ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of efficiently solvable semidefinite programs. We apply this method to derive arbitrarily good approximations to the optimal measure-and-prepare strategy in generic state estimation problems. Finally, we report its performance in combination with the criterion developed by Doherty et al. [1] for the calculation of the entanglement robustness of a relevant family of quantum states whose separability properties were unknown.
We consider the discrete-time voter model on complete bipartite graphs and study the quasi-stationary distribution (QSD) for the model as the size of one of the partitions tends to infinity while the other partition remains fixed. We show that the QSDs converge weakly to a nontrivial limit which features a consensus with the exception of a random number of dissenting vertices in the "large" partition. Moreover, we explicitly calculate the law of the number of dissenters and show that it follows the heavy-tailed Sibuya distribution with parameter depending on the size of the "small" partition. Our results rely on a discrete-time analogue of the well-known duality between the continuous-time voter model and coalescing random walks which we develop in the paper.
It is conjectured that the generalization of the Constantin-Lax-Majda model (gCLM) $\omega_t + a u\omega_x = u_x \omega$ due to Okamoto, Sakajo and Wunsch can develop a finite time singularity from smooth initial data for $a < 1$. For the endpoint case where $a$ is close to and less than $1$, we prove finite time asymptotically self-similar blowup of gCLM on a circle from a class of smooth initial data. For the gCLM on a circle with the same initial data, if the strength of advection $a$ is slightly larger than $1$, we prove that the solution exists globally with $|| \omega(t)||_{H^1}$ decaying in a rate of $O(t^{-1})$ for large time. The transition threshold between two different behaviors is $a=1$, which corresponds to the De Gregorio model.
Since it is not possible to predict when a Gamma-Ray Burst (GRB) will occur or when Active Galactic Nucleus (AGN) flaring activity starts, follow-up/monitoring ground telescopes must be located as uniformly as possible all over the world in order to collect data simultaneously with Fermi and Swift detections. However, there is a distinct gap in follow-up coverage of telescopes in the eastern U.S. region based on the operations of Swift. Motivated by this fact, we have constructed a 14" fully automated optical robotic telescope, Goddard Robotic Telescope (GRT), at the Goddard Geophysical and Astronomical Observatory. The aims of our robotic telescope are 1) to follow-up Swift/Fermi GRBs and 2) to perform the coordinated optical observations of Fermi Large Area Telescope (LAT) AGN. Our telescope system consists of off-the-shelf hardware. With the focal reducer, we are able to match the field of view of Swift narrow instruments (20' x 20'). We started scientific observations in mid-November 2008 and GRT has been fully remotely operated since August 2009. The 3 sigma upper limit in a 30-second exposure in the R filter is ~15.4 mag; however, we can reach to ~18 mag in a 600-second exposures. Due to the weather condition at the telescope site, our observing efficiency is 30-40% on average.
Two possibile applications of the optimized expansion for the free energy of the quantum-mechanical anharmonic oscillator are discussed. The first method is for the finite temperature effective potential; the second one, for the classical effective potential. The results of both methods show a quick convergence and agree well with the exact free energy in the whole range of temperatures. Postscript figures are available under request to AO email ROZYNEK@FUW.EDU.PL
We close a gap in the literature by showing that the full covering groups of the Mathieu group $M_{22}$ and of its automorphism group $Aut(M_{22})$ occur as the Galois group of $\mathbb{Q}$-regular Galois extensions of $\mathbb{Q}(t)$.
Formation process(es) of galactic bulges are not yet clarified although several mechanisms have been proposed. In a previous study, we suggested one possibility that galactic bulges have been formed from the cold gas inflowing through surrounding hot halo gas in massive dark matter halos at high redshifts. It was shown that this scenario leads to the bulge-to-total stellar mass ratio increasing with the galaxy mass, in agreement with the well-known observed trend. We here indicate that it also reproduces recent observational results that the mean stellar age of the bulge increases with the galaxy mass while the age gradient across the bulge decreases. We infer that this formation path applies mainly to high-mass galaxies and the bulges in lower-mass galaxies have different origins such as secular formation from the disc material.
