ShantanuT01/DACTYL-Pretraining huggingface dataset:
We examine the relationship between covariant and canonical (Ashtekar/Rovelli/Smolin) loop variables in the context of BF type topological field theories in 2+1 and 3+1 dimensions, with respective gauge groups SO(2,1) and SO(3,1). The latter model can be considered as the simplest topological gravity theory in 3+1 dimensions. We carry out the canonical quantization of this model in both the connection and loop representations, for the two spatial topologies $T^3$ and $S^2\times S^1$.
The hedgehog lattice (HL) is a three-dimensional topological spin texture hosting a periodic array of magnetic monopoles and antimonopoles. It has been studied theoretically for noncentrosymmetric systems with the Dzyaloshinskii-Moriya interaction, but the stability, as well as the magnetic and topological properties, remains elusive in the centrosymmetric case. We here investigate the ground state of an effective spin model with long-range bilinear and biquadratic interactions for a centrosymmetric cubic metal by simulated annealing. We show that our model stabilizes a HL composed of two pairs of left- and right-handed helices, resulting in no net scalar spin chirality, in stark contrast to the noncentrosymmetric case. We find that the HL turns into topologically-trivial conical states in an applied magnetic field. From the detailed analyses of the constituent spin helices, we clarify that the ellipticity and angles of the helical planes change gradually while increasing the magnetic field. We discuss the results in comparison with the experiments for a centrosymmetric cubic metal SrFeO$_3$.
We study special values of a modular function $\Lambda$ which is one of generalized $\lambda$ functions. We show special values of $\Lambda$ at imaginary quadratic points are algebraic integers. Further we prove that $\Lambda$ and the modular invariant function generate the modular function field with respect to the modular subgroup $\Gamma_1(N)$.
The characteristics of a meaningful effective field theory (EFT) analysis are discussed and compared with traditional approaches to NN scattering. A key feature of an EFT treatment is a systematic expansion in powers of momentum, which is demonstrated using an error analysis introduced by Lepage. A clear graphical determination of the radius of convergence for the momentum expansion is also obtained. I use these techniques to compare cutoff regularization, two forms of dimensional regularization, and the dibaryon approach, using a simple model for illustration. The naturalness of the parameters and predictions for other observables are also shown.
We dedicate this paper to the topological analysis of subwavelength solutions in Floquet metamaterials. This work should be considered as a basis for further investigation on whether topological properties of the bulk materials are linked to the occurrence of edge modes. The subwavelength solutions being described by a periodically parameterized time-periodic linear ordinary differential equation $\left\{\frac{d}{dt}X = A_\alpha(t)X\right\}_{\alpha \in \mathbb{T}^d}$, we put ourselves in the general setting of periodically parameterized time-periodic linear ordinary differential equations and introduce a way to (topologically) classify a Floquet normal form $F,~P$ of the associated fundamental solution $\left\{X_\alpha(t) = P(\alpha,t)\exp(tF_\alpha)\right\}_{\alpha \in \mathbb{T}^d}$. This is achieved by analysing the topological properties of the eigenvalues and eigenvectors of the monodromy matrix $X_\alpha(T)$ and the Lyapunov transformation $P(\alpha,t)$. The corresponding topological invariants can then be applied to the setting of Floquet metamaterials. In this paper these general results are considered in the case of honeycomb Floquet metamaterials. We provide two interesting examples of topologically non-trivial time-modulated honeycomb structures.
It has been suggested that the observed $D_s - D^0$ lifetime difference can be `understood' as due to $SU(3)_{Fl}$ breaking in the phase spaces for the exclusive $D^0$ and $D_s$ channels `removing' the need for weak annihilation. It is pointed out that several of the statements in this argument are misleading or even inconsistent with a state-of-the-art description of heavy flavour decays based on the operator product expansion.
