ShantanuT01/DACTYL-Pretraining huggingface dataset:
The conjecture of Lehmer is proved to be true. The proof mainly relies upon: (i) the properties of the Parry Upper functions $f_{house(\alpha)}(z)$ associated with the dynamical zeta functions $\zeta_{house(\alpha)}(z)$ of the R\'enyi--Parry arithmetical dynamical systems, for $\alpha$ an algebraic integer $\alpha$ of house "$house(\alpha)$" greater than 1, (ii) the discovery of lenticuli of poles of $\zeta_{house(\alpha)}(z)$ which uniformly equidistribute at the limit on a limit "lenticular" arc of the unit circle, when $house(\alpha)$ tends to $1^+$, giving rise to a continuous lenticular minorant ${\rm M}_{r}(house(\alpha))$ of the Mahler measure ${\rm M}(\alpha)$, (iii) the Poincar\'e asymptotic expansions of these poles and of this minorant ${\rm M}_{r}(house(\alpha))$ as a function of the dynamical degree. With the same arguments the conjecture of Schinzel-Zassenhaus is proved to be true. An inequality improving those of Dobrowolski and Voutier ones is obtained. The set of Salem numbers is shown to be bounded from below by the Perron number $\theta_{31}^{-1} = 1.08545\ldots$, dominant root of the trinomial $-1 - z^{30} + z^{31}$. Whether Lehmer's number is the smallest Salem number remains open. A lower bound for the Weil height of nonzero totally real algebraic numbers, $\neq \pm 1$, is obtained (Bogomolov property). For sequences of algebraic integers of Mahler measure smaller than the smallest Pisot number, whose houses have a dynamical degree tending to infinity, the Galois orbit measures of conjugates are proved to converge towards the Haar measure on $|z|=1$ (limit equidistribution).
Constraints on the clustered mass density \Omega_m of the universe derived from the mean intracluster gas fraction of X-ray clusters may be biased by a single-phase assumption for the thermodynamic structure of the intracluster medium (ICM). We propose a descriptive model for multiphase structure in which a spherically symmetric ICM contains isobaric density perturbations with radially dependent variance \sigma^2(r)=\sigma_c^2 (1+r^2/r_c^2)^{-\eps}. The model extends the work of Gunn & Thomas (1996) which assumed radially independent density fluctuations thoughout the ICM. Fixing the X-ray emission profile and emission weighted temperature, we explore two independently observable signatures of the model in the {\sigma_c,\eps} space. For bremsstrahlung dominated emission, the central Sunyaev--Zeldovich (SZ) decrement in the multiphase case is increased over the single-phase case and multiphase X-ray spectra in the range 0.1-20 keV are flatter in the continuum and exhibit stronger low energy emission lines than their single-phase counterpart. We quantify these effects for a fiducial 10^8 K cluster and demonstrate how the combination of SZ and X-ray spectroscopy can be used to identify a preferred location in the {\sigma_c,\eps} plane. From these parameters, the correct value of mean ICM gas fraction in the multiphase model results, allowing an unbiased estimate of \Omega_m to be recovered. The consistency of recent determinations of the Hubble constant from SZ and X-ray observations with values determined by other methods suggests that biases in ICM gas fractions are small, \ltsim 20%.
We present a detailed description of the first direct measurement of the spatial correlation function of X-ray selected AGN. This result is based on an X-ray flux-limited sample of 219 AGN discovered in the contiguous 80.7 deg^2 region of the ROSAT North Ecliptic Pole (NEP) Survey. Clustering is detected at the 4 sigma level at comoving scales in the interval r = 5-60 h^-1 Mpc. Fitting the data with a power law of slope gamma=1.8, we find a correlation length of r_0 = 7.4 (+1.8, -1.9) h^-1 Mpc (Omega_M=0.3, Omega_Lambda=0.7). The median redshift of the AGN contributing to the signal is z_xi=0.22. This clustering amplitude implies that X-ray selected AGN are spatially distributed in a manner similar to that of optically selected AGN. Furthermore, the ROSAT NEP determination establishes the local behavior of AGN clustering, a regime which is poorly sampled in general. Combined with high-redshift measures from optical studies, the ROSAT NEP results argue that the AGN correlation strength essentially does not evolve with redshift, at least out to z~2.2. In the local Universe, X-ray selected AGN appear to be unbiased relative to galaxies and the inferred X-ray bias parameter is near unity, b_X~1. Hence X-ray selected AGN closely trace the underlying mass distribution. The ROSAT NEP AGN catalog, presented here, features complete optical identifications and spectroscopic redshifts. The median redshift, X-ray flux, and X-ray luminosity are z=0.41, f_X=1.1*10^-13 cgs, and L_X=9.2*10^43 h_70^-2 cgs (0.5-2.0 keV), respectively. Unobscured, type 1 AGN are the dominant constituents (90%) of this soft X-ray selected sample of AGN.
