ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Lieb-Robinson theorem states that the speed at which the correlations between two distant nodes in a spin network can be built through local interactions has an upper bound, which is called the Lieb-Robinson velocity. Our central aim is to demonstrate how to observe the Lieb-Robinson velocity in an Ising spin chain with a strong transverse field. We adopt and compare four correlation measures for characterizing different types of correlations, which include correlation function, mutual information, quantum discord, and entanglement of formation. We prove that one of correlation functions shows a special behavior depending on the parity of the spin number. All the information-theoretical correlation measures demonstrate the existence of the Lieb-Robinson velocity. In particular, we find that there is a sudden switch of the Lieb-Robinson speed with the increasing of the number of spin.
In this paper we extend the notion of digraphical regular representations in the context of Haar digraphs. Given a group $G$, a {\em Haar digraph} $\Gamma$ over $G$ is a bipartite digraph having a bipartition $\{X,Y\}$ such that $G$ is a group of automorphisms of $\Gamma$ acting regularly on $X$ and on $Y$. We say that $G$ admits a {\em Haar digraphical representation} (HDR for short), if there exists a Haar digraph over $G$ such that its automorphism group is isomorphic to $G$. In this paper, we classify finite groups admitting a HDR.
This paper is concerned with two properties of positive weak solutions of quasilinear elliptic equations with nonlinear gradient terms. First, we show a Liouville-type theorem for positive weak solutions of the equation involving the $m$-Laplacian operator \begin{equation*} -\Delta_{m}u=u^q|\nabla u|^p\ \ \ \mathrm{in}\ \mathbb{R}^N, \end{equation*} where $N\geq1$, $m>1$ and $p,q\geq0$. The technique of Bernstein gradient estimates is ultilized to study the case $p<m$. Moreover, a Liouville-type theorem for supersolutions under subcritial range of exponents \begin{equation*} q(N-m)+p(N-1)<N(m-1) \end{equation*} is also established. Then, we use a degree argument to obtain the existence of positive weak solutions for a nonlinear Dirichlet problem of the type $-\Delta_m u = f(x,u,\nabla u)$, with $f$ satisfying certain structure conditions. Our proof is based on a priori estimates, which will be accomplished by using a blow-up argument together with the Liouville-type theorem in the half-space. As another application, some new Harnack inequalities are proved.
Relations between subexponential densities and locally subexponential distributions are discussed. It is shown that the class of subexponential densities is neither closed under convolution roots nor closed under asymptotic equivalence. A remark is given on the closure under convolution roots for the class of convolution equivalent distributions.
The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well.   In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative algebra and affine algebraic geometry.
We systematically investigate short-timescale ($<$10-day rest-frame) CIV broad absorption-line (BAL) variability to constrain quasar-wind properties and provide insights into BAL-variability mechanisms in quasars. We employ data taken by the Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) project, as the rapid cadence of these observations provides a novel opportunity to probe BAL variability on shorter rest-frame timescales than have previously been explored. In a sample of 27 quasars with a median of 58 spectral epochs per quasar, we have identified 15 quasars ($55^{+18}_{-14}$%), 19 of 37 CIV BAL troughs ($51^{+15}_{-12}$%), and 54 of 1460 epoch pairs ($3.7 \pm 0.5$%) that exhibit significant CIV BAL equivalent-width variability on timescales of less than 10 days in the quasar rest frame. These frequencies indicate that such variability is common among quasars and BALs, though somewhat rare among epoch pairs. Thus, models describing BALs and their behavior must account for variability on timescales down to less than a day in the quasar rest frame. We also examine a variety of spectral characteristics and find that in some cases, BAL variability is best described by ionization-state changes, while other cases are more consistent with changes in covering fraction or column density. We adopt a simple model to constrain the density and radial distance of two outflows appearing to vary by ionization-state changes, yielding outflow density lower limits consistent with previous work.
