ShantanuT01/DACTYL-Pretraining huggingface dataset:
Periodic boundary conditions have not a unique implementation in magnetic systems where all spins interact with each other through a power law decaying interaction of the form $1/r^\alpha$, $r$ being the distance between spins. In this work we present a comparative study of the finite size effects oberved in numerical simulations by using first image convention and full infinite of periodic boundary conditions in one and two-dimensional spin systems with those type of interactions, including the ferromagnetic, antiferromagnetic and competitive interactions cases. Our results show no significative differences between the finite size effects produced by both types of boundary conditions when the low temperature phase has zero global magnetization, while it depends on the ratio $\alpha/d$ for systems with a low temperature ferromagnetic phase. In the last case the first image convention gives much more stronger finite size effects than the other when the system enters into the classical regime $\alpha/d \leq 3/2$.
We formulate the ten-dimensional super-Yang-Mills theory in a twisted superspace with 8+1 supercharges. Its constraints do not imply the equations of motion and we solve them. As a preliminary step for a complete formulation in a twisted superspace, we give a superspace path-integral formulation of the N=2, d=4 super-Yang-Mills theory without matter. The action is the sum of a Chern--Simons term depending on a super-connection plus a BF-like term. The integration over the superfield B implements the twisted superspace constraints on the super-gauge field, and the Chern-Simons action reduces to the known action in components.
For a degenerate autonomous Kirchhoff equation which is set on $\mathbb{R}^N$ and involves the Berestycki-Lions type nonlinearity, we cope with the cases $N=2,3$ and $N\geq5$ by using mountain pass and symmetric mountain pass approaches and by using Clark theorem respectively.
Let k be an algebraically closed field of characteristic 0. The question of irreducibility of the punctual Hilbert scheme Hilb_d P^n and its Gorenstein locus for various d was studied in [CEVV8, CN9, CN10, CN11]. In this short paper we prove that the subschemes corresponding to the Gorenstein algebras having Hilbert function (1,5,5,1) are smoothable i.e. lie in the closure of the locus of smooth subschemes. Among the Gorenstein algebras of length 12 the smoothability of algebras having such Hilbert function seems to be the most inapproachable using non-direct tools e.g. structural theorems.
From the previously obtained solutions of the Fokker - Planck equation for Rayleigh gas (small impurity of heavy particles in a thermostat of light particles) with sources and without them, the entropy production was calculated. In a system without source (isolated system) shown that it holds theorem of Prigogine, and in a system with sources (open system) implementation of the principle of Ziegler (MEPP) depends on the relaxation direction. In an open system entropy production is compensate by a negative production of entropy, i.e. by a negentropy production. The algebraic sum of entropy and negentropy productions is called the generalized entropy production. From the balance of entropy and negentropy productions in an open system formulated a possible variation of the second law for open systems in a form: "At the relaxation of an open system to a nonequilibrium steady state, a generalized entropy production decreases in absolute value and equal to zero in a nonequilibrium steady state." Keywords: Fokker-Planck equation, Prigogine theorem, principle of maximum entropy production, the second law, negentropy.
Two-point density-density correlation functions for the diffusive binary reaction system $A+A\to\emptyset$ are obtained in one dimension via Monte Carlo simulation. The long-time behavior of these correlation functions clearly deviates from that of a recent analytical prediction of Bares and Mobilia [Phys. Rev. Lett. {\bf 83}, 5214 (1999)]. An alternative expression for the asymptotic behavior is conjectured from numerical data.
In this article, we consider the limited data problem for spherical mean transform. We characterize the generation and strength of the artifacts in a reconstruction formula. In contrast to the third's author work [Ngu15b], the observation surface considered in this article is not flat. Our results are comparable to those obtained in [Ngu15b] for flat observation surface. For the two dimensional problem, we show that the artifacts are $k$ orders smoother than the original singularities, where $k$ is vanishing order of the smoothing function. Moreover, if the original singularity is conormal, then the artifacts are $k+\frac{1}{2}$ order smoother than the original singularity. We provide some numerical examples and discuss how the smoothing effects the artifacts visually. For three dimensional case, although the result is similar to that [Ngu15b], the proof is significantly different. We introduce a new idea of lifting the space.