The temporal heating and subsequent cooling of the crusts of transiently accreting neutron stars carries unique information about their structure and a variety of nuclear reaction processes. We report on a new Chandra Director's Discretionary Time observation of the globular cluster Terzan 5, aimed to monitor the transiently accreting 11-Hz X-ray pulsar IGR J17480-2446 after the cessation of its recent 10-week long accretion outburst. During the observation, which was performed ~125 days into quiescence, the source displays a thermal spectrum that fits to a neutron star atmosphere model with a temperature for an observer at infinity of kT~92 eV. This is ~10% lower than found ~75 days earlier, yet ~20% higher than the quiescent base level measured prior to the recent outburst. This can be interpreted as cooling of the accretion-heated neutron star crust, and implies that crust cooling is observable after short accretion episodes. Comparison with neutron star thermal evolution simulations indicates that substantial heat must be released at shallow depth inside the neutron star, which is not accounted for in current nuclear heating models.
We investigate the decay of entanglement of generalized N-particle Greenberger-Horne-Zeilinger (GHZ) states interacting with independent reservoirs. Scaling laws for the decay of entanglement and for its finite-time extinction (sudden death) are derived for different types of reservoirs. The latter is found to increase with the number of particles. However, entanglement becomes arbitrarily small, and therefore useless as a resource, much before it completely disappears, around a time which is inversely proportional to the number of particles. We also show that the decay of multi-particle GHZ states can generate bound entangled states.
The graviton soft wall model (GSW) provides a unified description of the scalar glueball and meson spectra with a unique energy scale. This success has led us to extend the analysis to the description of the spectra of other hadrons. We use this model to calculate masses of the odd and even ground states of glueballs for various spins, and show that the GSW model is able to reproduce the Regge trajectory of these systems. In addition, the spectra of the $\rho$, $a_1$ and the $\eta$ mesons will be addressed. Results are in excellent agreement with current experimental data.Furthermore such an achievement is obtained without any additional parameters. Indeed, the only two parameters appearing in these spectra are those that were previously fixed by the light scalar meson and glueball spectra. Finally, in order to describe the $\pi$ meson spectrum, a suitable modification of the dilaton profile function has been included in the analysis to properly take into account the Goldstone realization of chiral symmetry. The present investigation confirms that the GSW model provides an excellent description of the spectra of mesons and glueballs with only a small number of parameters unveiling a relevant predicting power.
In this paper we offer some new identities associated with mock theta functions and establish new Bailey pairs related to indefinite quadratic forms. We believe our proof is instructive use of changing base of Bailey pairs, and offers new information on some Bailey pairs that have proven important in the study of Mock theta functions.
We present a scotogenic model, i.e. a one-loop neutrino mass model with dark right-handed neutrino gauge singlets and one inert dark scalar gauge doublet $\eta$, which has symmetries that lead to co-bimaximal mixing, i.e. to an atmospheric mixing angle $\theta_{23} = 45^\circ$ and to a $CP$-violating phase $\delta = \pm \pi/2$, while the mixing angle $\theta_{13}$ remains arbitrary. The symmetries consist of softly broken lepton numbers $L_\alpha$ ($\alpha = e,\mu,\tau$), a non-standard $CP$ symmetry, and three $Z_2$ symmetries. We indicate two possibilities for extending the model to the quark sector. Since the model has, besides $\eta$, three scalar gauge doublets, we perform a thorough discussion of its scalar sector. We demonstrate that it can accommodate a Standard Model-like scalar with mass $125\, \mathrm{GeV}$, with all the other charged and neutral scalars having much higher masses.
