ShantanuT01/DACTYL-Pretraining huggingface dataset:
We explore the large to moderate scale anisotropy in distant radio sources using the TGSS ADR1 catalog. We use different measures, i.e. number counts, sky brightness and flux per source, for this study. In agreement with earlier results, we report a significant excess of clustering signal above the angular scale of roughly $10$ degrees (i.e. $l\lessapprox 20-30$). We find that some survey areas have a systematically low/high flux and argue this may be the cause of the observed signal of excess power at low multipoles. With mocks we demonstrate the effect of such large scale flux systematics and recover TGSS like excess clustering signal by assuming $20\%$ flux uncertainties over $\sim 10^\circ \times 10^\circ$ size patches. We argue that that TGSS at this stage, i.e. TGSS ADR1, is not suitable for large scale clustering measurements. We find that the measure, flux per source, shows evidence of isotropy for all multipoles $l > 2$ despite the presence of systematics in the data.
For any positive integers $n$ and $m$, $\mathbb{H}_{n,m}:=\mathbb{H}_n\times\mathbb{C}^{(m,n)}$ is called the Siegel-Jacobi space, with the Jacobi group acting on it. The Jacobi forms are defined on this space. In this article we compute the Chern connection of the Siegel-Jacobi space and use it to obtain derivations of Jacobi forms. Using these results, we constructed a series of invariant differential operators for Siegel-Jacobi forms. Also two kinds of Maass-Shimura type differential operators for $\mathbb{H}_{n,m}$ are obtained.
The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies $\nu$ of the order or higher than the frequency associated with the Kondo effect $k_B T_K/h$, with $T_K$ the Kondo temperature. The carbon nanotube is coupled via an on-chip resonant circuit to a quantum noise detector, a superconductor-insulator-superconductor junction. We find for $h \nu \approx k_B T_K$ a Kondo effect related singularity at a voltage bias $eV \approx h \nu $, and a strong reduction of this singularity for $h \nu \approx 3 k_B T_K$, in good agreement with theory. Our experiment constitutes a new original tool for the investigation of the non-equilibrium dynamics of many-body phenomena in nanoscale devices.
We develop the kinetic theory of Hamiltonian systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a general kinetic equation that can be applied to spatially inhomogeneous systems and that takes into account memory effects. This equation is valid at order 1/N in a proper thermodynamic limit and it coincides with the kinetic equation obtained from the BBGKY hierarchy. For N tending to infinity, it reduces to the Vlasov equation describing collisionless systems. We describe the process of phase mixing and violent relaxation leading to the formation of a quasi stationary state (QSS) on the coarse-grained scale. We interprete the physical nature of the QSS in relation to Lynden-Bell's statistical theory and discuss the problem of incomplete relaxation. In the second part of the paper, we consider the relaxation of a test particle in a thermal bath. We derive a Fokker-Planck equation by directly calculating the diffusion tensor and the friction force from the Klimontovich equation. We give general expressions of these quantities that are valid for possibly spatially inhomogeneous systems with long correlation time. We show that the diffusion and friction terms have a very similar structure given by a sort of generalized Kubo formula. We also obtain non-markovian kinetic equations that can be relevant when the auto-correlation function of the force decreases slowly with time. An interest of our approach is to develop a formalism that remains in physical space (instead of Fourier space) and that can deal with spatially inhomogeneous systems.
Fix a container polygon $P$ in the plane and consider the convex hull $P_n$ of $n\geq 3$ independent and uniformly distributed in $P$ random points. In the focus of this paper is the vertex number of the random polygon $P_n$. The precise variance expansion for the vertex number is determined up to the constant-order term, a result which can be considered as a second-order analogue of the classical expansion for the expectation of R\'enyi and Sulanke (1963). Moreover, a sharp Berry-Esseen bound is derived for the vertex number of the random polygon $P_n$, which is of the same order as the square-root of the variance. The main idea behind the proof of both results is a decomposition of the boundary of the random polygon $P_n$ into random convex chains and a careful merging of the variance expansions and Berry-Esseen bounds for the vertex numbers of the individual chains.