We numerically investigate the Olami-Feder-Christensen model on a quenched random graph. Contrary to the case of annealed random neighbors, we find that the quenched model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling, with universal critical exponents. In addition, a power law relation between the size and the duration of an avalanche exists. We propose that this may represent the correct mean-field limit of the model rather than the annealed random neighbor version.
We consider a dynamic metapopulation involving one large population of size N surrounded by colonies of size \varepsilon_NN, usually called peripheral isolates in ecology, where N\to\infty and \varepsilon_N\to 0 in such a way that \varepsilon_NN\to\infty. The main population periodically sends propagules to found new colonies (emigration), and each colony eventually merges with the main population (fusion). Our aim is to study the genealogical history of a finite number of lineages sampled at stationarity in such a metapopulation. We make assumptions on model parameters ensuring that the total outer population has size of the order of N and that each colony has a lifetime of the same order. We prove that under these assumptions, the scaling limit of the genealogical process of a finite sample is a censored coalescent where each lineage can be in one of two states: an inner lineage (belonging to the main population) or an outer lineage (belonging to some peripheral isolate). Lineages change state at constant rate and inner lineages (only) coalesce at constant rate per pair. This two-state censored coalescent is also shown to converge weakly, as the landscape dynamics accelerate, to a time-changed Kingman coalescent.
We have developed the method that allows us to estimate the magnetic field strength at the horizon of a supermassive black hole (SMBH) through the observed polarization of optical emission of the accreting disk surrounding SMBH. The known asymptotic formulae for the Stokes parameters of outgoing radiation are azimuthal averaged, which corresponds to an observation of the disk as a whole. We consider two models of the embedding 3D-magnetic field, the regular field, and the regular field with an additional chaotic (turbulent) component. It is shown that the second model is preferable for estimating the magnetic field in NGC 4258. For estimations we used the standard accretion disk model assuming that the same power-law dependence of the magnetic field follows from the range of the optical emission down to the horizon. The observed optical polarization from NGC 4258 allowed us to find the values 10^3 - 10^4 Gauss at the horizon, depending on the particular choice of the model parameters. We also discuss the wavelength dependencies of the light polarization, and possibly applying them for a more realistic choice of accretion disk parameters.
The main goal of the paper is to establish a sufficient condition for a two-valenced association scheme to be schurian and separable. To this end, an analog of the Desargues theorem is introduced for a noncommutative geometry defined by the scheme in question. It turns out that if the geometry has enough many Desarguesian configurations, then under a technical condition the scheme is schurian and separable. This result enables us to give short proofs for known statements on the schurity and separability of quasi-thin and pseudocyclic schemes. Moreover, by the same technique we prove a new result: given a prime $p$, any $\{1,p\}$-scheme with thin residue isomorphic to an elementary abelian $p$-group of rank greater than two, is schurian and separable.
Strongly correlated Fermi systems are among the most intriguing, best experimentally studied and fundamental systems in physics. These are, however, in defiance of theoretical understanding. The ideas based on the concepts like Kondo lattice and involving quantum and thermal fluctuations at a quantum critical point have been used to explain the unusual physics. Alas, being suggested to describe one property, these approaches fail to explain the others. This means a real crisis in theory suggesting that there is a hidden fundamental law of nature, which remains to be recognized. A theory of fermion condensation quantum phase transition, preserving the extended quasiparticles paradigm and intimately related to unlimited growth of the effective mass as a function of temperature, magnetic field etc, is capable to resolve the problem. We discuss the construction of the theory and show that it delivers theoretical explanations of vast majority of experimental results in strongly correlated systems such as heavy-fermion metals and quasi-two-dimensional Fermi systems.
