ShantanuT01/DACTYL-Pretraining huggingface dataset:
Frustrated magnetic interactions in a quasi-two-dimensional [111] slab of pyrochlore lattice were studied. For uniform nearest neighbor (NN) interactions, we show that the complex magnetic problem can be mapped onto a model with two independent degrees of freedom, tri-color and binary sign. This provides a systematic way to construct the complex classical spin ground states with collinear and coplanar bi-pyramid spins. We also identify `partial but extended' zero-energy excitations amongst the ground states. For nonuniform NN interactions, the coplanar ground state can be obtained from the collinear bi-pyramid spin state by collectively rotating two spins of each tetrahedron with an angle, $\alpha$, in an opposite direction. The latter model with $\alpha \sim 30^\circ$ fits the experimental neutron data from SCGO well.
The new method of solution of the Bethe-Salpeter equation for quark-antiquark pseudoscalar bound state is proposed. With the help of integral representation the results are directly obtained in Minkowski space. Dressing of Greens functions is naturally considered providing thus the correct inclusion of the running coupling constant and the quark propagators as well as. The first numerical results are presented for a simplified ladder approximation.
We describe new boundary conditions for AdS$_2$ in Jackiw-Teitelboim gravity. The asymptotic symmetry group is enhanced to $\r{Diff}(S^1)\ltimes C^\infty(S^1)$ whose breaking to $\r{SL}(2,\R)\times \r{U}(1)$ controls the near-AdS$_2$ dynamics. The action reduces to a boundary term which is a generalization of the Schwarzian theory and can be interpreted as the coadjoint action of the warped Virasoro group. This theory reproduces the low-energy effective action of the complex SYK model. We compute the Euclidean path integral and derive its relation to the random matrix ensemble of Saad, Shenker and Stanford. We study the flat space version of this action, and show that the corresponding path integral also gives an ensemble average, but of a much simpler nature. We explore some applications to near-extremal black holes.
We show that information on the probability density of local fluctuations can be obtained from a numerical renormalisation group calculation of a reduced density matrix. We apply this approach to the Anderson-Holstein impurity model to calculate the ground state probability density $\rho(x)$ for the displacement $x$ of the local oscillator. From this density we can deduce an effective local potential for the oscillator and compare its form with that obtained from a semiclassical approximation as a function of the coupling strength. The method is extended to infinite dimensional Holstein-Hubbard model using dynamical mean field theory. We use this approach to compare the probability densities for the displacement of the local oscillator in the normal, antiferromagnetic and charge ordered phases.
For all rank two Toda systems with an arbitrary singular source, we use a unified approach to prove: (i) The pair of local masses $(\sigma_1,\sigma_2)$ at each blowup point has the expression $$\sigma_i=2(N_{i1}\mu_1+N_{i2}\mu_2+N_{i3}),$$ where $N_{ij}\in\mathbb{Z},~i=1,2,~j=1,2,3.$ (ii) Suppose at each vortex point $p_t$, $(\alpha_1^t,\alpha_2^t)$ are integers and $\rho_i\notin 4\pi\mathbb{N}$, then all the solutions of Toda systems are uniformly bounded. (iii) If the blow up point $q$ is not a vortex point, then $$u^k(x)+2\log|x-x^k|\leq C,$$ where $x^k$ is the local maximum point of $u^k$ near $q$. (iv) If the blow up point $q$ is a vortex point $p_t$ and $\alpha_t^1,\alpha_t^2$ and $1$ are linearly independent over $Q$, then $$u^k(x)+2\log|x-p_t|\leq C.$$ The Harnack type inequalities of (iii) or (iv) is important for studying the bubbling behaves near each blow up point.