We study edges states of graphene ribbons in the quantized Hall regime, and show that they can be described within a continuum model (the Dirac equation) when appropriate boundary conditions are adopted. The two simplest terminations, zigzag and armchair edges, are studied in detail. For zigzag edges, we find that the lowest Landau level states terminate in two types of edge states, dispersionless and current-carrying surface states. The latter involve components on different sublattices that may be separated by distances far greater than the magnetic length. For armchair edges, the boundary conditions are met by admixing states from different valleys, and we show that this leads to a single set of edges states for the lowest Landau level and two sets for all higher Landau levels. In both cases, the resulting Hall conductance step for the lowest Landau level is half that between higher Landau levels, as observed in experiment.
Hot stars emit large amounts of X-rays, which are assumed to originate in the supersonic stellar wind. Part of the emitted X-rays is subsequently absorbed in the wind and influences its ionization state. Because hot star winds are driven radiatively, the modified ionization equilibrium affects the radiative force. We review the recent progress in modelling the influence of X-rays on the radiative equilibrium and on the radiative force. We focus particularly on single stars with X-rays produced in wind shocks and on binaries with massive components, which belong to the most luminous objects in X-rays.
The LIGO-Virgo collaboration recently reported a puzzling event, GW190814, with component masses of 23 and 2.6 solar masses. Motivated by the relatively small rate of such a coalescence and the fact that the mass of the secondary is close to the total mass of known binary neutron star (bNS) systems, we propose that GW190814 was a second-generation merger from a hierarchical triple system, i.e., the remnant from the bNS coalescence was able to merge again with the 23 Msun black hole (BH) tertiary. We show that this occurs at a sufficiently high probability provided that the semimajor axis of the outer orbit is less than a few AU at the time of bNS coalescence. It remains to be explored whether the conditions for the formation of such tight triple systems are commonly realized in the Universe, especially in low metallicity (less than 0.1 solar) environments. Our model provides a number of predictions. (1) The spin of the secondary in GW190814-like systems is 0.6 to 0.7. (2) The component mass distribution from a large sample of LIGO sources should have a narrow peak between 2.5 and ~3.5 Msun, whereas the range between ~3.5 and ~5 Msun stays empty (provided that stellar evolution does not generate such BHs in the "mass gap"). (3) About 90% (10%) of GW190814-like events have an eccentricity of e > 2x10^{-3} (> 0.1) near gravitational wave frequency of 10 mHz. (4) A significant fraction (> 10%) of bNS mergers should have signatures of a massive tertiary at a distance of a few AU in the gravitational waveform. (5) There are 10^5 undetected radio-quiet bNS systems with a massive BH tertiary in the Milky Way.
We present a measurement of the intrinsic space density of intermediate redshift ($z\sim0.5$), massive ($M_{*} \sim 10^{11} \ \text{M}_{\odot}$), compact ($R_{e} \sim 100$ pc) starburst ($\Sigma_{SFR} \sim 1000 \ \text{M}_{\odot} \ \text{yr}^{-1} \text{kpc}^{-1}$) galaxies with tidal features indicative of them having undergone recent major mergers. A subset of them host kiloparsec scale, $>1000 \ \text{km}\ \text{s}^{-1}$ outflows and have little indication of AGN activity, suggesting that extreme star formation can be a primary driver of large-scale feedback. The aim for this paper is to calculate their space density so we can place them in a better cosmological context. We do this by empirically modeling the stellar populations of massive, compact starburst galaxies. We determine the average timescale for which galaxies that have recently undergone an extreme nuclear starburst would be targeted and included in our spectroscopically selected sample. We find that massive, compact starburst galaxies targeted by our criteria would be selectable for $\sim 148 ^{+27}_{-24}$ Myr and have an intrinsic space density $n_{\text{CS}} \sim (1.1^{+0.5}_{-0.3}) \times 10^{-6} \ \ \text{Mpc}^{-3}$. This space density is broadly consistent with our $z\sim0.5$ compact starbursts being the most extremely compact and star forming low redshift analogs of the compact star forming galaxies in the early Universe as well as them being the progenitors to a fraction of intermediate redshift post starburst and compact quiescent galaxies.