The discovery of a persistent radio source coincident with the first repeating fast radio burst, FRB 121102, and offset from the center of its dwarf host galaxy has been used as evidence for a link with young millisecond magnetars born in superluminous supernovae (SLSNe) or long-duration gamma-ray bursts (LGRBs). A prediction of this scenario is that compact radio sources offset from the centers of dwarf galaxies may serve as signposts for at least some FRBs. Recently, Reines et al. 2019 presented the discovery of 20 such radio sources in nearby ($z\lesssim 0.055$) dwarf galaxies, and argued that these cannot be explained by emission from HII regions, normal supernova remnants, or normal radio supernovae. Instead, they attribute the emission to accreting wandering massive black holes. Here, we explore the alternative possibility that these sources are analogs of FRB 121102. We compare their properties -- radio luminosities, spectral energy distributions, light curves, ratios of radio-to-optical flux, and spatial offsets -- to FRB 121102, a few other well-localized FRBs, and potentially related systems, and find that these are all consistent as arising from the same population. We further compare their properties to the magnetar nebula model used to explain FRB 121102, as well as to theoretical off-axis LGRB light curves, and find overall consistency. Finally, we find a consistent occurrence rate relative to repeating FRBs and LGRBs. We outline key follow-up observations to further test these possible connections.
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and empiricist interpretations of the mathematical formalism of quantum mechanics, iii) the distinction between measurement and preparation. It will be demonstrated that an interpretation of violation of Bell's inequality by quantum mechanics as evidence of non-locality of the quantum world is a consequence of a particular choice between these alternatives. Also a distinction must be drawn between two forms of realism, viz. a) realist interpretations of quantum mechanics, b) the possibility of hidden-variables (sub-quantum) theories.
We investigate type IIB strings on $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathrm{S}^3\times\mathrm{S}^1$ with mixed Ramond-Ramond (R-R) and Neveu-Schwarz-Neveu-Schwarz (NS-NS) flux. By suitably gauge-fixing the closed string Green-Schwarz (GS) action of this theory, we derive the off-shell symmetry algebra and its representations. We use these to determine the non-perturbative worldsheet S-matrix of fundamental excitations in the theory. The analysis involves both massive and massless modes in complete generality. The S-matrix we find involves a number of phase factors, which in turn satisfy crossing equations that we also determine. We comment on the nature of the heaviest modes of the theory, but leave their identification either as composites or bound-states to a future investigation.
We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition, and multiqubit gates, be with the use of a quantum bus or direct capacitive couplings. We apply our method to the paradigmatic cases of 1D and 2D Fermi-Hubbard models, involving couplings with nearest and next-nearest neighbours. Furthermore, we propose an optimal architecture for this model and discuss the benchmarking of the simulations in realistic circuit quantum electrodynamics setups.
The 3-dimensional gauge-Higgs system describes the non-perturbative infrared effects of the high-temperature phase of the Standard Model. We calculate the two-loop self-energies in the 3-dimensional SU(2) Higgs model and in the corresponding gauged non-linear $\sigma$-model. As an application of the results, we estimate the dynamically generated vector boson mass in the symmetric phase of the Higgs model by means of gap equations.
We have used the velocity dispersion as an age indicator to constrain the ages of a large sample of main sequence Vega-like stars in order to study the lifetimes and temporal evolution of the dust disks around them. We use HIPPARCOS measurements to compute stellar velocities in the sky plane. The velocity dispersion of Vega-like stars is found to be systematically smaller than that of the normal main sequence field stars for all spectral types, suggesting that the main sequence dusty systems, on average, are younger than normal field stars. The debris disks seem to survive longer around late type stars as compared to early type stars. Further, we find a strong correlation between fractional dust luminosity ((f_{d} \equiv L_{dust}/L_{\star})) and velocity dispersion of stars with dust disks. Fractional dust luminosity is found to drop off steadily with increasing stellar age from early pre-main sequence phase to late main sequence phase.
We express the leading electromagnetic corrections in K-> pi pi amplitudes as integrals over the virtual photon squared-momentum Q^2. The high Q^2 behavior is obtained via the operator product expansion. The low Q^2 behavior is calculated using chiral perturbation theory. We model the intermediate Q^2 region using resonance contributions in order to enforce the matching of these two regimes. The results confirm our previous estimates that the electromagnetic corrections provide a reasonably small shift in the delta I - 3/2 amplitude.