The correlation between black hole mass and the stellar mass of the bulge of the host galaxy has attracted much attention ever since its discovery. While traditional investigations of this correlation have treated elliptical galaxies as single, monolithic spheroids, the recent realization that massive elliptical galaxies have undergone significant late-time ($z \lesssim 2$) dissipationless assembly since their initially dense "red nugget" phase strongly suggests that black holes in present-day ellipticals should be associated only with their cores and not with their extended envelopes. We perform two-dimensional image decomposition of Two Micron All Sky Survey $K_s$-band images to derive the stellar mass of the cores of 35 nearby ellipticals with reliably measured black hole masses. We revisit the relation between black hole mass and bulge stellar mass by combining classical bulges with the cores of ellipticals. The new relation exhibits nearly identical slope ($M_{\bullet} \propto M_{\text{core}}^{1.2}$) as the conventional relation but a factor of $\sim2$ higher normalization and moderately larger intrinsic scatter (0.4 dex). At a core mass of $10^{11}\,M_{\odot}$, $M_{\bullet}/M_{\text{core}} = 0.9\%$, but it rises to $M_{\bullet}/M_{\text{core}}=1.5\%$ for the most massive cores with mass $10^{12}\,M_{\odot}$. Fast and slow rotator ellipticals follow the same correlation. The $M_{\bullet}-M_{\text{core}}$ relation provides a revised benchmark for studies of black hole-galaxy coevolution in the high-redshift Universe.
We study higher-spin ($S \geq 1$) generalization of the one-dimensional Kondo-Heisenberg model, in which the local spin-$S$ moments of the Kondo lattice model interact with each other via the antiferromagnetic Heisenberg interaction ($J_{\text{H}}$), by analytical and numerical methods. The strong-coupling (i.e., large Kondo-coupling) expansion maps out an insulating phase at half-filling whose magnetic correlation depends on the parity of $2S$ as well as a ferromagnetic metallic phase which dominates the strong-coupling region at generic fillings. Then, we carried out the Density-Matrix Renormalization Group (DMRG) simulations for $S=1$ to closely investigate the phase structure at large but finite Kondo coupling. At half-filling, the Kondo coupling and $J_{\text{H}}$ do not compete and the insulating spin-gapless phase is stable, while the competition of the two leads to a stepwise collapse of the strong-coupling ferromagnetism via an intervening dimerized insulating phase with power-law spin correlation at quarter-filling.
Energy for a nucleus is considered in macroscopic limit, in terms of nucleon numbers. Further considered for a nuclear system is the Hohenberg-Kohn energy functional, in terms of proton and neutron densities. Finally, Skyrme-Hartree-Fock calculations are carried out for a half-infinite particle-stable nuclear-matter. In each case, the attention is focused on the role of neutron-proton asymmetry and on the nuclear symmetry energy. We extend the considerations on the symmetry term from an energy formula to the respective term in the Hohenberg-Kohn functional. We show, in particular, that in the limit of an analytic functional, and subject to possible Coulomb corrections, it is possible to construct isoscalar and isovector densities out of the proton and neutron densities, that retain a universal relation to each other, approximately independent of asymmetry. In the so-called local approximation, the isovector density is inversely proportional to the symmetry energy in uniform matter at the local isoscalar density. Generalized symmetry coefficient of a nuclear system is related, in the analytic limit of a functional, to an integral of the isovector density. We test the relations, inferred from the Hohenberg-Kohn functional, in the Skyrme-Hartree-Fock calculations of half-infinite matter. Within the calculations, we obtain surface symmetry coefficients and parameters characterizing the densities, for the majority of Skyrme parameterizations proposed in the literature. The volume-to-surface symmetry-coefficient ratio and the displacement of nuclear isovector relative to isoscalar surfaces both strongly increase as the slope of symmetry energy in the vicinity of normal density increases.
