law with a photon index of ~ 1.8 which suggests a slow synchrotron cooling scenario. The photon index is approximately constant across this extended feature. We compare and discuss our observations of this complex nebula with previous X-ray investigations. We do not obtain any significant pulsation from the central pulsar in the soft (0.2-12 keV) and hard (10-60 keV) X-ray data. The non-detection is mainly due to the loss of the precise imaging ability to accurately determine the source contribution. The spectra of XIS and HXD can be directly connected without a significant spectral break according to our analysis. Future observations of NuSTAR and Astro-H would be able to resolve the contamination and provide an accurate hard X-ray measurement of CTA 1.
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify for many applications. Provided a derived analogue of Schlessinger's condition holds, the theorem reduces to verifying conditions on the underived part and on cohomology groups. Another simplification is that functors need only be defined on nilpotent extensions of discrete rings. Finally, there is a pre-representability theorem, which can be applied to associate explicit geometric stacks to dg-manifolds and related objects.
As part of our program to map the large-scale distribution of galaxies behind the Milky Way, we used the Parkes 210 ft (64 m) radio telescope for pointed HI observations of a sample of low surface-brightness (due to heavy obscuration) spiral galaxies selected from the deep optical Zone of Avoidance (ZOA) galaxy catalog in the Hydra/Antlia region (Kraan-Korteweg 2000a). Searching a simultaneous velocity range of either 300 to 5500 km/s or 300 to 10500 km/s to an rms level of typically 2 - 4 mJy resulted in detections in 61 of the 139 pointings, leading to a total of 66 detections (an additional detection was made in a reference position, and two other pointings revealed two and four independent signals respectively). Except for 2 strong HI emitters identified in the shallow Zone of Avoidance HI survey (Henning et al. 2000), all HI detections are new. An analysis of the properties of the observed and detected galaxies prove that pointed HI observations of highly obscured galaxies allow the tracing of a population of nearby, intrinsically large and bright spiral galaxies that otherwise would not be recovered. The new data identified a previously unrecognized nearby group at l=287.5, b=-9.5, V=1700 km/s, the continuation of the Hydra/Antlia filament on the opposite side of the Galactic plane, and helped to delimit a distinct void in the ZOA centered at 2000 km/s.
We present a mock catalog of gravitationally lensed quasars at $z_\text{qso}<7.5$ with simulated images for the Rubin Observatory Legacy Survey of Space and Time (LSST). We adopt recent measurements of quasar luminosity functions to model the quasar population, and use the CosmoDC2 mock galaxy catalog to model the deflector galaxies, which successfully reproduces the observed galaxy velocity dispersion functions up to $z_d\sim1.5$. The mock catalog is highly complete for lensed quasars with Einstein radius $\theta_E>0\farcs07$ and quasar absolute magnitude $M_{i}<-20$. We estimate that there are $\sim10^3$ lensed quasars discoverable in current imaging surveys, and LSST will increase this number to $\sim2.4\times10^3$. Most of the lensed quasars have image separation $\Delta \theta>0\farcs5$, which will at least be marginally resolved in LSST images with seeing of $\sim0\farcs7$. There will be $\sim200$ quadruply-lensed quasars discoverable in the LSST. The fraction of quad lenses among all discoverable lensed quasars is about $\sim10\%-15\%$, and this fraction decreases with survey depth. This mock catalog shows a large diversity in the observational features of lensed quasars, in terms of lensing separation and quasar-to-deflector flux ratio. We discuss possible strategies for a complete search of lensed quasars in the LSST era.
In situ NMR spectroscopy is a powerful technique to investigate charge storage mechanisms in carbon-based supercapacitors thanks to its ability to distinguish ionic and molecular species adsorbed in the porous electrodes from those in the bulk electrolyte. The NMR peak corresponding to the adsorbed species shows a clear change of chemical shift as the applied potential difference is varied. This variation in chemical shift is thought to originate from a combination of ion reorganisation in the pores and changes in ring current shifts due to the changes of electronic density in the carbon. While previous Density Functional Theory calculations suggested that the electronic density has a large effect, the relative contributions of these two effects is challenging to untangle. Here, we use mesoscopic simulations to simulate NMR spectra and investigate the relative importance of ion reorganisation and ring currents on the resulting chemical shift. The model is able to predict chemical shifts in good agreement with NMR experiments and indicates that the ring currents are the dominant contribution. A thorough analysis of a specific electrode/electrolyte combination for which detailed NMR experiments have been reported allows us to confirm that local ion reorganisation has a very limited effect but the relative quantities of ions in pores of different sizes, which can change upon charging/discharging, can lead to a significant effect. Our findings suggest that in situ NMR spectra of supercapacitors may provide insights into the electronic structure of carbon materials in the future.