We apply the time-dependent variational principle, the nuclear field theory, and the boson expansion method to the Lipkin model to discuss anharmonicities of collective vibrational excitations. It is shown that all of these approaches lead to the same anharmonicity to leading order in the number of particles. Comparison with the exact solution of the Lipkin model shows that these theories reproduce it quite well.
The classification of map-germs up to the natural right-left equivalence (also known as A-equivalence) is often complicated. Certainly it is more complicated than K-equivalence which is extremely easy to work with because the associated tangent spaces are not 'mixed' modules as they are in the A-equivalence case.   In this paper we use a version of K-equivalence, denoted $_V$K-equivalence, that is defined using K-equivalences that preserve a variety in the source of maps to classify maps up to A-equivalence. This is possible through making clear the connection between the two equivalences - previous work by Damon mostly focussed on the relation between the codimensions associated to the maps.   To demonstrate the power and efficiency of the method we give a classification of certain A$_e$-codimension 2 maps from $n$-space to $n+1$-space. The proof using $_V$K-equivalence is considerably shorter - by a wide margin - than one using A-equivalence directly.
In this paper, we find formulas for the number of representations of certain diagonal octonary quadratic forms with coefficients $1,2,3,4$ and $6$. We obtain these formulas by constructing explicit bases of the space of modular forms of weight $4$ on $\Gamma_0(48)$ with character.
Sylvester doubles sums, introduced first by Sylvester are symmetric expressions of the roots of two polynomials. Sylvester's definition of double sums makes no sense in the presence of multiple roots, since the definition involves denominators that vanish when there are multiple roots. The aim of this paper is to give a new definition of Sylvester double sums making sense in the presence of multiple roots, which coincides with the definition by Sylvester in the case of simple roots, to prove that double sums indexed by $(k,\ell)$ are equal up to a constant if they share the same value for $k+\ell$, as well a proof of the relationship between double sums and subresultants, i.e. that they are equal up to a constant. In the simple root case, proofs of these properties are already known. The more general proofs given here are using generalized Vandermonde determinants and symmetric multivariate Hermite interpolation as well as an induction on the length of the remainder sequence of $P$ and $Q$.
Face presentation attacks have become a major threat to face recognition systems and many countermeasures have been proposed in the past decade. However, most of them are devoted to 2D face presentation attacks, rather than 3D face masks. Unlike the real face, the 3D face mask is usually made of resin materials and has a smooth surface, resulting in reflectance differences. So, we propose a novel detection method for 3D face mask presentation attack by modeling reflectance differences based on intrinsic image analysis. In the proposed method, the face image is first processed with intrinsic image decomposition to compute its reflectance image. Then, the intensity distribution histograms are extracted from three orthogonal planes to represent the intensity differences of reflectance images between the real face and 3D face mask. After that, the 1D convolutional network is further used to capture the information for describing different materials or surfaces react differently to changes in illumination. Extensive experiments on the 3DMAD database demonstrate the effectiveness of our proposed method in distinguishing a face mask from the real one and show that the detection performance outperforms other state-of-the-art methods.
We report a Hitomi observation of IGR J16318-4848, a high-mass X-ray binary system with an extremely strong absorption of N_H~10^{24} cm^{-2}. Previous X-ray studies revealed that its spectrum is dominated by strong fluorescence lines of Fe as well as continuum emission. For physical and geometrical insight into the nature of the reprocessing material, we utilize the high spectroscopic resolving power of the X-ray microcalorimeter (the soft X-ray spectrometer; SXS) and the wide-band sensitivity by the soft and hard X-ray imager (SXI and HXI) aboard Hitomi. Even though photon counts are limited due to unintended off-axis pointing, the SXS spectrum resolves Fe K{\alpha_1} and K{\alpha_2} lines and puts strong constraints on the line centroid and width. The line width corresponds to the velocity of 160^{+300}_{-70} km s^{-1}. This represents the most accurate, and smallest, width measurement of this line made so far from any X-ray binary, much less than the Doppler broadening and shift expected from speeds which are characteristic of similar systems. Combined with the K-shell edge energy measured by the SXI and HXI spectra, the ionization state of Fe is estimated to be in the range of Fe I--IV. Considering the estimated ionization parameter and the distance between the X-ray source and the absorber, the density and thickness of the materials are estimated. The extraordinarily strong absorption and the absence of a Compton shoulder component is confirmed. These characteristics suggest reprocessing materials which are distributed in a narrow solid angle or scattering primarily with warm free electrons or neutral hydrogen.