A distributional equation as a criterion for invariant measures of Markov processes associated to L\'evy-type operators is established. This is obtained via a characterization of infinitesimally invariant measures of the associated generators. Particular focus is put on the one-dimensional case where the distributional equation becomes a Volterra-Fredholm integral equation, and on solutions to L\'evy-driven stochastic differential equations. The results are accompanied by various illustrative examples.
We study in further detail particle models displaying a boundary-induced absorbing state phase transition [Phys. Rev. E. {\bf 65}, 046104 (2002) and Phys. Rev. Lett. {\bf 100}, 165701 (2008)] . These are one-dimensional systems consisting of a single site (the boundary) where creation and annihilation of particles occur and a bulk where particles move diffusively. We study different versions of these models, and confirm that, except for one exactly solvable bosonic variant exhibiting a discontinuous transition and trivial exponents, all the others display non-trivial behavior, with critical exponents differing from their mean-field values, representing a universality class. Finally, the relation of these systems with a $(0+1)$-dimensional non-Markovian process is discussed.
Using photometry from Data Release 10 of the northern footprint of the Sloan Digital Sky Survey, we detect two new stellar streams with lengths of between $25\arcdeg$ and $50\arcdeg$. The streams, which we designate Hermus and Hyllus, are at distances of between 15 and 23 kpc from the Sun and pass primarily through Hercules and Corona Borealis. Stars in the streams appear to be metal poor, with [Fe/H] $\sim -2.3$, though we cannot rule out metallicities as high as [Fe/H] = -1.2. While Hermus passes within $1\arcdeg$ (in projection) of the globular cluster NGC 6229, a roughly one magnitude difference in distance modulus, combined with no signs of connecting with NGC 6229's Roche lobe, argue against any physical association between the two. Though the two streams almost certainly had different progenitors, similarities in preliminary orbit estimates suggest that those progenitors may themselves have been a product of a single accretion event.
The metallic compound FeP belongs to the class of materials that feature a complex noncollinear spin order driven by magnetic frustration. While its double-helix magnetic structure with a period $\lambda_{\text{s}} \approx 5c$, where $c$ is the lattice constant, was previously well determined, the relevant spin-spin interactions that lead to that ground state remain unknown. By performing extensive inelastic neutron scattering measurements, we obtained the spin-excitation spectra in a large part of the momentum-energy space. The spectra show that the magnons are gapped with a gap energy of $\sim$5 meV. Despite the 3D crystal structure, the magnon modes display strongly anisotropic dispersions, revealing a quasi-one-dimensional character of the magnetic interactions in FeP. The physics of the material, however, is not determined by the dominating exchange, which is ferromagnetic. Instead, the weaker two-dimensional antiferromagnetic interactions between the rigid ferromagnetic spin chains drive the magnetic frustration. Using linear spin-wave theory, we were able to construct an effective Heisenberg Hamiltonian with an anisotropy term capable of reproducing the observed spectra. This enabled us to quantify the exchange interactions in FeP and determine the mechanism of its magnetic frustration.
We obtain the reflection matrices for the scattering of elementary magnons from certain open boundaries, corresponding to open strings ending on D7 and D5 branes in $AdS_5\times S^5$. In each case we consider two possible orientations for the vacuum state. We show that symmetry arguments are sufficient to determine the reflection matrices up to at most two unknown functions. The D7 reflection matrices obey the boundary Yang Baxter-Equation. This is automatic for one vacuum orientation, and requires a natural choice of ratio between two unknowns for the other. In contrast, the D5 reflection matrices do not obey the boundary Yang Baxter-Equation. In both cases we show consistency with the existent weak and strong coupling results.