We consider a bipartite quantum system S=AB such that the part A is isolated from the environment E and only the part B interacts with E. Under such circumstances, entanglement of the system may experience decreases and increases, during the evolution of the system. Here, we show that the entanglement of the system can exceed its initial value, under such local interaction, even though, at the initial moment, there is no entanglement in the environment and the system and the environment are only classically correlated. The case which is studied in this paper possesses another interesting feature too: The reduced dynamics of the system can be modeled as a completely positive map. In addition, we introduce the concept of inaccessible entanglement to explain why entanglement can exceed its initial value, under local interactions, in open quantum systems.
The current success of modern visual reasoning systems is arguably attributed to cross-modality attention mechanisms. However, in deliberative reasoning such as in VQA, attention is unconstrained at each step, and thus may serve as a statistical pooling mechanism rather than a semantic operation intended to select information relevant to inference. This is because at training time, attention is only guided by a very sparse signal (i.e. the answer label) at the end of the inference chain. This causes the cross-modality attention weights to deviate from the desired visual-language bindings. To rectify this deviation, we propose to guide the attention mechanism using explicit linguistic-visual grounding. This grounding is derived by connecting structured linguistic concepts in the query to their referents among the visual objects. Here we learn the grounding from the pairing of questions and images alone, without the need for answer annotation or external grounding supervision. This grounding guides the attention mechanism inside VQA models through a duality of mechanisms: pre-training attention weight calculation and directly guiding the weights at inference time on a case-by-case basis. The resultant algorithm is capable of probing attention-based reasoning models, injecting relevant associative knowledge, and regulating the core reasoning process. This scalable enhancement improves the performance of VQA models, fortifies their robustness to limited access to supervised data, and increases interpretability.
Let p be an odd prime. Let F_p^* be the no-null part of the finite field of p elements. Let K = Q(zeta) be the p-cyclotomic field and let O_K be the ring of integers of K. Let pi be the prime ideal of K lying over p. An integer B \in O_K is said singular if B^{1/p} not \in K and if B O_K = b^p where b is an ideal of O_K. An integer B \in O_K is said semi-primary if B = beta mod pi^2 where the natural beta is coprime with p. Let sigma be a Q-isomorphism of the field K generating the Galois group Gal(K/Q). When p is irregular, there exists at least one subgroup Gamma of order p of the class group of K annihilated by a polynomial sigma - mu with mu \in F_p^*. We prove the existence, for each Gamma, of singular semi-primary integers B where B O_K= b^p with class Cl(b) \in Gamma and B^{sigma-mu} \in K^p and we describe their pi-adic expansion. This paper is at a strictly elementary level.
Null shells are a useful geometric construction to study the propagation of infinitesimally thin concentrations of massless particles or impulsive waves. After recalling the necessary and sufficient conditions obtained in [28] that allow for the matching of two spacetimes with null embedded hypersurfaces as boundaries, we will address the problem of matching across Killing horizons of zero order in the case when the symmetry generators are to be identified. The results are substantially different depending on whether the boundaries are non-degenerate or degenerate, and contain or not fixed points (in particular, in the former case the shells have zero pressure but non-vanishing energy density and energy flux in general). We will present the explicit form of the so-called step function in each situation. We will then concentrate on the case of actual Killing horizons admitting a bifurcation surface, where a complete description of the shell and its energy-momentum tensor can be obtained. We will conclude particularizing to the matching of two spacetimes with spherical, plane or hyperbolic symmetry without imposing this symmetry on the shell itself.