We present a quasiparticle interference study of clean and Mn surface-doped TaAs, a prototypical Weyl semimetal, to test the screening properties as well as the stability of Fermi arcs against Coulomb and magnetic scattering. Contrary to topological insulators, the impurities are effectively screened in Weyl semimetals. The adatoms significantly enhance the strength of the signal such that theoretical predictions on the potential impact of Fermi arcs can be unambiguously scrutinized. Our analysis reveals the existence of three extremely short, previously unknown scattering vectors. Comparison with theory traces them back to scattering events between large parallel segments of spin-split trivial states, strongly limiting their coherence. In sharp contrast to previous work [R. Batabyal et al., Sci. Adv. 2, e1600709 (2016)], where similar but weaker subtle modulations were interpreted as evidence of quasiparticle interference originating from Femi arcs, we can safely exclude this being the case. Overall, our results indicate that intra- as well as inter-Fermi arc scattering are strongly suppressed and may explain why-in spite of their complex multiband structure-transport measurements show signatures of topological states in Weyl monopnictides.
We study the crossover from low- to high-temperature fluctuations including critical fluctuations in confined isotropic O$(n)$-symmetric systems on the basis of a finite-size renormalization-group approach at fixed dimension $d$ introduced previously [V. Dohm, Phys. Rev. Lett. {\bf 110}, 107207 (2013)]. Our theory is formulated within the $\varphi^4$ lattice model in a $d$-dimensional block geometry with periodic boundary conditions. We derive the finite-size scaling functions $F^{\text ex}$ and $X$ of the excess free energy density and of the thermodynamic Casimir force, respectively, for $1\leq n \leq \infty$, $2<d<4$. Applications are given for $ L_\parallel^{d-1} \times L$ slab geometries with a finite aspect ratio $\rho=L/L_\parallel$ as well as for the film limit $\rho \to 0$ at fixed $L$. For $n=1$ and $\rho=0$ the low-temperature limits of $F^{\text ex}$ and $X$ vanish whereas they are finite for $n\geq 2$ and $\rho = 0$ due to the effect of the Goldstone modes. For $n=1$ and $\rho>0$ we find a finite low-temperature limit of $F^{\text ex}$ which deviates from that of the the Ising model. We attribute this deviation to the nonuniversal difference between the $\varphi^4$ model with continuous variables $\varphi$ and the Ising model with discrete spin variables $s=\pm1$. For $n\geq 2$ and $\rho>0$, a logarithmic divergence of $F^{\text ex}$ in the low-temperature limit is predicted, in excellent agreement with Monte Carlo (MC) data for the $d=3$ $XY$ model. For $2\leq n \leq \infty$ and $0\leq \rho<\rho_0=0.8567$ the Goldstone modes generate a negative (attractive) low-temperature Casimir force that vanishes for $\rho = \rho_0$ and becomes positive (repulsive) for $\rho > \rho_0$. Our predictions are compared with MC data for Ising, $XY$, and Heisenberg models in slab geometries with $0.01\leq\rho\leq1$. Good overall agreement is found.
Motivated by the spin current problem in chiral helimagnet, we rigorously elucidated the hidden Galilean invariance in the chiral XY model under the magnetic field. The Lie group analysis is applied to the differential equations of the continuum theory of the chiral helimagnet with the parity-violating Dzyaloshinskii-Morya coupling under a transversal magnetic field. Lie point symmetries and the invariant solutions under these symmetries are found. They present sliding solutions that come up as a consequence of breaking of both spin rotational symmetry by the external magnetic field and a parity violation due to the Dzyaloshinskii-Morya interaction. We found that variational symmetries are related with translations in space and time, the corresponding energy and momentum conservation laws are derived. We therefore succeeded in justifying the existence of the transport spin current in chiral helimagnet.
This article introduces the Stochastic Texture Difference method for analyzing data at prescribed spatial and value scales. This method relies on constrained random walks around each pixel, describing how nearby image values typically evolve on each side of this pixel. Textures are represented as probability distributions of such random walks, so a texture difference operator is statistically defined as a distance between these distributions in a suitable reproducing kernel Hilbert space. The method is thus not limited to scalar pixel values: any data type for which a kernel is available may be considered, from color triplets and multispectral vector data to strings, graphs, and more. By adjusting the size of the neighborhoods that are compared, the method is implicitly scale-dependent. It is also able to focus on either small changes or large gradients. We demonstrate how it can be used to infer spatial and data value characteristic scales in measured signals and natural images.