Encountered in the literature generalisations of general relativity to independent area variables are considered, the discrete (generalised Regge calculus) and continuum ones. The generalised Regge calculus can be either with purely area variables or, as we suggest, with area tensor-connection variables. Just for the latter, in particular, we prove that in analogy with corresponding statement in ordinary Regge calculus (by Feinberg, Friedberg, Lee and Ren), passing to the (appropriately defined) continuum limit yields the generalised continuum area tensor-connection general relativity.
If $X = V(f) \subset \mathbb P^N$ is a reduced complex hypersurface, the hessian of $f$ (or by abusing the terminology the hessian of $X$) is the determinant of the matrix of the second derivatives of the form $f$, that is the determinant of the hessian matrix of $f$. Hypersurfaces with vanishing hessian were studied systematically for the first time in the fundamental paper [GN], where Gordan and M. Noether analyze Hesse's claims in [Hesse1, Hesse2] according to which these hypersurfaces are necessarily cones. Of course cones have vanishing hessian.   Clearly the claim is true if deg(X)=2 so that the first relevant case for the problem is that of cubic hypersurfaces. One immediately sees that $V(x_0x_3^2 + x_1x_3x_4 + x_2x_4^2)\subset \mathbb P^4$ is a cubic hypersurface with vanishing hessian but not a cone (for example one could check that the first partial derivatives of the equation are linearly independent). As firstly pointed out in [GN], the claim is true for $N\leq 3$ and in general false for every $N\geq 4$.   Here we prove that for $N\leq 6$ an irreducible cubic hypersurface with vanishing hessian in $\mathbb P^N$ is either a cone or a scroll in linear spaces tangent to the dual of the image of the polar map of the hypersurface. We also provide canonical forms and a projective characterization of {\it Special Perazzo Cubic Hypersurfaces}, which, a posteriori, exhaust the class of cubic hypersurfaces with vanishing hessian, not cones, for $N\leq 6$. Finally we show by pertinent examples the technical difficulties arising for $N\geq 7$.
High-entropy perovskite thin films, as the prototypical representative of the high-entropy oxides with novel electrical and magnetic features, have recently attracted great attention. Here, we reported the electronic structure and charge transport properties of sol-gel-derived high-entropy Ba(Zr0.2Sn0.2Ti0.2Hf0.2Nb0.2)O3 thin films annealed at various temperatures. By means of X-ray photoelectron spectroscopy and absorption spectrum, it is found that the conduction-band-minimum shifts downward and the valence-band-maximum shifts upward with the increase of annealing temperature, leading to the narrowed band gap. Electrical resistance measurements confirmed a semiconductor-like behavior for all the thin films. Two charge transport mechanisms, i.e., the thermally-activated transport mechanism at high temperatures and the activation-less transport mechanism at low temperatures, are identified by a self-consistent analysis method. These findings provide a critical insight into the electronic band structure and charge transport behavior of Ba(Zr0.2Sn0.2Ti0.2Hf0.2Nb0.2)O3, validating it as a compelling high-entropy oxide material for future electronic/energy-related technologies.
The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak inter-chain coupling. A gapless phase with quasi long-range spiral correlations has been predicted to occur in this regime if easy-plane (XY) anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase and a spiral phase. We study the level crossings of the spectrum,the dimer correlation function, the structure factor and the spin stiffness within these phases, as well as at the transition points. As the inter-chain coupling decreases we observe a transition in the anisotropic XY case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic XY cases are found to be qualitatively the same, however, in the regime of weak inter-chain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.
Context: One of the most prominent processes suggested to heat the corona to well above 10^6 K builds on nanoflares, short bursts of energy dissipation.   Aims: We compare observations to model predictions to test the validity of the nanoflare process.   Methods: Using extreme UV data from AIA/SDO and HMI/SDO line-of-sight magnetograms we study the spatial and temporal evolution of a set of loops in active region AR 11850.   Results: We find a transient brightening of loops in emission from Fe xviii forming at about 7.2 MK while at the same time these loops dim in emission from lower temperatures. This points to a fast heating of the loop that goes along with evaporation of material that we observe as apparent upward motions in the image sequence. After this initial phases lasting for some 10 min, the loops brighten in a sequence of AIA channels showing cooler and cooler plasma, indicating the cooling of the loops over a time scale of about one hour. A comparison to the predictions from a 1D loop model shows that this observation supports the nanoflare process in (almost) all aspects. In addition, our observations show that the loops get broader while getting brighter, which cannot be understood in a 1D model.