5d transition metal oxides offer new opportunities to test our understanding of the interplay of correlation effects and spin-orbit interactions in materials in the absence of a single dominant interaction. The subtle balance between solid-state interactions can result in new mechanisms that minimize the interaction energy, and in material properties of potential use for applications. We focus here on the 5d transition metal oxide NaOsO3, a strong candidate for the realization of a magnetically driven transition from a metallic to an insulating state exploiting the so-called Slater mechanism. Experimental results are derived from non-resonant and resonant x-ray single crystal diffraction at the Os L-edges. A change in the crystallographic symmetry does not accompany the metal-insulator transition in the Slater mechanism and, indeed, we find no evidence of such a change in NaOsO3. An equally important experimental observation is the emergence of the (300) Bragg peak in the resonant condition with the onset of magnetic order. The intensity of this space-group forbidden Bragg peak continuously increases with decreasing temperature in line with the square of intensity observed for an allowed magnetic Bragg peak. Our main experimental results, the absence of crystal symmetry breaking and the emergence of a space-group forbidden Bragg peak with developing magnetic order, support the use of the Slater mechanism to interpret the metal-insulator transition in NaOsO3. We successfully describe our experimental results with simulations of the electronic structure and, also, with an atomic model based on the established symmetry of the crystal and magnetic structure.
Four-dimensional supersymmetric SU(N) Yang-Mills theory on a sphere has highly charged baryon-like states built from anti-symmetric combinations of the adjoint scalars. We show that these states, which are equivalently described as holes in a free fermi sea of a reduced matrix model, are D-branes. Their excitations are stringlike and effectively realize Dirichlet and Neumann boundary conditions in various directions. The low energy brane dynamics should realize an emergent gauge theory that is local on a new space. We show that the Gauss' Law associated to this emergent gauge symmetry appears from combinatorial identities relating the stringy excitations. Although these excitations are not BPS, they can be near-BPS and we can hope to study them in perturbation theory. Accordingly, we show that the Chan-Paton factors expected for strings propagating on multiple branes arise dynamically, allowing the emergent gauge symmetry to be non-Abelian.
We present the results of a blind search for intervening HI 21 cm absorption toward 260 radio sources in the redshift range 0<z<2.74 with the Green Bank Telescope. The survey has the sensitivity to detect sub-damped Lyman-alpha (DLA) systems for HI spin temperatures $T_s/f$ = 100 K, and despite the successful re-detection of ten known 21 cm absorbers in the sample, we detect no new absorption lines in the full survey. Sources detected in 21 cm absorption were also searched for hydroxyl (OH) 18 cm absorption and we re-detect 1667 MHz OH absorption toward PKS 1830-211. We searched for intervening HI 21 cm absorption along the line of sight in each source achieving a total redshift coverage of $\Delta z$ = 88.64 (comoving absorption path of $\Delta X$ = 159.5) after removing regions affected by radio frequency interference. We compute a 95% confidence upper limit on the column density frequency distribution $f(N_{\rm HI})$ and set a statistical constraint on the spin temperature $T_s$ in the range 100-1000 K, consistent with prior redshifted optical DLA surveys and HI 21 cm emission observations at the same redshifts. We infer a value for the cosmological mass density of neutral gas, $\Omega_{\rm HI}$. Through comparison with prior $\Omega_{\rm HI}$ measurements, we place a statistical constraint on the mean spin temperature of $T_s/f$ = 175 K. Our derived $\Omega_{\textrm {HI}}$ values support a relative mild evolution in $\Omega_{\textrm {HI}}$ over the last 11 Gyr and are consistent with other methods that measure $\Omega_{\textrm {HI}}$.
We report on the fabrication of nano-devices on the \hkl[-1 0 1] surface of a Weyl semimetal, a macroscopic crystal of TaAs, and low-temperature transport measurements. We can implement electron beam lithography by peeling off and transferring the resist for nanofabrication onto the irregular crystal. We fabricate the device electrodes with superconducting Niobium nitride (NbN) to control the current flow through the intended active area of the devices. Our device structure enables the reduction of the current jetting effect, and we demonstrate the negative magnetoresistance measurement as a function of angle. The high field magnetotransport show three distinct oscillation frequencies corresponding to the three bands at the Fermi level. Resistance measured in the low magnetic field shows the usual weak anti-localization dip near the zero-field -- a signature of a Weyl material. Our method of fabricating devices with superconducting electrodes provides a way to probe the electrical properties of macroscopic single crystals at the nanoscale. As we use conventional lithographic techniques for patterning, this method can be extended to a wide gamut of electrode materials and a large class of 3D quantum materials.
