ShantanuT01/DACTYL-Pretraining huggingface dataset:
Quantum entanglement is considered, by and large, to be a very delicate and non-robust phenomenon that is very hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated, in part, by a quest for a quantum analog of the PCP theorem researches have tried to establish whether or not we can preserve quantum entanglement at "constant" temperatures that are independent of system size. This would imply that any quantum state with energy at most, say 0.05 of the total available energy of the Hamiltonian, would be highly-entangled. To this date, no such systems were found, and moreover, it became evident that even embedding local Hamiltonians on robust, albeit "non-physical" topologies, namely expanders, does not guarantee entanglement robustness. In this study, we indicate that such robustness may be possible after all: We construct an infinite family of O(1)-local Hamiltonians, corresponding to check terms of a quantum error-correcting code with the following property of inapproximability: any quantum state with energy at most 0.05 w.r.t. the total available energy cannot be even approximately simulated by classical circuits of bounded (sub-logarithmic) depth. In a sense, this implies that even providing a "witness" to the fact that the local Hamiltonian can be "almost" satisfied, already requires some measure of long-range entanglement. Our construction is but a first step in what, we believe, is a whole range of possible entanglement - robust local Hamiltonians. A natural next step, we believe, is to devise such local Hamiltonians that resist approximation in terms of bounded-depth quantum circuits (e.g. NLTS), and even find such robust forms of entanglement that are useful for some computation.
We consider tachyonic braneworld with a bulk cosmological constant and investigate a configurational entropy of various magnitudes of scale factor. It is found that for a bulk negative/zero cosmological constant, the configurational entropy has a global minimum when the magnitude of scale factor reaches the critical value. This result seems to have intriguing implications such that an accelerated rate of the universe and cosmological inflation rate for radiation/matter domination are able to be determined by such critical value. We also find that the configurational entropy almost monotonically decreases for a bulk positive cosmological constant as the magnitude of scale factor grows up. We find an exact solution of tachyonic braneworld in a bulk de Sitter space. It is shown that such system under scalar perturbations is stable for some constraint relation. Furthermore, we also find that tachyonic braneworld model with a bulk negative/zero cosmological constant is always stable under scalar perturbations.
Direct determination of fundamental stellar parameters has many profound and wide-ranging impacts throughout astrophysics. These determinations are rooted in high angular resolution observations. In particular, as long-baseline optical interferometry has matured over the past decade, increasingly large survey samples are serving to empirically ground the basic parameters of these building blocks of the universe. True imaging and improved parametric fitting are becoming routinely available, an essential component of fully characterizing stars, stellar environments, and planets these stars may host.
The electronic structure of bulk fcc GaAs, fcc and tetragonal CrAs, and CrAs/GaAs supercells, computed within LMTO local spin-density functional theory, is used to extract the band alignment (band offset) for the [1,0,0] GaAs/CrAs interface in dependence of the spin orientation. With the lateral lattice constant fixed to the experimental bulk GaAs value, a local energy minimum is found for a tetragonal CrAs unit cell with a slightly ($\approx$ 2%) reduced longitudinal ([1,0,0]) lattice constant. Due to the identified spin-dependent band alignment, half-metallicity of CrAs no longer is a key requirement for spin-filtering. Encouraged by these findings, we study the spin-dependent tunneling current in [1,0,0] GaAs/CrAs/GaAs heterostructures within the non-equilibrium Green's function approach for an effective tight-binding Hamiltonian derived from the LMTO electronic structure. Results indicate that these heterostructures are probable candidates for efficient room-temperature all-semiconductor spin-filtering devices.