Several clusters of red supergiants have been discovered in a small region of the Milky Way close to the base of the Scutum-Crux Arm and the tip of the Long Bar. Population synthesis models indicate that they must be very massive to harbour so many supergiants. Among them, Stephenson 2, with a core grouping of 26 RSGs, is a strong candidate to be the most massive cluster in the Galaxy. It is located close to a region where a strong over-density of RSGs had been found. We explore the actual cluster size and its possible connection to this over-density. We have performed a cross-match between DENIS, USNO-B1 and 2MASS to identify candidate obscured luminous red stars around Ste 2, and in a control nearby region, finding >600 candidates. More than 400 are sufficiently bright in I to allow observation with a 4-m class telescope. We have observed a subsample of ~250 stars, using AF2 on the WHT telescope in La Palma, obtaining intermediate-resolution spectroscopy in the 7500--9000A range. We derive spectral types and luminosity classes for all these objects and measure their radial velocities. Our targets are G and K supergiants, late (>=M4) M giants, and M-type bright giants (luminosity class II) and supergiants. We find ~35 RSGs with radial velocities similar to Ste 2 members, spread over the two areas surveyed. In addition, we find ~40 RSGs with radial velocities incompatible in principle with a physical association. Our results show that Ste 2 is not an isolated cluster, but part of a huge structure likely containing hundreds of RSGs, with radial velocities compatible with the terminal velocity at this Galactic longitude (and a distance ~6kpc). In addition, we find evidence of several populations of massive stars at different distances along this line of sight [ABRIDGED].
Using nanoprobe X-ray diffraction microscopy, we investigate the relationship between residual strains from crystal growth in CsPbBr$_3$ thin film crystals, their stability, and local bandgap. We find that out-of-plane compressive strain that arises from cooldown from crystallization is detrimental to material stability under X-ray irradiation. We also find that the optical photoluminescence red shifts as a result of the out-of-plane compressive strain. The sensitivity of bandgap to strain suggests possible applications such as stress-sensitive sensors. Mosaicity, the formation of small misorientations in neighboring crystalline domains we observe in some CsPbBr$_3$ single crystals, indicates the significant variations in crystal quality that can occur even in single-crystal halide perovskites. The nano-diffraction results suggest that reducing local strains is a necessary path to enhance the stability of perovskite optoelectronic materials and devices from light-emitting diodes to high-energy detectors.
In this paper, we discuss a two-dimensional numerical study of isothermal high Mach number Bondi--Hoyle--Lyttleton flow around a small accretor. The flow is found to be unstable at high Mach numbers, with the instability appearing even for a larger accretor. The instability appears to be the unstable radial mode of the accretion column predicted by earlier analytic work.
We study the Cauchy problem for the Gross-Pitaevskii equation with a nonlocal interaction potential of Hartree type in three space dimensions. If the potential is even and positive definite or a positive function and its Fourier transform decays sufficiently rapidly the problem is shown to be globally well-posed for large rough data which not necessarily have finite energy and also in a situation where the energy functional is not positive definite. The proof uses a suitable modification of the I-method.
Novel filled skutterudites EpyNi4Sb12-xSnx (Ep = Ba and La) have been prepared by arc melting followed by annealing at 250C, 350C and 450C up to 30 days in sealed quartz vials. A maximum filling level of y = 0.93 and y = 0.65 was achieved for the Ba and La filled skutterudite, respectively. Single-phase samples with the composition Ni4Sb8.2Sn3.8, Ba0.42Ni4Sb8.2Sn3.8 and Ba0.92Ni4Sb6.7Sn5.3 were employed for measurements of the physical properties i.e. temperature dependent electrical resistivity, Seebeck coefficient and thermal conductivity.   Resistivity data showed a crossover from metallic to semiconducting behaviour. The corresponding gap width was extracted from maxima in the Seebeck coefficient data as a function of temperature. Temperature dependent single crystal X-ray structure analyses (at 100 K, 200 K and 300 K) revealed the thermal expansion coefficients, Einstein and Debye temperatures for two selected samples Ba0.73Ni4Sb8.1Sn3.9 and Ba0.95Ni4Sb6.1Sn5.9. These data compare well with Debye temperatures from measurements of specific heat (4.4 K < T < 200 K).   Several mechanical properties were measured and evaluated. Thermal expansion coefficients are 11.8.10-6 K-1 for Ni4Sb8.2Sn3.8 to 13.8.10-6 K-1 for Ba0.92Ni4Sb6.7Sn5.3. Room temperature Vicker's hardness values (up to a load of 24.5 mN) vary within the range of 2.6 GPa to 4.7 GPa. Severe plastic deformation (SPD) via high-pressure torsion (HPT) was used to introduce nanostructuring. Physical properties before and after HPT were compared, showing no significant effect on the material's thermoelectric behaviour.