The aim of the present work is to show that recent results of the authors on the approximation of distributions of sums of independent summands by the infinitely divisible laws on convex polyhedra can be shown via an alternative class of approximating infinitely divisible distributions. We will also generalize the results to the infinite-dimensional case.
Electrical conductance through various nanocontacts between gold electrodes is studied by using the density functional theory, scalar-relativistic pseudopotentials, generalized gradient approximation for the exchange-correlation energy and the recursion-transfer-matrix method along with channel decomposition. The nanocontact is modeled with pyramidal fcc(100) tips and 1 to 5 gold atoms between the tips. Upon elongation of the contact by adding gold atoms between the tips, the conductance at Fermi energy E_F evolves from G ~ 3 G_0 to G ~ 1 G_0 (G_0 = 2e/h^2). Formation of a true one-atom point contact, with G ~ 1 G_0 and only one open channel, requires at least one atom with coordination number 2 in the wire. Tips that share a common vertex atom or tips with touching vertex atoms have three partially open conductance channels at E_F, and the symmetries of the channels are governed by the wave functions of the tips. The long 5-atom contact develops conductance oscillations and conductance gaps in the studied energy range -3 < E-E_F < 5 eV, which reflects oscillations in the local density of electron states in the 5-atom linear "gold molecule" between the electrodes, and a weak coupling of this "molecule" to the tips.
We report on spin dependent transport measurements in carbon nanotubes based multi-terminal circuits. We observe a gate-controlled spin signal in non-local voltages and an anomalous conductance spin signal, which reveal that both the spin and the orbital phase can be conserved along carbon nanotubes with multiple ferromagnetic contacts. This paves the way for spintronics devices exploiting both these quantum mechanical degrees of freedom on the same footing.
Achieving tunability of two dimensional (2D) transition metal dichalcogenides (TMDs) functions calls for the introduction of hybrid 2D materials by means of localized interactions with zero dimensional (0D) materials. A metal-semiconductor interface, as in gold (Au) - molybdenum disulfide (MoS2), is of great interest from the standpoint of fundamental science as it constitutes an outstanding platform to investigate plasmonic-exciton interactions and charge transfer. The applied aspects of such systems introduce new options for electronics, photovoltaics, detectors, gas sensing, catalysis, and biosensing. Here we consider pristine MoS2 and study its interaction with Au nanoislands, resulting in local variations of photoluminescence (PL) associated with various Au-MoS2 hybrid configurations. By controllably depositing monolayers of Au on MoS2 to form Au nanostructures of given size and thickness, we investigate the electronic structure of the resulting hybrid systems. We present strong evidence of PL quenching of MoS2 as a result of charge transfer from MoS2 to Au: p-doping of MoS2. The results suggest new avenues for 2D nanoelectronics, active control of transport or catalytic properties.
We study the role of fermionic resonances in realistic composite Higgs models. We consider the low energy effective description of a model in which the Higgs arises as the pseudo-Goldstone boson of an SO(5)/SO(4) global symmetry breaking pattern. Assuming that only fermionic resonances are present below the cut-off of our effective theory, we perform a detailed analysis of the electroweak constraints on such a model. This includes the exact one-loop calculation of the T parameter and the anomalous Zbb coupling for arbitrary new fermions and couplings. Other relevant observables, like b to s gamma and Delta B=2 processes have also been examined. We find that, while minimal models are difficult to make compatible with electroweak precision tests, models with several fermionic resonances, such as the ones that appear in the spectrum of viable composite Higgs models from warped extra dimensions, are fully realistic in a large region of parameter space. These fermionic resonances could be the first observable signature of the model at the LHC.
Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by {\gamma}pr(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that {\gamma}pr(G) {\leq} 4n/7 holds for every graph G with {\delta}(G) {\geq} 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.