We have observed a sample of Seyfert (Sy) galaxies with the global Very Long Baseline Interferometry (VLBI) to test the predictions of the unification scheme for the Sy galaxies which hypothesises that Sys of Type 1 and of Type 2 constitute a single population of objects. If Sy 1 and Sy 2 galaxies differ only in the orientation of the axisymmmetric active nucleus with respect to the observer, then, the parsec scale radio structures of the two types should be similar.   The overall goal of the thesis is to rigorously test the predictions of the unified scheme hypothesis for the Sy galaxies.   We chose a sample of 10 Sy 1s and 10 Sy 2s such that the two subsamples were intrinsically similar within the framework of the unified scheme. This was done by matching them as far as possible in the orientation-independent parameters {\it viz.}, host galaxy properties and measures of intrinsic Active Galactic Nuclei (AGN) power.   We here present the results obtained from these observations and their implications on the unification scheme. We also discuss the results obtained from the measurements at all IRAS and 2-10 keV X-ray wavebands for our Sy galaxy sample using data from the literature.
In graph theory, knowing the number of complete subgraphs with r vertices that a graph g has, limits the number of its complete subgraphs with s vertices, for s > r. A useful upper bound is provided by the Kruskal-Katona theorem, but this bound is often not tight. In this note, we add to the known cases where this bound is tight and begin an investigation of tight bounded graph sequences.
We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problems are suggested.
Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded coefficients) on sets of integers having a positive upper density.
We propose a source of multimode squeezed light that can be used for the superresolving microscopy beyond the standard quantum limit. This source is an optical parametric amplifier with a properly chosen diaphragm on its output and a Fourier lens. We demonstrate that such an arrangement produces squeezed prolate spheroidal waves which are the eigen modes of the optical imaging scheme used in microscopy. The degree of squeezing and the number of spatial modes in illuminating light, necessary for the effective object field reconstruction, are evaluated
Let X be an abelian variety of dimension g. In a recent preprint O'Grady defines modified diagonal classes \Gamma^m on X^m and he conjectures that the class of \Gamma^m in the Chow ring of X^m is torsion for m \geq 2g+1. We prove a generalization of this conjecture.
This report concerns the energy of a zero-temperature many-body system of spin 1/2 fermions in the unitary limit. In a previous report (arXiv:0705.0944) this energy was determined to be xi~0.24 in units of the free gas kinetic energy, appreciably lower than most reports giving ~0.45$. In our calculation the 2-body interaction satisfied exactly the unitary limit i.e. infinite scattering length and effective range r_0=0. In the present report results with r_0>0are shown. A strong dependence on the effective range is found. It is for example found that an increase to r_0=1 fm increases xi to ~ 0.4 close to other reports of xi in the unitary limit. It is concluded that because of the singular character of the unitary limit it is necessary to verify that the interaction actually satisfies unitarity.   The calculations done here in a pp-ladder approximation show a resonance in the in-medium interaction close to (and in) the unitary limit. This was already found in the previous work.
Let $\Phi $ be a Drinfeld $\mathbf{F}\_{q}[T]$-module of rank 2, over a finite field $L=\mathbf{F}\_{q^{n}}$. We will study the cyclic property of the structure $L^{\Phi}.$ We will prove that the latter is cyclic only for trivial extensions of $\mathbf{F}\_{q}$.
In this paper we study the Cauchy problem for one multidimensional compressible nonlocal model of the dissipative quasi-geostrophic equations. First, we obtain the local existence and uniqueness of the smooth non-negative solution or the strong solution in time. Secondly, for the sub-critical and critical case $1\le\alpha\leq 2$, we obtain the global existence and uniqueness results of the nonnegative smooth solution. Then, we prove the global existence of the weak solution for $0\le \alpha\le 2$ and $\nu\ge 0$. Finally, for the sub-critical case, we establish the global $H^1$ and $L^p, p>2,$ decay rate of the smooth solution as $t\to\infty$.