We present a result of X-ray supernovae (SNe) survey using the Swift satellite public archive. An automatic searching program was designed to search X-ray SNe among all of the Swift archival observations between November 2004 and February 2011. Using the C++ program, 24 X-ray detectable supernovae have been found in the archive and 3 of them were newly-discovered in X-rays which are SN 1986L, SN 2003lx, and SN 2007od. In addition, SN 2003lx is a Type Ia supernova which may be the second X-ray detectable Type Ia after SN 2005ke (Immler et al. 2006). Calibrated data of luminous type Ib/c supernovae was consistent to the X-ray emission model done by Chevalier & Fransson (1994). Statistics about the luminosities and hardness ratio have been done to purpose of getting the X-ray emission features of the X-ray supernovae. The results from this work help investigating the X-ray evolution of SNe and developing similar X-ray SNe surveys in various X-rays missions.
Using a superfield generalization of the tadpole method, we study the one-loop effective potential for a Wess Zumino model modified by a higher-derivative term, inspired by the Lee-Wick model. The one-loop K\"{a}hlerian potential is also obtained by other methods and compared with the effective potential.
With the release of Gaia DR2, it is now possible to measure the proper motions (PMs) of the lowest mass, ultra-faint satellite galaxies in the Milky Way's (MW) halo for the first time. Many of these faint satellites are posited to have been accreted as satellites of the Magellanic Clouds (MCs). Using their 6-dimensional phase space information, we calculate the orbital histories of 13 ultra-faint satellites and five classical dwarf spheroidals in a combined MW+LMC+SMC potential to determine which galaxies are dynamically associated with the MCs. These 18 galaxies are separated into four classes: i.) long-term Magellanic satellites that have been bound to the MCs for at least the last two consecutive orbits around the MCs (Carina 2, Carina 3, Horologium 1, Hydrus 1); ii.) Magellanic satellites that were recently captured by the MCs $<$ 1 Gyr ago (Reticulum 2, Phoenix 2); iii.) MW satellites that have interacted with the MCs (Sculptor 1, Tucana 3, Segue 1); and iv.) MW satellites (Aquarius 2, Canes Venatici 2, Crater 2, Draco 1, Draco 2, Hydra 2, Carina, Fornax, Ursa Minor). Results are reported for a range of MW and LMC masses. Contrary to previous work, we find no dynamical association between Carina, Fornax, and the MCs. Finally, we determine that the addition of the SMC's gravitational potential affects the longevity of satellites as members of the Magellanic system (long-term versus recently captured), but it does not change the total number of Magellanic satellites.
In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin's measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which it is possible to fully determine the state of a system via specific sets of 'two-slit' experiments.
We construct the (bosonic) effective worldvolume action of an M-theory Kaluza-Klein monopole in a background given by the bosonic sector of eleven-dimensional massive supergravity, i.e. a "massive Kaluza-Klein monopole". As a consistency check we show that the direct dimensional reduction along the isometry direction of the Taub-NUT space leads to the massive D-6-brane. We furthermore perform a double dimensional reduction in the massless case and obtain the effective worldvolume action of a type IIA Kaluza-Klein monopole.
We analyze free elementary particles with rest mass $m$ and total energy $E < m c^2$ in the Rindler wedge, outside Reissner-Nordstrom black holes and in the spacetime of relativistic (and non-relativistic) stars, and use Unruh-DeWitt-like detectors to calculate the associated particle detection rate in each case. The (mean) particle position is identified with the spatial average of the excitation probability of the detectors, which are supposed to cover the whole space. Our results are shown to be in harmony with General Relativity classical predictions. Eventually we reconcile our conclusions with Earth-based experiments which are in good agreement with $E \geq m c^2$.