The apparent anisotropies of the galaxy clustering in observable redshift space provide a unique opportunity to simultaneously probe cosmic expansion and gravity on cosmological scales via the Alcock--Paczynski effect and redshift-space distortions. While the improved theoretical models have been proposed and developed to describe the apparent anisotropic clustering at weakly non-linear scales, the applicability of these models is still limited in the presence of the non--perturbative smearing effect caused by the randomness of the relative velocities. Although the cosmological constraint from the anisotropic clustering will be certainly improved with a more elaborate theoretical model, we here consider an alternative way by using the statistical power of both the power spectrum and bispectrum at large scales. Based on the Fisher matrix analysis, we estimate the benefit of combining the power spectra and bispectra, finding that the constraints on the cosmic expansion and growth of structure will be improved by a factor of two. This compensates for the loss of constraining power using the power spectrum alone due to the randomness of the relative velocities.
In the article we study mappings of Carnot groups satisfy moduli inequalities. We prove that homeomorphisms satisfy the moduli inequalities ($Q$-homeomor\-phisms) with a locally integrable function $Q$ are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem we prove that mappings inverse to Sobolev homeomorphisms of finite distortion of the class $W^1_{\nu,\text{loc}}(\Omega;\Omega')$ belong to the Sobolev class $W^1_{1,\text{loc}}(\Omega';\Omega)$.
This thesis is devoted to the study of quantum mechanical effects that arise in systems of reduced dimensionality. Specifically, we investigate coherence and correlation effects in quantum transport models. In the first part, we present a theory of Markovian and non- Markovian current correlations in nanoscopic conductors. The theory is applied to obtain the spectrum of quantum noise and high-order current correlations at finite frequencies in quantum-dot systems. One of the main conclusions is that only the non-Markovian approach contains the physics of vacuum fluctuations. In the second part, we study the coupling of superconducting qubits to optical atomic systems and to cavity resonators. We propose a hybrid quantum system consisting of a flux qubit coupled to NV centers in diamond. We also demonstrate the existence of the so-called Bloch-Siegert shift in the ultra-strong coupling regime between a flux qubit and a LC resonator. Throughout the thesis, we make special emphasis on the study of decoherence effects produced by the distinct dissipative baths to which the various types of qubits presented in this thesis are inevitably coupled.
The phonon renormalization across the semiconductor-to-metal crossover in FeSi is investigated by inelastic neutron scattering combined with \textit{ab-initio} lattice dynamical calculations. A significant part of reciprocal space with a particular focus on the 110$-$001 scattering plane is mapped by the time-of-flight inelastic neutron scattering data taken below and above the crossover. Individual momentum values are investigated in more detail as a function of temperature. The data reveal that the anomalous phonon softening upon metallization is not exclusive to the high symmetry $R$ and $\Gamma$ points. Several other phonon modes around the $R$-point as well as the phonon modes at the $M$ and $X$ points of the Brillouin zone exhibit anomalous phonon softening with magnitudes comparable to that observed at the $R$-point. The momentum dependence of the phonon softening is reproduced by the lattice dynamical calculation based on the density functional perturbation theory. We discuss our findings with respect to the nature of the semiconductor-to-metal crossover in FeSi, for which different microscopic origins have been proposed, i.e., lattice thermal disorder and electronic correlation effects.
We make some progress on a question of Babai from the 1970s, namely: for $n, k \in \mathbb{N}$ with $k \le n/2$, what is the largest possible cardinality $s(n,k)$ of an intersecting family of $k$-element subsets of $\{1,2,\ldots,n\}$ admitting a transitive group of automorphisms? We give upper and lower bounds for $s(n,k)$, and show in particular that $s(n,k) = o (\binom{n-1}{k-1})$ as $n \to \infty$ if and only if $k = n/2 - \omega(n)(n/\log n)$ for some function $\omega(\cdot)$ that increases without bound, thereby determining the threshold at which `symmetric' intersecting families are negligibly small compared to the maximum-sized intersecting families. We also exhibit connections to some basic questions in group theory and additive number theory, and pose a number of problems.