We mapped the filamentary infrared dark cloud (IRDC) G304.74+01.32 at 350 $\mu$m with the SABOCA bolometer. The new SABOCA data have a factor of 2.2 times higher resolution than our previous LABOCA 870 $\mu$m map of the cloud. We also employed the Herschel far-IR and submillimetre, and WISE IR data available for G304.74. The SABOCA data show that G304.74 is composed of a dense filamentary structure with a mean width of only $0.18\pm0.05$ pc. The percentage of LABOCA clumps that are found to be fragmented into SABOCA cores is $36\%\pm16\%$. The WISE data suggest that $65\%\pm18\%$ of the SABOCA cores host young stellar objects (YSOs). The mean dust temperature of the clumps, derived by comparing the Herschel/SPIRE flux densities, was found to be $15.0 \pm 0.8$ K. The mean mass, beam-averaged H$_2$ column density, and H$_2$ number density of the LABOCA clumps are estimated to be $55\pm10$ M$_{\odot}$, $(2.0\pm0.2)\times10^{22}$ cm$^{-2}$, and $(3.1\pm0.2)\times10^4$ cm$^{-3}$. The corresponding values for the SABOCA cores are $29\pm3$ M$_{\odot}$, $(2.9\pm0.3)\times10^{22}$ cm$^{-2}$, and $(7.9\pm1.2)\times10^4$ cm$^{-3}$. The G304.74 filament is estimated to be thermally supercritical by a factor of $\gtrsim3.5$ on the scale probed by LABOCA, and by a factor of $ \gtrsim1.5$ for the SABOCA filament. Our data strongly suggest that G304.74 has undergone hierarchical fragmentation. The IRDC G304.74 has a seahorse-like morphology in the Herschel images, and the filament appears to be attached by elongated, perpendicular striations. Besides the presence of perpendicularly oriented, dusty striations and potential embedded intermediate-mass YSOs, G304.74 is a relatively nearby ($d\sim2.5$ kpc) IRDC, which makes it a useful target for future star formation studies. Owing to its observed morphology, we propose that G304.74 could be nicknamed the Seahorse Nebula.
We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi-Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi-Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the varieties by the complex multiplication symmetry. The geometric structure that provides a conceptual interpretation of the relation between geometry and the conformal field theory is discrete, and turns out to be given by the torsion points on the abelian varieties.
Topologically stable magnetic skyrmion has a much lower depinning current density that may be useful for memory as well as neuromorphic computing. However, skyrmion-based devices suffer from the Magnus force originating from the skyrmion Hall effect, which may result in unwanted skyrmion annihilation if the magnitude of the driving current gets too large. A design of an artificial neuron and a synapse using a synthetic antiferromagnetically coupled bilayer device, which nullifies the Magnus force, is demonstrated in this work. The leak term in the artificial leaky integrate-and-fire neuron is achieved by engineering the uniaxial anisotropy profile of the neuronal device. The synaptic device has a similar structure as the neuronal device but has a constant uniaxial anisotropy. The synaptic device also has a linear and symmetric weight update, which is a highly desirable trait of an artificial synapse. Neuronal and synaptic devices based on magnetic domain-wall (DW) motion are also studied and compared to skyrmionic devices. Our simulation results show the energy required to perform such operation in DW or skyrmion-based devices is on the order of a few fJ.
We study the fermionic zero modes around 1 instanton operators for 5d supersymmetric gauge theories of type USp, SO and the exceptional groups. The major motivation is to try to understand the global symmetry enhancement pattern in these theories.
Compact object mergers are possible progenitors of short bursts. We analyze properties of compact object mergers using the StarTrack population synthesis code, and find that the double neutron star population is dominated by short lived systems, thus they merge within host galaxies, while black hole neutron star binaries merge outside of the host galaxies. We summarize the differences between these two types of mergers.
The surface morphologies of poly(chloro-p-xylylene) films were measured using atomic force microscopy and analyzed within the frame work of the dynamic scaling theory. The evolution of polymer films grown with fixed experimental parameters showed drastic changes of dynamic roughening behavior, which involve unusually high growth exponent (beta = 0.65+-0.03) in the initial growth regime, followed by a regime characterized by beta~0, and finally a crossover to beta = 0.18+-0.02 in a steady growth regime. Detailed scaling analysis of the surface fluctuation in Fourier space in terms of power spectral density revealed a gradual crossover in the global roughness exponent, analogous to a phase transition between two equilibrium states, from a morphology defined by alpha=1.36+-0.13 to the other morphology characterized by alpha=0.93+-0.04 as the film thickness increases. Our experimental results which significant deviate from the well established descriptions of film growth clearly exhibit that the dynamic roughening of polymer film is deeply affected by strong molecular interactions and relaxations of polymer chains.