Hadronic electroweak corrections to the muon anomalous magnetic moment (g-2) are reviewed. Emphasis is on clarification of discrepancies among various published studies. A theorem on non-renormalization of the transversal part of a correlator of two vector currents and an axial current is reviewed and its consequences in the form of superconvergent sum rules are discussed.
The renormalized quantum stress energy tensor $\left<T_{\mu}^{\nu}\right>_{ren}$ for a massive spinor field around global monopoles is constructed within the framework of Schwinger-DeWitt approximation, valid whenever the Compton length of the quantum field is much less than the characteristic radius of the curvature of the background geometry. The results obtained shows that the quantum massive spinor field in the global monopole spacetime violates all the pointwise energy conditions.
One of the possible approaches to the construction of massive higher spin interactions is to use their gauge invariant description based on the introduction of the appropriate set of Stueckelberg fields. Recently, the general properties of such approach were investigated in [1]. The main findings of this work can be formulated in two statements. At first, there always exist enough field redefinitions to bring the vertex into abelian form where there are some corrections to the gauge transformations but the gauge algebra is undeformed. At second, with the further (as a rule higher derivative) field redefinitions one can bring the vertex into trivially gauge invariant form expressed in terms of the gauge invariant objects of the free theory.   Our aim in this work is to show (using a simple example) how these general properties are realised in the so-called Fradkin-Vasiliev formalism and to see the effects (if any) that the presence of massless field, and hence of some unbroken gauge symmetries, can produce. As such example we take the gravitational interaction for massive spin-3/2 field so we complete the investigation started in [2] relaxing all restrictions on the number of derivatives and allowed field redefinitions. We show that in spite of the presence of massless spin-2 field, the first statement is still valid, while there exist two abelian vertices which are not equivalent on-shell to the trivially gauge invariant ones. Moreover, it is one of this abelian vertices that reproduce the minimal interaction for massive spin-3/2.
The correlations, entanglement entropy, and fidelity susceptibility are calculated for a one-dimensional spin-1/2 XXZ chain with anisotropic power-law long range interactions by employing the density matrix renormalization group method. In particular, this long-range interaction is assigned to ferromagnetic for transversal components, while it can be either ferro- or antiferromagnetic for the longitudinal spin component. Two ground-state phase diagrams are established versus the anisotropy of the interactions which not only changes the phase boundaries of the counterparts with short-range interactions, but also leads to the emergence of exotic phases. We found that the long-range interactions of the z-component results in a Wigner crystal phase, whereas the transversal one may break a continuous symmetry, resulting in a continuous symmetry breaking phase.
We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to $Du$. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given.
This paper presents a fast approach for penalized least squares (LS) regression problems using a 2D Gaussian Markov random field (GMRF) prior. More precisely, the computation of the proximity operator of the LS criterion regularized by different GMRF potentials is formulated as solving a Sylvester-like matrix equation. By exploiting the structural properties of GMRFs, this matrix equation is solved columnwise in an analytical way. The proposed algorithm can be embedded into a wide range of proximal algorithms to solve LS regression problems including a convex penalty. Experiments carried out in the case of a constrained LS regression problem arising in a multichannel image processing application, provide evidence that an alternating direction method of multipliers performs quite efficiently in this context.
We analyse, in NLO, the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of eigenfunctions with positive eigenvalues, \omega, together with a small contribution from a continuum of eigenfunctions with negative \omega, provide an excellent description of high-precision HERA F_2 data in the region, x<0.001, Q^2 > 6 GeV^2. The phases of the eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first eigenfunction decouples completely or almost completely from the proton. This suggests that there exist an additional ground state, which is naturally saturated and may have the properties of the soft pomeron.