The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V, where V is a fourteen-dimensional representation of S_8, by an ideal I_8, so the modular fivefold (P^1)^8 // GL(2) is Proj(Sym* (V)/I_8). We show that there is a unique cubic hypersurface S in PV whose equation s is skew-invariant, and that the singular locus of S is the modular fivefold. In particular, over Z[1/3], the modular fivefold is cut out by the 14 partial derivatives of s. Better: these equations generate I_8. In characteristic 3, the cubic s is needed to generate the ideal. The existence of such a cubic was predicted by Dolgachev. Over Q, we recover the 14 quadrics found by computer calculation by Koike, and our approach yields a conceptual representation-theoretic description of the presentation. Additionally we find the graded Betti numbers of a minimal free resolution in any characteristic.   The proof over Q is by pure thought, using Lie theory and commutative algebra. Over Z, the assistance of a computer was necessary. This result will be used as the base case describing the equations of the moduli space of an arbitrary number of points on P^1, with arbitrary weighting, in a later paper, completing the program of our previous paper (Duke Math. J.). The modular fivefold, and corresponding ring, are known to have a number of special incarnations, due to Deligne-Mostow, Kondo, and Freitag-Salvati Manni, for example as ball quotients or ring of modular forms respectively.
We present an alternative to the well-known Anderson's formula for the probability that a first exit time from the planar region between two slopping lines -a_1 t -b_1 and a_2 t + b_2 by a standard Brownian motion is greater than T. As the Anderson's formula, our representation is an infinite series from special functions. We show that convergence rate of both formulas depends only on terms (a_1 + a_2)(b_1 + b_2) and (b_1 + b_2)^2 /T and deduce simple rules of appropriate representation's choose. We prove that for any given set of parameters a_1, b_1, a_2, b_2, T the sum of first 6 terms ensures precision 10^{-16}.
A common assumption in open quantum systems in general is that the noise induced by the environment, due to the continuous interaction between a quantum system and its environment, is responsible for the disappearance of quantum properties of this quantum system. Interestingly, we show that an environment can be engineered and controlled to direct an arbitrary quantum system towards a maximally entangled state and thus can be considered as a resource for quantum information processing. Barreiro et.al. [Nature 470, 486 (2011)] demonstrated this idea experimentally using an open-system quantum simulator up to five trapped ions . In this paper, we direct an arbitrary initial mixed state of two and four qubits, which is interacting with its environment, into a maximally entangled state . We use QASM simulator and also an IBM Q real processor, with and without errors mitigating, to investigate the effect of the noise on the preparation of the initial mixed state of the qubits in addition to the population of the target state.
This paper proves a new general K-network constrained energy reliability global factorization theorem. As in the unconstrained case, beside its theoretical mathematical importance the theorem shows how to do parallel processing in exact network constrained energy reliability calculations in order to reduce the processing time of this NP-hard problem. Followed by a new simple factorization formula for its calculation, we propose a new definition of constrained energy network reliability motivated by the factorization theorem and the accomplishment of parallel processing, something impossible with the original definition.
We study quantum spin systems described by Heisenberg-like models at finite temperature with a strict site-occupation constraint imposed by a procedure originally proposed by V. N. Popov and S. A. Fedotov \cite{Popov-88}. We show that the strict site-occupation constraint modifies quantitatively the behaviour of physical quantities when compared to the case for which this constraint is fixed in the average by means of a Lagrange multiplier method. The relevance of the N\'eel state with the strict site-occupation contraint of the spin lattice is studied. With an exact site-occupation the transition temperature of the antiferromagnetic N\'eel and spin liquid order parameters are twice as large as the critical temperature one gets with an average Lagrange multiplier method. We consider also a mapping of the low-energy spin Hamiltonian into a $QED_3$ Lagrangian of spinons. In this framework we compare the dynamically generated mass to the one obtained by means of an average site-occupation constraint.
In this paper, we will continue to estmate g_1(n|m) for general n and m.
The isospin dependence of the spin-orbit potential is investigated for an effective Skyrme-like energy functional suitable for density dependent Hartree-Fock calculations. The magnitude of the isospin dependence is obtained from a fit to experimental data on finite spherical nuclei. It is found to be close to that of relativistic Hartree models. Consequently, the anomalous kink in the isotope shifts of Pb nuclei is well reproduced.