We prove existence and regularity of minimizers for a class of functionals defined on Borel sets in $R^n$. Combining these results with a refinement of the selection principle introduced by the authors in arXiv:0911.0786, we describe a method suitable for the determination of the best constants in the quantitative isoperimetric inequality with higher order terms. Then, applying Bonnesen's annular symmetrization in a very elementary way, we show that, for $n=2$, the above-mentioned constants can be explicitly computed through a one-parameter family of convex sets known as ovals. This proves a further extension of a conjecture posed by Hall in J. Reine Angew. Math. 428 (1992).
We present generalized methods for calculating lower bounds on the ground-state entropy per site, $S_0$, or equivalently, the ground-state degeneracy per site, $W=e^{S_0/k_B}$, of the antiferromagnetic Potts model. We use these methods to derive improved lower bounds on $W$ for several lattices.
We sketch the major steps in a functional integral derivation of a new set of Stochastic Gross-Pitaevsky equations (GPE) for a Bose-Einstein condensate (BEC) confined to a trap at zero temperature with the averaged effects of non-condensate modes incorporated as stochastic sources. The closed-time-path (CTP) coarse-grained effective action (CGEA) or the equivalent influence functional method is particularly suitable because it can account for the full back-reaction of the noncondensate modes on the condensate dynamics self-consistently. The Langevin equations derived here containing nonlocal dissipation together with colored and multiplicative noises are useful for a stochastic (as distinguished from say, a kinetic) description of the nonequilibrium dynamics of a BEC. This short paper contains original research results not yet published anywhere.
We investigate the statistical properties of translation invariant random fields (including point processes) on Euclidean spaces (or lattices) under constraints on their spectrum or structure function. An important class of models that motivate our study are hyperuniform and stealthy hyperuniform systems, which are characterised by the vanishing of the structure function at the origin (resp., vanishing in a neighbourhood of the origin). We show that many key features of two classical statistical mechanical measures of randomness - namely, fluctuations and entropy, are governed only by some particular local aspects of their structure function. We obtain exponents for the fluctuations of the local mass in domains of growing size, and show that spatial geometric considerations play an important role - both the shape of the domain and the mode of spectral decay. In doing so, we unveil intriguing oscillatory behaviour of spatial correlations of local masses in adjacent box domains. We describe very general conditions under which we show that the field of local masses exhibit Gaussian asymptotics, with an explicitly described limit. We further demonstrate that stealthy hyperuniform systems with joint densities exhibit degeneracy in their asymptotic entropy per site. In fact, our analysis shows that entropic degeneracy sets in under much milder conditions than stealthiness, as soon as the structure function fails to be logarithmically integrable.
We apply the Cornwall-Jackiw-Tomboulis (CJT) formalism to the scalar $\lambda \phi^{4}$ theory in canonical-noncommutative spacetime. We construct the CJT effective potential and the gap equation for general values of the noncommutative parameter $\theta_{\mu\nu}$. We observe that under the hypothesis of translational invariance, which is assumed in the effective potential construction, differently from the commutative case ($\theta_{\mu\nu}= 0$), the renormalizability of the gap equation is incompatible with the renormalizability of the effective potential. We argue that our result, is consistent with previous studies suggesting that a uniform ordered phase would be inconsistent with the infrared structure of canonical noncommutative theories.
In information theory the reliability function and its bounds, describing the exponential behavior of the error probability, are the most important quantitative characteristics of the channel performance. From a general point of view, these bounds provide certain measures of distinguishability of a given set of states. In an earlier paper we introduced quantum analogs of the random coding and the expurgation lower bounds for the case of pure signal states. Here we discuss the general case, in particular, we prove the previously conjectured expurgation bound and find the quantum cutoff rate in the case of arbitrary mixed signal states.