We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in formulas for characters of certain representations of the symmetric group. Such formulas have previously been proven algebraically. In this paper, we present a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set on cyclic permutations.
We include the treatment of quadrupolar fields beyond the Fr\"ohlich interaction in the first-principles electron-phonon vertex in semiconductors. Such quadrupolar fields induce long-range interactions that have to be taken into account for accurate physical results. We apply our formalism to Si (nonpolar), GaAs, and GaP (polar) and demonstrate that electron mobilities show large errors if dynamical quadrupoles are not properly treated.
Warm inflation is extended from the canonical field to the noncanonical field with a general Lagrangian density having coupling form of kinetic and potential terms. We develop the motion equation of the noncanonical inflaton field, and notice the motion equation has an annoying coupling term $\mathcal{L}_{X\varphi}\dot\varphi^2$, which makes the inflation difficult to solve. It is found that a special field redefinition exists, making the motion equation of inflaton uncoupled. Then we can solve inflation in the special field representation for convenience. The relation of field redefinition between the special uncoupled field and general noncanonical field is obtained. The motion equations and slow roll approximations of noncanonical warm inflation in the special field representation are developed. Then we give two examples to show how to translate a general noncanonical Lagrangian density in the coupled $\varphi$ representation, to the uncoupled $\phi$ representation. Finally, the cosmological perturbations generated by the new kind of warm inflation is calculated.
There are many kinds of models which describe the dynamics of dark energy (DE). Among all we adopt an equation of state (EoS) which varies as a function of time. We adopt Markov Chain Monte Carlo method to constrain the five parameters of our models. As a consequence, we can show the characteristic behavior of DE during the evolution of the universe. We constrain the EoS of DE with use of the avairable data of gamma-ray bursts and type Ia supernovae (SNe Ia) concerning the redshift-luminosity distance relations. As a result, we find that DE is quintessence-like in the early time and phantom-like in the present epoch or near the future, where the change occurs rather rapidly at $z\sim0.3$.
The main purpose of the note is to exclude the existence of certain submaximal curves in fake projective planes. This will lead to lower bounds on multipoint Seshadri constants of `fake' $\mathcal{O}(1)$ on fake projective planes.
Observations of the FR I radio galaxy Centaurus A in radio, X-ray and gamma-ray bands provide evidence for lepton acceleration up to several TeV and clues about hadron acceleration to tens of EeV. Synthesising the available observational constraints on the physical conditions and particle content in the jets, inner lobes and giant lobes of Centaurus A, we aim to evaluate its feasibility as an ultra-high-energy cosmic-ray source. We apply several methods of determining jet power and affirm the consistency of various power estimates of ~ 1 x 10^43 erg s^-1. Employing scaling relations based on previous results for 3C 31, we estimate particle number densities in the jets, encompassing available radio through X-ray observations. Our model is compatible with the jets ingesting ~ 3 x 10^21 g s^-1 of matter via external entrainment from hot gas and ~ 7 x 10^22 g s^-1 via internal entrainment from jet-contained stars. This leads to an imbalance between the internal lobe pressure available from radiating particles and magnetic field, and our derived external pressure. Based on knowledge of the external environments of other FR I sources, we estimate the thermal pressure in the giant lobes as 1.5 x 10^-12 dyn cm^-2, from which we deduce a lower limit to the temperature of ~ 1.6 x 10^8 K. Using dynamical and buoyancy arguments, we infer ~ 440-645 Myr and ~ 560 Myr as the sound-crossing and buoyancy ages of the giant lobes respectively, inconsistent with their spectral ages. We re-investigate the feasibility of particle acceleration via stochastic processes in the lobes, placing new constraints on the energetics and on turbulent input to the lobes. The same 'very hot' temperatures that allow self-consistency between the entrainment calculations and the missing pressure also allow stochastic UHECR acceleration models to work.