We associate to a real projective variety $X$ two convex cones which are fundamental in real algebraic geometry: the cone $P_X$ of quadratic forms nonnegative on $X$, and the cone $\Sigma_X$ of sums of squares of linear forms. The dual cone $\Sigma_X^\ast$ is a spectrahedron and we show that its convexity properties are closely related to homological properties of $X$. For instance, we show that all extreme rays of $\Sigma_X^\ast$ have rank one if and only if X has Castelnuovo-Mumford regularity two. More generally, if $\Sigma_X^\ast$ has an extreme ray of rank $p > 1$, then $X$ does not satisfy the property $N_{2,p}$. We show that the converse also holds in a wide variety of situations: the smallest $p$ for which property $N_{2,p}$ does not hold is equal to the smallest rank of an extreme ray of $\Sigma_X^\ast$ greater than one. These results allow us to generalize the work of Blekherman-Smith-Velasco on equality of nonnegative polynomials and sums of squares from irreducible varieties to reduced schemes and to classify all spectrahedral cones with only rank one extreme rays. Our results have applications to the positive semidefinite matrix completion problem and to the truncated moment problem on projective varieties.
Based on the Melnikov method, we investigate chaotic behaviors in the extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations. Our results show that the temporal perturbation coming from a thermal quench of the spinodal region in the phase diagram may cause the temporal chaos only when the perturbation amplitude is above a critical value, which involves the angular momentum . Under the spatial perturbation, however, it is found that the spatial chaos always occurs, which is independent of the perturbation amplitude.
In this Letter we consider a general quadratic parity-preserving theory for a general flat connection. Imposing a local symmetry under the general linear group singles out the general teleparallel equivalent of General Relativity carrying both torsion and non-metricity. We provide a detailed discussion on the teleparallel equivalents of General Relativity and how the two known equivalents, formulated on Weitzenb\"ock and symmetric teleparallel geometries respectively, can be interpreted as two gauge-fixed versions of the general teleparallel equivalent. We then explore the viability of the general quadratic theory by studying the spectrum around Minkowski. The linear theory generally contains two symmetric rank-2 fields plus a 2-form and, consequently, extra gauge symmetries are required to obtain potentially viable theories.
Approximate equations are derived for the motion of a gyroscope on the earth's gravitational field using the Einstein, Infeld, Hoffmann surface integral method. This method does not require a knowledge of the energy-momentum-stress tensor associated with the gyroscope and uses only its exterior field for its characterization. The resulting equations of motion differ from those of previous derivations.
High precision measurements of the parity-violating asymmetry in polarized electron scattering from nuclei can be used to extract information on nuclear and nucleon structure or to determine Standard Model couplings and higher-order radiative corrections. To this end, low uncertainties are also required in the effects that inevitably arise from modeling the underlying nuclear structure. An experimental precision of a few tenths of a percent may be attainable for the asymmetry if the appropriate kinematic range is chosen, as will be discussed here for the case of $^{12}$C. And given this, the dual goal of ascertaining both the sizes of various nuclear structure related effects and of providing estimates of their uncertainties for this particular target will be discussed.
Suppose we are given a family of choice functions on pairs from a given finite set. The set is considered as a set of alternatives (say candidates for an office) and the functions as potential "voters". The question is, what choice functions agree, on every pair, with the majority of some finite subfamily of the voters? For the problem as stated, a complete characterization was given in \citet{shelah2009mdp}, but here we allow each voter to abstain. There are four cases.
It is shown that for 2D field theories only the first order coefficient of the gravitationally dressed RG $\beta$-function is scheme independent. This is valid even for matter theories with one dimensionless coupling, where the first two coefficients of the original $\beta$-function are scheme independent.
In this paper, we are concerned with the numerical solution of one type integro-differential equation by a probability method based on the fundamental martingale of mixed Gaussian processes. As an application, we will try to simulate the estimation of ruin probability with an unknown parameter driven not by the classical L\'evy process but by the mixed fractional Brownian motion.