The symbol invariant is used to describe the Springer correspondence for the classical groups by Lusztig. And the fingerprint invariant can be used to describe the Kazhdan-Lusztig map. They are invariants of rigid semisimple operators described by pairs of partitions $(\lambda^{'}, \lambda^{"})$. We construct a nice representative element of the rigid semisimple operators with the same symbol invariant. The fingerprint of the representative element can be obtained immediately. We also discuss the representative element of rigid semisimple operator with the same fingerprint invariant. Our construction can be regarded as the maps between these two invariants.
We analyze simulated maps of the Cosmology Large Angular Scale Surveyor (CLASS) experiment and recover a nearly cosmic-variance limited estimate of the reionization optical depth $\tau$. We use a power spectrum-based likelihood to simultaneously clean foregrounds and estimate cosmological parameters in multipole space. Using software specifically designed to constrain $\tau$, the amplitude of scalar fluctuations $A_s$, and the tensor-to-scalar ratio $r$, we demonstrate that the CLASS experiment will be able to estimate $\tau$ within a factor of two of the full-sky cosmic variance limit allowed by cosmic microwave background polarization measurements. Additionally, we discuss the role of CLASS's $\tau$ constraint in conjunction with gravitational lensing of the CMB on obtaining a $\gtrsim4\sigma$ measurement of the sum of the neutrino masses.
Density functional theory $(DFT)$ studies show that doping of $3d TM$ atoms into $Mg_4^{0,+} (TMMg_3^{0,+})$ can alter the endothermic nature of molecular hydrogen adsorption on bare $Mg_4^{0,+}$. $H_2$ adsorption on $TMMg_3^{0,+}$ clusters depends on the $TM(3d)$ orbital contribution to the frontier molecular orbitals of the clusters. In $H_2TMMg_3^{0,+}$ complexes, $H_2$ is adsorbed through donation and back donation of electronic charges with $TMMg_3^{0,+}$ clusters. $H_2$ binding energy is the maximum for $NiMg_3$ (-0.76 eV) and $FeMg_3^+$ (-0.48 eV) among the neutral and cationic $TMMg_3$ clusters, respectively. The geometry of $H_2$ adsorption complex entirely depends on the geometry of the host cluster. The lowest energy symmetrical structures of both $NiMg_3$ and $FeMg_3^+$ clusters are less efficient than some slightly higher energy low symmetrical geometrical isomers for adsorption of multiple hydrogen molecules (13.28 $H_2$ $wt\%$ for $NiMg_3$ and 7.89 $H_2$ $wt\%$ for $FeMg_3^+$). Greater exposer of $TM^{0,+}$ along with its lower Mg coordination number make host clusters more suitable for hydrogen storage.
Using a high-resolution cosmological hydrodynamic simulation, we present a method to constrain extinction due to intergalactic grey dust based on the observed magnitudes of distant Type IA supernovae. We apply several simple prescriptions to relate the intergalactic dust density to the gas density in the simulation, thereby obtaining dust extinctions that may be directly compared to the observed distribution of supernova magnitudes. Our analysis is sensitive to the spatial distribution of grey dust, but is not dependent on its intrinsic properties such as its opacity or grain size. We present an application of our technique to the supernova data of Perlmutter et al., who find that their high redshift sample is ~0.2 magnitudes fainter than the expectation for a non-accelerating, low-density universe. We find that for grey dust to be responsible, it must be distributed quite smoothly, e.g., tracing intergalactic gas. More realistic dust distributions, such as dust tracing the metal density, are inconsistent with observations at the 1.5-2 sigma level. Upcoming observations and improved modelling of the dust distribution should lead to stronger constraints on intergalactic grey dust extinction.
The effect of long range dipole-dipole interactions on the thermal fluctuations of the magnetization of an assembly of single-domain ferromagnetic particles is considered. If orientational correlations between the particles are neglected, the evolution of the magnetization orientations may be described by a nonlinear Fokker-Planck equation (FPE) reducing to the usual linear one in the limit of infinite dilution [W.F. Brown Jr, Phys. Rev. 130, 1677 (1963)]. The thermally activated relaxation time scale of the assembly is estimated, leading to a simple modification of the axially symmetric asymptotes for the superparamagnetic relaxation time.