A semi-classical model based on quantum time concepts is presented for the evaluation of bremsstrahlung emission probabilities in alpha decay of nuclei. The contribution to the bremsstrahlung emission from the different regions in tunneling is investigated using realistic double folded nuclear and Coulomb potentials. Within this model, the contribution from the radiation emitted in front of the barrier before tunneling is much larger than that while leaving the barrier. A comparison with the data on $^{210}$Po shows that the results are sensitive to the nuclear potential and the rectangular well used in many of the quantum mechanical approaches can even give qualitatively different results.
In 2010 it was proved that a 3-regular matchstick graph of girth 5 must consist at least of 30 vertices. The smallest known example consisted of 180 vertices. In this article we construct an example consisting of 54 vertices and prove its geometrical correctness.
We analyze the quantum penny flip game using geometric algebra and so determine all possible unitary transformations which enable the player Q to implement a winning strategy. Geometric algebra provides a clear visual picture of the quantum game and its strategies, as well as providing a simple and direct derivation of the winning transformation, which we demonstrate can be parametrized by two angles. For comparison we derive the same general winning strategy by conventional means using density matrices.
We have used the publicly available data from the Sloan Digital Sky Survey and 2dF QSO Redshift Survey to test the hypothesis that QSOs are ejected from active galaxies with periodic non-cosmological redshifts. For two different intrinsic redshift models, namely the Karlsson $\log(1+z)$ model and Bell's decreasing intrinsic redshift (DIR) model, we do two tests respectively. First, using different criteria, we generate four sets of QSO-galaxy pairs and find there is no evidence for a periodicity at the predicted frequency in $\log(1+z)$, or at any other frequency. We then check the relationship between high redshift QSOs and nearby active galaxies, and we find the distribution of projected distance between high redshift QSOs and nearby active galaxies and the distribution of redshifts of those active galaxies are consistent with a distribution of simulated random pairs, completely different from Bell's previous conclusion. We also analyze the periodicity in redshifts of QSOs, and no periodicity is found in high completeness samples, contrary to the DIR model. These results support that QSOs are not ejected from active galaxies.
We report the discovery of the first hyperluminous infrared galaxy (HyLIG) in the course of the European Large Area ISO Survey (ELAIS). This object has been detected by ISO at 6.7, 15, and 90 microns, and is found to be a broad-line, radio-quiet quasar at a redshift: z = 1.099. From a detailed multi-component model fit of the spectral energy distribution, we derive a total infrared luminosity: L_IR (1-1000 microns) ~ 1.0 x 10E13 h_65^-2 L_sun (q_0 = 0.5), and discuss the possible existence of a starburst contributing to the far-IR output. Observations to date present no evidence for lens magnification. This galaxy is one of the very few HyLIGs with an X-ray detection. On the basis of its soft X-ray properties, we suggest that this broad-line object may be the face-on analogue of narrow-line, Seyfert-like HyLIGs.
The measurement of neutron star mass and radius is one of the most direct way to distinguish between various dense matter equations of state. The mass and radius of accreting neutron stars hosted in low mass X-ray binaries can be constrained by several methods, including photospheric radius expansion from type-I X-ray bursts and from quiescent spectra. In this paper, we apply for the first time these two methods simultaneously to constrain the mass and radius of Aql X-1, as a reliable distance estimation, high signal-to-noise ratio quiescent spectra from Chandra and XMM-Newton, and photospheric radius expansion bursts from RXTE are available. This is also used to verify the consistency between the two methods, and to narrow down the uncertainties of the neutron star mass and radius. It is found that the distance to Aql X-1 should be in the range of $4.0-5.75$ kpc, based on the overlapping confidence regions between photospheric radius expansion burst and quiescent spectra methods. In addition, we show that the mass and radius determined for the compact star in Aql X-1 are compatible with strange star equations of state and conventional neutron star models.
New exact solutions to the field equations in the Einstein--Gauss--Bonnet modified theory of gravity for a 5--dimensional spherically symmetric static distribution of a perfect fluid is obtained. The Frobenius method is used to obtain this solution in terms of an infinite series. Exact solutions are generated in terms of polynomials from the infinite series. The 5--dimensional Einstein solution is also found by setting the coupling constant to be zero. All models admit a barotropic equation of state. Linear equations of state are admitted in particular models with the energy density profile of isothermal distributions. We examine the physicality of the solution by studying graphically the isotropic pressure and the energy density. The model is well behaved in the interior and the weak, strong and dominant energy conditions are satisfied.