We use a distribution function analysis to estimate the mass of the Milky Way out to 100 kpc using a large sample of halo stars. These stars are compiled from the literature, and the vast majority (~98%) have 6D phase-space information. We pay particular attention to systematic effects, such as the dynamical influence of the Large Magellanic Cloud (LMC), and the effect of unrelaxed substructure. The LMC biases the (pre-LMC infall) halo mass estimates towards higher values, while realistic stellar halos from cosmological simulations tend to underestimate the true halo mass. After applying our method to the Milky Way data we find a mass within 100 kpc of M(< 100 kpc) = 6.07 +/- 0.29 (stat.) +/- 1.21 (sys.) x 10^11 M_Sun. For this estimate, we have approximately corrected for the reflex motion induced by the LMC using the Erkal et al. model, which assumes a rigid potential for the LMC and MW. Furthermore, stars that likely belong to the Sagittarius stream are removed, and we include a 5% systematic bias, and a 20% systematic uncertainty based on our tests with cosmological simulations. Assuming the mass-concentration relation for Navarro-Frenk-White haloes, our mass estimate favours a total (pre-LMC infall) Milky Way mass of M_200c = 1.01 +/- 0.24 x 10^12 M_Sun, or (post-LMC infall) mass of M_200c = 1.16 +/- 0.24 x 10^12 M_Sun when a 1.5 x 10^11 M_Sun mass of a rigid LMC is included.
Liu et al. (2019) recently reported the detection of a 68 [+11/-13] solar mass (Msun) black hole (BH) paired with an 8.2 [+0.9/-1.2] Msun B-type sub-giant star in the 78.9-day spectroscopic binary system LB-1. Such a black hole is over twice as massive as any other known stellar-mass black hole with non-compact companions2 and its mass approaches those that result from BH-BH coalescences that are detected by gravitational wave interferometers. Its presence in a solar-like metallicity environment challenges conventional theories of massive binary evolution, stellar winds and core-collapse supernovae, so that more exotic scenarios seem to be needed to explain the existence and properties of LB-1. Here, we show that the observational diagnostics used to derive the BH mass results from the orbital motion of the B-type star, not that of the BH. As a consequence, no evidence for a massive BH remains in the data, therefore solving the existing tension with formation models of such a massive BH at solar metallicity and with theories of massive star evolution in general.
In this paper, we prove that 2 dimensional transversal small perturbations of d-dimensional Euclidean planes under the skew mean curvature flow lead to global solutions which converge to the unperturbed planes in suitable norms. And we clarify the long time behaviors of the solutions in Sobolev spaces.
After a preliminary discussion of the relevance of the field nature of gravitation interaction, both for the fundamental interaction of particles and the topology of space time, a method is proposed to produce and detect a dynamical gravitational field, allowing the determination of the order of magnitude of its propagation velocity.
When the branch character has root number -1, the corresponding anticyclotomic Katz p-adic L-function identically vanishes. In this case, we study the $\mu$-invariant of the cyclotomic derivative of Katz p-adic L-function. As an application, this proves the non-vanishing of the anticyclotomic regulator of a self-dual CM modular form with the root number -1. The result also plays a crucial role in the recent work of Hsieh on the Eisenstein ideal approach to a one-sided divisibility of the CM main conjecture.
The anomalous hysteresis is reported in photo current density-voltage (J-V) curves of perovskite solar cells. The origins responsible for hysteresis are primarily attributed to ferroelectricity, trapping/de-trapping, and ions migration. Meanwhile, a switchable photovoltaic effect is disclosed in lateral structure perovskite solar cells, where a p-i-n structure is formed after poling the device with a reverse bias. Considering the normal sandwiched structure of perovskite solar cells, i.e. the intrinsic perovskite layer is situated in an electric field built by p-type (Spiro-OMeTAD) and n-type (TiO2) layers, the poling process also works in such devices. The migration of ions will induce a new electric field with opposite direction as inherent built-in electric field. As a consequence, less collection of photogenerated carriers is predicted due to the built-in electric field is partially screened. Here, the ions induced electric field is experimentally demonstrated by exploring the external quantum efficiency (EQE) spectra under various forward voltage biases. The anomalous hysteresis observed on J-V curves is explained based on the insight of ions migrations under bias voltage. The external applied voltage presents significant influence on the stability of solar cells. Meanwhile, a novel phenomenon of negative capacitance is initially detected at low frequency, which is ascribed to the position reversal of negatively and positively charged ions under forward bias.