In this paper we consider Gorenstein stable surfaces with $K^2_X=1$ and positive geometric genus. Extending classical results, we show that such surfaces admit a simple description as weighted complete intersection.   We exhibit a wealth of surfaces of all possible Kodaira dimensions that occur as normalisations of Gorenstein stable surfaces with $K_X^2=1$; for $p_g=2$ this leads to a rough stratification of the moduli space.   Explicit non-Gorenstein examples show that we need further techniques to understand all possible degenerations.
We present a coherent database of spectroscopic observations of far-IR fine-structure lines from the Herschel/PACS archive for a sample of 170 local AGN, plus a comparison sample of 20 starburst galaxies and 43 dwarf galaxies. Published Spitzer/IRS and Herschel/SPIRE line fluxes are included to extend our database to the full 10-600 $\mu m$ spectral range. The observations are compared to a set of CLOUDY photoionisation models to estimate the above physical quantities through different diagnostic diagrams. We confirm the presence of a stratification of gas density in the emission regions of the galaxies, which increases with the ionisation potential of the emission lines. The new [OIV]25.9$\mu m$/[OIII]88$\mu m$ vs [NeIII]15.6$\mu m$/[NeII]12.8$\mu m$ diagram is proposed as the best diagnostic to separate: $i)$ AGN activity from any kind of star formation; and $ii)$ low-metallicity dwarf galaxies from starburst galaxies. Current stellar atmosphere models fail to reproduce the observed [OIV]25.9$\mu m$/[OIII]88$\mu m$ ratios, which are much higher when compared to the predicted values. Finally, the ([NeIII]15.6$\mu m$ + [NeII]12.8$\mu m$)/([SIV]10.5$\mu m$ + [SIII]18.7$\mu m$) ratio is proposed as a promising metallicity tracer to be used in obscured objects, where optical lines fail to accurately measure the metallicity. The diagnostic power of mid- to far-infrared spectroscopy shown here for local galaxies will be of crucial importance to study galaxy evolution during the dust-obscured phase at the peak of the star formation and black-hole accretion activity ($1 < z < 4$). This study will be addressed by future deep spectroscopic surveys with present and forthcoming facilities such as JWST, ALMA, and SPICA.
We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations for which the fluid density and spatial three-velocity converge to a solution of the Poisson-Euler equations of Newtonian gravity. The results presented here generalize those of \cite{Oli06} to allow for a larger class of initial data. As in \cite{Oli06}, the proof is based on a non-local symmetric hyperbolic formulation of the Einstein-Euler equations which contain a singular parameter $\ep=v_T/c$ with $v_T$ a characteristic speed associated to the fluid and $c$ the speed of light. Energy and dispersive estimates on weighted Sobolev spaces are the main technical tools used to analyze the solutions in the singular limit $\ep\searrow 0$.
Terrestrial laser scanner is a kind of fast, high-precision data acquisition device, which had been more and more applied to the research areas of forest inventory. In this study, a kind of automated low-cost terrestrial laser scanner was designed and implemented based on a two-dimensional laser radar sensor SICK LMS-511 and a stepper motor. The new scanner was named as BEE, which can scan the forest trees in three dimension. The BEE scanner and its supporting software are specifically designed for forest inventory. The experiments have been performed by using the BEE scanner in an artificial ginkgo forest which was located in Haidian district of Beijing. Four square plots were selected to do the experiments. The BEE scanner scanned in the four plots and acquired the single scan data respectively. The DBH, tree height and tree position of trees in the four plots were estimated and analyzed. For comparison, the manual measured data was also collected in the four plots. The tree stem detection rate for all four plots was 92.75%; the root mean square error of the DBH estimation was 1.27cm; the root mean square error of the tree height estimation was 0.24m; the tree position estimation was in line with the actual position. Experimental results show that the BEE scanner can efficiently estimate the structure parameters of forest trees and has a good potential in practical application of forest inventory.