Charge carriers in the quantum Hall regime propagate via one-dimensional conducting channels that form along the edges of a two-dimensional electron gas. Controlling their transmission through a gate-tunable constriction, also called quantum point contact (QPC), is fundamental for many coherent transport experiments. However, in graphene, tailoring a QPC with electrostatic gates remains challenging due to the formation of p-n junctions below gate electrodes along which electron and hole edge channels co-propagate and mix, short-circuiting the constriction. Here we show that this electron-hole mixing is drastically reduced in high mobility boron-nitride/graphene/boron-nitride van-der-Waals heterostructures thanks to the full degeneracy lifting of the Landau levels, enabling QPC operation with full channel pinch-off. We demonstrate gate-tunable selective transmission of quantum Hall edge channels through the QPC, both in the integer and the fractional quantum Hall regimes. This gate-control of edge channel propagation in graphene van-der-Waals heterostructures opens the door to quantum Hall interferometry and electron quantum optics experiments in the integer and fractional quantum Hall regimes of graphene.
In this work we consider the identifiability of two coefficients $a(u)$ and $c(x)$ in a quasilinear elliptic partial differential equation from observation of the Dirichlet-to-Neumann map. We use a linearization procedure due to Isakov [On uniqueness in inverse problems for semilinear parabolic equations. Archive for Rational Mechanics and Analysis, 1993] and special singular solutions to first determine $a(0)$ and $c(x)$ for $x \in \Omega$. Based on this partial result, we are then able to determine $a(u)$ for $u \in \mathbb{R}$ by an adjoint approach.
Neural field equations are used to describe the spatiotemporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under the assumption that each population in the network is large, the activity is described in terms of a population average. The discrete network is then approximated by a continuum. In this article we make the two approximation steps explicit. Extending a model by Bressloff and Newby, we describe the evolution of the activity in a discrete network of finite populations by a Markov chain. In order to determine finite-size effects - deviations from the mean field limit due to the finite size of the populations in the network - we analyze the fluctuations of this Markov chain and set up an approximating system of diffusion processes. We show that a well-posed stochastic neural field equation with a noise term accounting for finite-size effects on traveling wave solutions is obtained as the strong continuum limit.
A strongly coupled plasma of quark and gluon quasiparticles at temperatures from $ 1.1 T_c$ to $3 T_c$ is studied by path integral Monte Carlo simulations. This method extends previous classical nonrelativistic simulations based on a color Coulomb interaction to the quantum regime. We present the equation of state and find good agreement with lattice results. Further, pair distribution functions and color correlation functions are computed indicating strong correlations and liquid-like behavior.
Hadwiger integrals employ the intrinsic volumes as measures for integration of real-valued functions. We provide a formula for the expected values of Hadwiger integrals of Gaussian-related random fields. The expected Hadwiger integrals of random fields are both theoretically interesting and potentially useful in applications such as sensor networks, image processing, and cell dynamics. Furthermore, combining the expected integrals with a functional version of Hadwiger's theorem, we obtain expected values of more general valuations on Gaussian-related random fields.
We investigate the adsorption of cobalt phthalocyanine (CoPc) molecules on a thin layer of cobalt oxide grown on Ir(100). To that end we compare the results of low-temperature scanning tunneling microscopy (STM) with those of ab-initio density functional theory (DFT) calculations and reveal the adsorption geometry. We find that the CoPc molecules lie flat on the surface and that their central cobalt atom forms a chemical bond to a substrate oxygen ion. However, this bond contributes only modestly to the adsorption energy, while van-der-Waals forces dominate the potential landscape and determine to a large extend the geometry as well as the distortion of substrate and molecule. Furthermore they lead to attractive molecule-molecule interactions at higher molecular coverages. The DFT calculations predict energetic positions of the molecular orbitals which are compared to scanning tunneling spectroscopy (STS) measurements.