The voter model on $\mathbb{Z}^d$ is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological species occupying space. When $d \geq 3$, the set of (extremal) stationary distributions is a family of measures $\mu_\alpha$, for $\alpha$ between 0 and 1. A configuration sampled from $\mu_\alpha$ is a strongly correlated field of 0's and 1's on $\mathbb{Z}^d$ in which the density of 1's is $\alpha$. We consider such a configuration as a site percolation model on $\mathbb{Z}^d$. We prove that if $d \geq 5$, the probability of existence of an infinite percolation cluster of 1's exhibits a phase transition in $\alpha$. If the voter model is allowed to have sufficiently spread-out interactions, we prove the same result for $d \geq 3$.
The purpose of this paper is to describe one-shot-learning gesture recognition systems developed on the \textit{ChaLearn Gesture Dataset}. We use RGB and depth images and combine appearance (Histograms of Oriented Gradients) and motion descriptors (Histogram of Optical Flow) for parallel temporal segmentation and recognition. The Quadratic-Chi distance family is used to measure differences between histograms to capture cross-bin relationships. We also propose a new algorithm for trimming videos --- to remove all the unimportant frames from videos. We present two methods that use combination of HOG-HOF descriptors together with variants of Dynamic Time Warping technique. Both methods outperform other published methods and help narrow down the gap between human performance and algorithms on this task. The code has been made publicly available in the MLOSS repository.
We evaluate the electron emission current density from jellium metallic surfaces in the Thomas-Fermi-von-Weizs\"acker approximation. We implement the weighted density approximation (WDA) for description of the exchange and correlation energy of interacting electrons. We find the emission mechanism exhibits crossover from quantum to classical over-barrier escape of electrons from the surface. Well below a surface-specific threshold field strength $E_d$, electron tunneling is mainly affected by the change of the metal workfunction, and is less sensitive to the detailed shape of the surface barrier. In particular, since the position of the image charge plane for electrons leaving the surface does not precisely coincide with the centroid of the induced screening charge at the surface in response to the applied electric field, we find an effective increase in the metal workfunction by $\Delta W \sim 0.01$ eV, which decreases the dark current.
Transition rates among different states in a system of non-interacting quantum particles in contact with a heat reservoir include the factor $1\mp \bar{n}_i$, with a minus sign for fermions and a plus sign for bosons, where $\bar{n}_i$ is the average occupation number of the final state. It is shown that this factor can be related to the difference of the chemical potential from that of an ideal classical mixture; this difference is formally equivalent to the excess chemical potential in a classical system of interacting particles. Using this analogy, Widom's insertion formula is used in the calculation of transition rates. The result allows an alternative derivation of quantum statistics from the condition that transition rates depend only on the number of particles in the target energy level. Instead, if transition rates depend on the particle number only in the origin level, the statistics of ewkons is obtained; this is an exotic statistics that can be applied to the description of dark energy.
We study a numerical solution to Einstein's equation for a compact object composed of null particles. The solution avoids quantum scale regimes and hence neither relies upon nor ignores the interaction of quantum mechanics and gravitation. The solution exhibits a deep gravitational well yet remains singularity free. In fact, the solution is geometrically flat in the vicinity of the origin with the flat region being of any desirable scale. The solution is also observationally distinct from a black hole because a photon from infinity aimed at an object centered on the origin passes through the origin and escapes to infinity with a time delay.
In this paper we prove that the Euler equation describing the motion of an ideal fluid in $\R^d$ is well-posed in a class of functions allowing spatial asymptotic expansions as $|x|\to\infty$ of any a priori given order. These asymptotic expansions can involve log terms and lead to a family of conservation laws. Typically, the solutions of the Euler equation with initial data in the Schwartz class develop non-trivial spatial asymptotic expansions of the type considered here.