Cataclysmic Variables (CV) are close binary systems, in which the primary, the more massive star, is a white dwarf. CVs usually exhibit a number of periodicities, most of which are now understood. However, recently, a new phenomenon was discovered that does not fit the standard picture. Two objects have been discovered to show periods that are much longer than orbital, and have no relation to it, either in light curves or in radial velocity (RV) variations measured from spectroscopy. Here, we show that the precession of the fast rotating magnetically accreting white dwarf can successfully explain these phenomena. The theory of compact objects predicts certain relations between the spin and precession periods, and our finding provides a good test for the theory and establishes a qualitative model to be explored both theoretically and observationally. Detection of precession can become a powerful tool in searching for the internal properties of compact stars, which would be otherwise inaccessible for us.
We present the first results of our spatially axisymmetric core-collapse supernova simulations with full Boltzmann neutrino transport, which amount to a time-dependent 5-dimensional (2 in space and 3 in momentum space) problem in fact. Special relativistic effects are fully taken into account with a two-energy-grid technique. We performed two simulations for a progenitor of 11.2M, employing different nuclear equations-of-state (EOS's): Lattimer and Swesty's EOS with the incompressibility of K = 220MeV (LS EOS) and Furusawa's EOS based on the relativistic mean field theory with the TM1 parameter set (FS EOS). In the LS EOS the shock wave reaches ~700km at 300ms after bounce and is still expanding whereas in the FS EOS it stalled at ~200km and has started to recede by the same time. This seems to be due to more vigorous turbulent motions in the former during the entire post-bounce phase, which leads to higher neutrino-heating efficiency in the neutrino-driven convection. We also look into the neutrino distributions in momentum space, which is the advantage of the Boltzmann transport over other approximate methods. We find non-axisymmetric angular distributions with respect to the local radial direction, which also generate off-diagonal components of the Eddington tensor. We find that the r {\theta}-component reaches ~10% of the dominant rr-component and, more importantly, it dictates the evolution of lateral neutrino fluxes, dominating over the {\theta}{\theta}-component, in the semi-transparent region. These data will be useful to further test and possibly improve the prescriptions used in the approximate methods.
We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting partial sums converges to the normal CDF with probability one. This implies almost sure convergence of empirical periodograms, almost sure convergence of spectra of circulant and reverse circulant matrices, and almost sure convergence of the CDF's generated from independent random variables by independent random orthogonal matrices.   For special trigonometric matrices, the speed of the almost sure convergence is described by the normal approximation and by the large deviation principle.
The role of bremsstrahlung in the emission from hot accretion flows around slowly accreting supermassive black holes is not thoroughly understood. In order to appraise the importance of bremsstrahlung relative to other radiative processes, we compute spectral energy distributions (SEDs) of accretion disks around slowly accreting supermassive black holes including synchrotron radiation, inverse Compton scattering, and bremsstrahlung. We compute SEDs for (i) four axisymmetric radiative general relativistic magnetohydrodynamics (RadGRMHD) simulations of $10^{8}M_{\odot}$ black holes with accretion rates between $10^{-8}\dot{M}_{\text{Edd}}$ and $10^{-5}\dot{M}_{\text{Edd}}$, (ii) four axisymmetric RadGRMHD simulations of M87$^\ast$ with varying dimensionless spin $a_\ast$ and black hole mass, and (iii) a 3D GRMHD simulation scaled for Sgr A$^\ast$. At $10^{-8}\dot{M}_{\text{Edd}}$, most of the luminosity is synchrotron radiation, while at $10^{-5}\dot{M}_{\text{Edd}}$ the three radiative processes have similar luminosities. In most models, bremsstrahlung dominates the SED near $512\text{ keV}$. In the M87$^\ast$ models, bremsstrahlung dominates this part of the SED if $a_{\ast} = 0.5$, but inverse Compton scattering dominates if $a_{\ast}= 0.9375$. Since scattering is more variable than bremsstrahlung, this result suggests that $512\text{ keV}$ variability could be a diagnostic of black hole spin. In the appendix, we compare some bremsstrahlung formulae found in the literature.