The question of computing the reductions modulo $p$ of two-dimensional crystalline $p$-adic Galois representations has been studied extensively, and partial progress has been made for representations that have small weights, very small slopes, or very large slopes. It was conjectured by Breuil, Buzzard, and Emerton that these reductions are irreducible if they have even weight and non-integer slope. We prove some instances of this conjecture for slopes up to $\frac{p-1}{2}$.
This is an expository account of Grothendieck's construction of Hilbert and Quot Schemes, following his talk `Techniques de construction et theoremes d'existence en geometrie algebriques IV : les schemas de Hilbert', Seminaire Bourbaki 221 (1960/61), together with further developments by Mumford and by Altman and Kleiman. Hilbert and Quot schemes are fundamental to modern Algebraic Geometry, in particular, for deformation theory and moduli constructions. These notes are based on a series of six lectures in the summer school `Advanced Basic Algebraic Geometry', held at the Abdus Salam International Centre for Theoretical Physics, Trieste, in July 2003.
We study the relation between the discrete--time version of the flashing ratchet known as Parrondo's games and a compression technique used very recently with thermal ratchets for evaluating the transfer of information -- negentropy -- between the Brownian particle and the source of fluctuations. We present some results concerning different versions of Parrondo's games, showing all of them a good qualitative agreement between the gain and the inverse of the entropy.
Relative motion in a two-component, trapped atomic gas provides a sensitive probe of interactions. By studying the lowest frequency excitations of a two spin-state gas confined in a magnetic trap, we have explored the transition from the collisionless to the hydrodynamic regime. As a function of collision rate, we observe frequency shifts as large as 6% as well as a dramatic, non-monotonic dependence of the damping rate. The measurements agree qualitatively with expectations for behavior in the collisionless and hydrodynamic limits and are quantitatively compared to a classical kinetic model.
We consider a stochastically continuous, affine Markov process in the sense of Duffie, Filipovic and Schachermayer, with cadlag paths, on a general state space D, i.e. an arbitrary Borel subset of R^d. We show that such a process is always regular, meaning that its Fourier-Laplace transform is differentiable in time, with derivatives that are continuous in the transform variable. As a consequence, we show that generalized Riccati equations and Levy-Khintchine parameters for the process can be derived, as in the case of $D = R_+^m \times R^n$ studied in Duffie, Filipovic and Schachermayer (2003). Moreover, we show that when the killing rate is zero, the affine process is a semi-martingale with absolutely continuous characteristics up to its time of explosion. Our results generalize the results of Keller-Ressel, Schachermayer and Teichmann (2011) for the state space $R_+^m \times R^n$ and provide a new probabilistic approach to regularity.
We solve a very general two-channel fermion-boson model describing charge transport within some background medium by means of a refined pseudo-site density matrix renormalization group (DMRG) technique. Performing a careful finite-size scaling analysis, we determine the ground-state phase diagram and convincingly prove that the model exhibits a metal-insulator quantum phase transition for the half-filled band case. In order to characterize the metallic and insulating regimes we calculate besides the local particle densities and fermion-boson correlation functions, the kinetic energy, the charge structure factor, the Luttinger liquid charge exponent and the single-particle excitation gap for a one-dimensional infinite system.
We determine the conditions for the existence or not of cycles for several families of generalized 3x + 1 mappings and develop a method to find them.