The nature and extent of the spin-entanglement in the triplet-triplet biexciton with total spin zero in correlated-electron $\pi$-conjugated systems continues to be an enigma. Differences in the ultrafast transient absorption spectra of free triplets versus the triplet-triplet can give a measure of the entanglement. This, however, requires theoretical understandings of transient absorptions from the optical spin-singlet, the lowest spin-triplet exciton as well as from the triplet-triplet state, whose spectra are often overlapping and hence difficult to distinguish. We present a many-electron theory of the electronic structure of the triplet-triplet, and of complete wavelength-dependent excited state absorptions (ESAs) from all three states in a heteroacene dimer of interest in the field of intramolecular singlet fission. The theory allows direct comparisons of ESAs with existing experiments as well as experimental predictions, and gives physical understandings of transient absorptions within a pictorial exciton basis that can be carried over to other experimental systems.
We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption "a" and the scattering coefficient "k" are to be recovered from the albedo operator. We show that "gauge equivalent" pairs (a,k) yield the same albedo operator, and that we can recover uniquely the class of gauge equivalent pairs. We apply this result to show unique determination of the media when the absorption "a" depends on the line of travel through each point while scattering "k" obeys a symmetry property. Previously known results concerned directional independent absorption.
The consistent construction of scattering amplitudes for processes with off-shell initial partons and involving electro-weak interactions is addressed.
Recently E. Bombieri and N. M. Katz (2010) have demonstrated that several well-known results about the distribution of values of linear recurrence sequences lead to interesting statements for Frobenius traces of algebraic curves. Here we continue this line of study and establish the M\"obius randomness law quantitatively for the normalised form of Frobenius traces.
Most differentiable neural architecture search methods construct a super-net for search and derive a target-net as its sub-graph for evaluation. There exists a significant gap between the architectures in search and evaluation. As a result, current methods suffer from an inconsistent, inefficient, and inflexible search process. In this paper, we introduce EnTranNAS that is composed of Engine-cells and Transit-cells. The Engine-cell is differentiable for architecture search, while the Transit-cell only transits a sub-graph by architecture derivation. Consequently, the gap between the architectures in search and evaluation is significantly reduced. Our method also spares much memory and computation cost, which speeds up the search process. A feature sharing strategy is introduced for more balanced optimization and more efficient search. Furthermore, we develop an architecture derivation method to replace the traditional one that is based on a hand-crafted rule. Our method enables differentiable sparsification, and keeps the derived architecture equivalent to that of Engine-cell, which further improves the consistency between search and evaluation. Besides, it supports the search for topology where a node can be connected to prior nodes with any number of connections, so that the searched architectures could be more flexible. For experiments on CIFAR-10, our search on the standard space requires only 0.06 GPU-day. We further have an error rate of 2.22% with 0.07 GPU-day for the search on an extended space. We can also directly perform the search on ImageNet with topology learnable and achieve a top-1 error rate of 23.8% in 2.1 GPU-day.
We review the continuous theory of dislocations from a mathematical point of view using mathematical tools, which were only partly available when the theory was developed several decades ago. We define a space of dislocation measures, which includes Hausdorff measures representing the dislocation measures of single dislocation curves. The evolution equation for dislocation measures is defined on this space. It is derived from four basic conditions, which must be satisfied by the model.
Relativistic mean field theory allowing for triaxial deformations is applied for a systematic study of fission barriers in the actinide region. Different pairing schemes are studied in details and it is shown that covariant density functional theory is able to describe fission barriers on a level of accuracy comparable with non-relativistic calculations, even with the best phenomenological macroscopic+microscopic approaches. Triaxiality in the region of the first saddle plays a crucial role in achieving that.
The averaging of the dynamic functions of the standard cosmological model (SCM) at its early stage with the dominance of the scalar field is carried out. It is shown that microscopic oscillations with Compton period provide the major contribution to the macroscopic energy density of the scalar field at large times at this stage. In this case, the effective equation of state of the scalar field oscillates between the inflationary and the extremely rigid ones, while the macroscopic equation of state is non-relativistic.