We propose a method for obtaining effective classical Hamiltonians \cal H for many-body quantum spin systems with large spins. This method uses the coherent-state representation of the partition function Z and the cumulant expansion in powers of 1/S. For the quantum Hamiltonian \hat H of a Heisenberg form, the 1/S corrections in \cal H have a non-Heisenberg many-spin form. The effective Hamiltonian \cal H can be treated by methods familiar for classical systems. The non-Heisenberg terms in \cal H may be responsible for such effects as spin-Peierls transition and uplifting of the classical degeneracy by quantum fluctuations.
We provide evidence that indicate the star cluster Pfleiderer 2, which is projected in a rich field, as a newly identified Galactic globular cluster. Since it is located in a crowded field, core extraction and decontamination tools were applied to reveal the cluster sequences in B, V and I Color-Magnitude Diagrams (CMDs). The main CMD features of Pfleiderer 2 are a tilted Red Giant Branch, and a red Horizontal Branch, indicating a high metallicity around solar. The reddening is E(B-V)=1.01. The globular cluster is located at a distance from the Sun d$_{\odot}$ = 16$\pm$2 kpc.   The cluster is located at 2.7 kpc above the Galactic plane and at a distance from the Galactic center of R$_{\rm GC}$=9.7 kpc, which is unusual for a metal-rich globular cluster.
In a recent paper, Geyer, Klimchitskaya, and Mostepanenko [Phys. Rev. A 67, 062102 (2003); quant-ph/0306038] proposed the final solution of the problem of temperature correction to the Casimir force between real metals. The basic idea was that one cannot use the dielectric permittivity in the frequency region where a real current may arise leading to Joule heating of the metal. Instead, the surface impedance approach is proposed as a solution of all contradictions. The purpose of this comment is to show that (i) the main idea contradicts to the fluctuation dissipation theorem, (ii) the proposed method to calculate the force gives wrong value of the temperature correction since the contribution of low frequency fluctuations is calculated with the impedance which is not applicable at low frequencies. In the impedance approach the right result for the reflection coefficients in the n=0 term of the Lifshitz formula is given.
We report the rectification of a constant wave radio frequency (RF) current by using a single-layer magnetic nanowire; a direct-current voltage is resonantly generated when the RF current flows through the nanowire. The mechanism of the rectification is discussed in terms of the spin torque diode effect reported for magnetic tunnel junction devices and the rectification is shown to be direct attributable to resonant spin wave excitation by the RF current.
Given a weight vector $\tau=(\tau_{1}, \dots, \tau_{n}) \in \mathbb{R}^{n}_{+}$ with each $\tau_{i}$ bounded by certain constraints, we obtain a lower bound for the Hausdorff dimension of the set of $\tau$-approximable points points over a manifold $\mathcal{M}$, where $\mathcal{M}$ is twice continuously differentiable. From this we produce a lower bound for the set of $\psi$-approximable points over a manifold where $\psi$ is a general approximation function with certain limits. The proof is based on a technique developed by Beresnevich et al. in arXiv:1712.03761, but we use an alternative mass transference style theorem.
In usual security proofs of quantum protocols the adversary (Eve) is expected to have full control over any quantum communication between any communicating parties (Alice and Bob). Eve is also expected to have full access to an authenticated classical channel between Alice and Bob. Unconditional security against any attack by Eve can be proved even in the realistic setting of device and channel imperfection. In this Letter we show that the security of QKD protocols is ruined if one allows Eve to possess a very limited access to the random sources used by Alice. Such knowledge should always be expected in realistic experimental conditions via different side channels.
We construct infinitely many incompressible Sobolev vector fields $u \in C_t W^{1,\tilde p}_x$ on the periodic domain $\mathbb{T}^d$ for which uniqueness of solutions to the transport equation fails in the class of densities $\rho \in C_t L^p_x$, provided $1/p + 1/\tilde p > 1 + 1/d$. The same result applies to the transport-diffusion equation, if, in addition $p'<d$.