By means of a simple model we investigate the possibility of an accelerated expansion of a 3-dimensional subspace in the presence of the variation of the effective 4-dimensional constant obeying the experimental constraint. Multidimensional cosmological solutions with m 2-form fields and l scalar fields are presented. Solutions corresponding to rank-3 Lie algebras are singled out and discussed. Each of solutions contain two factor spaces: one-dimensional space M_1 and Ricci-flat space M_2. A 3-dimensional subspace of M_2 is interpreted as "our" space. We show that there exists a time interval where accelerated expansion of our 3D space is compatible with a small enough variation of the effective gravitational constant G(\tau). This interval contains \tau_0 which is the point of minimum of G(\tau) (here \tau is the synchronous time variable). Special solutions with three phantom scalar fields are analyzed. It is shown that in the vicinity of the point \tau_0 the time variation of G(\tau) decreases in the sequence of Lie algebras A_3, C_3 and B_3 when the solutions with asymptotically power-law behavior of scale-factors for \tau \to \infty are considered. Exact solutions with asymptotically exponential accelerated expansion of 3D space are also considered.
The combination of optical and mid-infrared (MIR) photometry has been extensively used to select red active galactic nuclei (AGNs). Our aim is to explore the obscuration properties of these red AGNs with both X-ray spectroscopy and spectral energy distributions (SEDs). In this study, we re-visit the relation between optical/MIR extinction and X-ray absorption. We use IR selection criteria, specifically the $W1$ and $W2$ WISE bands, to identify 4798 AGNs in the $\it{XMM-XXL}$ area ($\sim 25$deg$^2$). Application of optical/MIR colours ($r- W2 > 6$) reveals 561 red AGNs (14$\%$). Of these, 47 have available X-ray spectra with at least 50 net (background-subtracted) counts per detector. For these sources, we construct SEDs from the optical to the MIR using the CIGALE code. The SED fitting shows that 44 of these latter 47 sources present clear signs of obscuration based on the AGN emission and the estimated inclination angle. Fitting the SED also reveals ten systems ($\sim20\%$) which are dominated by the galaxy. In these cases, the red colours are attributed to the host galaxy rather than AGN absorption. Excluding these ten systems from our sample and applying X-ray spectral fitting analysis shows that up to $76\%$ (28/37) of the IR red AGNs present signs of X-ray absorption. Thus, there are nine sources ($\sim20\%$ of the sample) that although optically red, are not substantially X-ray absorbed. Approximately $50\%$ of these sources present broad emission lines in their optical spectra. We suggest that the reason for this apparent discrepancy is that the r-W2 criterion is sensitive to smaller amounts of obscuration relative to the X-ray spectroscopy. In conclusion, it appears that the majority of red AGNs present considerable obscuration levels as shown by their SEDs. Their X-ray absorption is moderate with a mean of $\rm N_H \sim 10^{22}\, \rm{cm^{-2}}$.
We establish moment estimates for the invariant measure of a stochastic partial differential equation describing motion by mean curvature flow in (1+1) dimension, leading to polynomial stability of the associated Markov semigroup. We also prove maximal dissipativity for the related Kolmogorov operator.
Self-calibration techniques for analyzing galaxy cluster counts utilize the abundance and the clustering amplitude of dark matter halos. These properties simultaneously constrain cosmological parameters and the cluster observable-mass relation. It was recently discovered that the clustering amplitude of halos depends not only on the halo mass, but also on various secondary variables, such as the halo formation time and the concentration; these dependences are collectively termed assembly bias. Applying modified Fisher matrix formalism, we explore whether these secondary variables have a significant impact on the study of dark energy properties using the self-calibration technique in current (SDSS) and the near future (DES, SPT, and LSST) cluster surveys. The impact of the secondary dependence is determined by (1) the scatter in the observable-mass relation and (2) the correlation between observable and secondary variables. We find that for optical surveys, the secondary dependence does not significantly influence an SDSS-like survey; however, it may affect a DES-like survey (given the high scatter currently expected from optical clusters) and an LSST-like survey (even for low scatter values and low correlations). For an SZ survey such as SPT, the impact of secondary dependence is insignificant if the scatter is 20% or lower but can be enhanced by the potential high scatter values introduced by a highly correlated background. Accurate modeling of the assembly bias is necessary for cluster self-calibration in the era of precision cosmology.