The temperature evolution of structural effects associated with charge (CO) and spin order (SO) in La$_{1.67}$Sr$_{0.33}$NiO$_{4}$ has been investigated using neutron powder diffraction. We report an anomalous shrinking of the $c/a$ lattice parameter ratio that correlates with $T_{\rm CO}$. The sign of this change can be explained by the change in interlayer Coulomb energy between the static stripe-ordered state and the fluctuating stripe-ordered state or the charge-disordered state. In addition, we identify a contribution to the mean-square displacements of Ni and in-plane O atoms whose width correlates quite well with the size of the pseudogap extracted from the reported optical conductivity, with a non-Debye-like component that persists below and well above $T_{\rm CO}$. We infer that dynamic charge-stripe correlations survive to $T\sim2T_{\rm CO}$
Although photometric variations of chemically peculiar (CP) stars are frequently used to determine their rotational periods, the detailed mechanism of their light variability remains poorly understood. We simulate the light variability of the star HR 7224 using the observed surface distribution of silicon and iron. We used the TLUSTY model atmospheres calculated for the appropriate silicon and iron abundances to obtain the emergent flux and to predict the rotationally modulated light curve of the star. We also obtained additional photometric measurements and employed our own regression procedure to derive a more precise estimate of the light elements. We show that the light variation of the star can be explained as a result of i) the uneven surface distribution of the elements, ii) the flux redistribution from the ultraviolet to the visible part of the spectrum, and iii) rotation of the star. We show that the silicon bound-free transitions and iron bound-bound transitions provide the main contribution to the flux redistribution, although an additional source of opacity is needed. We confirm that numerous iron lines significantly contribute to the well-known depression at 5200 A and discuss the connection between iron abundance and the value of peculiarity index a. The uneven surface distribution of silicon and iron is able to explain most of the rotationally modulated light variation in the star HR 7224.
We report the crystal growth of a new compound, Yb3Os4Ge13, by using a Bi-flux method. X-ray diffraction measurement shows that it crystallizes in the quasi-skutterudite-type caged structure with a cubic space group of Pm-3n (No. 223). Magnetic measurements reveal almost fully localized Yb f-moments above 120 K. The resistivity exhibits a crossover from metallic to insulating behavior with a logarithmic increase below ~ 40 K. The specific heat coefficient shows a rapid upturn below ~5 K and exceeds 2 J mol-1 K-2 at 2 K. Our experimental analysis and electronic band structure calculations demonstrate that Yb3Os4Ge13 exhibits the Kondo effect due to strong hybridization of the localized Yb f-moments with the p-electrons of the surrounding Ge-cages.
We report on the discovery of 10 additional galaxy clusters detected in the ongoing Swift/BAT all-sky survey. Among the newly BAT-discovered clusters there are: Bullet, Abell 85, Norma, and PKS 0745-19. Norma is the only cluster, among those presented here, which is resolved by BAT. For all the clusters we perform a detailed spectral analysis using XMM-Newton and Swift/BAT data to investigate the presence of a hard (non-thermal) X-ray excess. We find that in most cases the clusters' emission in the 0.3-200keV band can be explained by a multi-temperature thermal model confirming our previous results. For two clusters (Bullet and Abell 3667) we find evidence for the presence of a hard X-ray excess. In the case of the Bullet cluster, our analysis confirms the presence of a non-thermal, power-law like, component with a 20-100 keV flux of 3.4 \times 10-12 erg cm-2 s-1 as detected in previous studies. For Abell 3667 the excess emission can be successfully modeled as a hot component (kT=~13keV). We thus conclude that the hard X-ray emission from galaxy clusters (except the Bullet) has most likely thermal origin.
We study deformations of pairs (X,D), with X smooth projective variety and D a smooth or a normal crossing divisor, defined over an algebraically closed field of characteristic 0. Using the differential graded Lie algebras theory and the Cartan homotopy construction, we are able to prove in a completely algebraic way the unobstructedness of the deformations of the pair (X,D) in many cases, e.g., whenever (X,D) is a log Calabi-Yau pair, in the case of a smooth divisor D in a Calabi Yau variety X and when D is a smooth divisor in |-m K_X|, for some positive integer m.