ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the set of two-qubit pure states with real amplitudes and their geometrical representation in the three-dimensional sphere. In this representation, we show that the maximally entangled states --those locally equivalent to the Bell States --form two disjoint circles perpendicular to each other. We also show that taking the natural Riemannian metric on the sphere, the set of states connected by local gates are equidistant to this pair of circles. Moreover, the unentangled, or so-called product states, are $\pi/4$ units away to the maximally entangled states. This is, the unentangled states are the farthest away to the maximally entangled states. In this way, if we define two states to be equivalent if they are connected by local gates, we have that there are as many equivalent classes as points in the interval $[0,\pi/4]$ with the point $0$ corresponding to the maximally entangled states. The point $\pi/4$ corresponds to the unentangled states which geometrically are described by a torus. Finally, for every $0< d < \pi/4$ the point $d$ corresponds to a disjoint pair of torus. We also show that if a state is $d$ units away from the maximally entangled states, then its entanglement entropy is $S(d) = 1- \log_2 \sqrt{\frac{(1+\sin 2 d)^{1+\sin 2 d}}{(1-\sin 2 d)^{-1+\sin 2 d}}}$. Finally, we also show how this geometrical interpretation allows us to clearly see that any pair of two-qubit states with real amplitudes can be connected with a circuit that only has single-qubit gates and one controlled-Z gate.
We consider a service system where agents are invited on-demand. Customers arrive exogenously as a Poisson process and join a customer queue upon arrival if no agent is available. Agents decide to accept or decline invitations after some exponentially distributed random time, and join an agent queue upon invitation acceptance if no customer is waiting. A customer and an agent are matched in the order of customer arrival and agent invitation acceptance under the non-idling condition, and will leave the system simultaneously once matched (service times are irrelevant here).   We consider a feedback-based adaptive agent invitation scheme, which controls the number of pending agent invitations, depending on the customer and/or agent queue lengths and their changes. The system process has two components -- `the difference between agent and customer queues' and `the number of pending invitations', and is a countable continuous-time Markov chain.   For the case when the customer arrival rate is constant, we establish fluid and diffusion limits, in the asymptotic regime where the customer arrival rate goes to infinity, while the agent response rate is fixed. We prove the process stability and fluid-scale limit interchange, which in particular imply that that both customer and agent waiting times in steady-state vanish in the asymptotic limit. To do this we develop a novel (multi-scale) Lyapunov drift argument; it is required because the process has non-trivial behavior on the state space boundary. When the customer arrival rate is time-varying, we present a fluid limit for the processes in the same asymptotic regime. Simulation experiments are conducted to show good performance of the invitation scheme and accuracy of fluid limit approximations.
The magnetar 1E~1547$-$5408 recently exhibited two periods of outburst, beginning on 2008 October 3 and 2009 January 22. Here we present an analysis of the persistent radiative evolution and a statistical study of the burst properties during the 2009 outburst using the {\em Swift} X-ray Telescope (XRT). We find that the 1--10 keV flux increased by a factor of $\sim500$ and hardened significantly, peaking $\sim6$ hours after the onset of the outburst. The observed pulsed fraction exhibited an anti-correlation with phase-averaged flux. Properties of the several hundred X-ray bursts during the 2009 outburst were determined and compared to those from other magnetar outburst events. We find that the peaks of the bursts occur randomly in phase but that the folded counts that compose the bursts exhibit a pulse which is misaligned with the persistent pulse phase. We also report a correlation between burst hardness and flux. We compare the hardness-flux evolution of the persistent emission of both outbursts to those from other magnetars and find that although there does exist an overall trend, the degree of hardening for a given increase in flux is not uniform from source to source. These results are discussed in the context of previous results and within the magnetar model.
The effects of density dependence of the symmetry energy on the collective modes and dynamical instabilities of cold and warm nuclear and stellar matter are studied in the framework of relativistic mean-field hadron models. The existence of the collective isovector and possibly an isoscalar collective mode above saturation density is discussed. It is shown that soft equations of state do not allow for a high density isoscalar collective mode, however, if the symmetry energy is hard enough an isovector mode will not disappear at high densities. The crust-core transition density and pressure are obtained as a function of temperature for $\beta$-equilibrium matter with and without neutrino trapping. An estimation of the size of the clusters formed in the non-homogeneous phase as well as the corresponding growth rates and distillation effect is made. It is shown that cluster sizes increase with temperature, that the distillation effect close to the inner edge of the crust-core transition is very sensitive to the symmetry energy, and that, within a dynamical instability calculation, the pasta phase exists in warm compact stars up to 10 - 12 MeV.
We use the Minimal Spanning Tree to characterize the aggregation level of given sets of points. We test 3 distances based on the histogram of the MST edges to discriminate between the distributions. We calibrate the method by using artificial sets following Poisson, King or NFW distributions. The distance using the mean, the dispersion and the skewness of the histogram of MST edges provides the more efficient results. We apply this distance to a subsample of the ENACS clusters and we show that the bright galaxies are significantly more aggregated than the faint ones. The contamination provided by uniformly distributed field galaxies is neglectible. On the other hand, we show that the presence of clustered groups on the same cluster line of sight masked the variation of the distance with the considered magnitude.
We consider gas at densities appropriate to protoplanetary disks and calculate its ability to cool due to line radiation emitted by H2O molecules within the gas. Our work follows that of Neufeld & Kaufman (1993; ApJ, 418, 263), expanding on their work in several key aspects, including use of a much expanded line database, an improved escape probability formulism, and the inclusion of dust grains, which can absorb line photons. Although the escape probabilities formally depend on a complicated combination of optical depth in the lines and in the dust grains, we show that the cooling rate including dust is well approximated by the dust-free cooling rate multiplied by a simple function of the dust optical depth. We apply the resultant cooling rate of a dust-gas mixture to the case of a solar nebula shock pertinent to the formation of chondrules, millimeter-sized melt droplets found in meteorites. Our aim is to assess whether line cooling can be neglected in chondrule-forming shocks or if it must be included. We find that for typical parameters, H2O line cooling shuts off a few minutes past the shock front; line photons that might otherwise escape the shocked region and cool the gas will be absorbed by dust grains. During the first minute or so past the shock, however, line photons will cool the gas at rates ~ 10,000 K/hr, dropping the temperature of the gas (and most likely the chondrules within the gas) by several hundred K. Inclusion of H2O line cooling therefore must be included in models of chondrule formation by nebular shocks.
The composite galaxy NGC 4102 hosts a LINER nucleus and a starburst. We mapped NGC 4102 in the 12.8 micron line of [NeII], using the echelon spectrometer TEXES on the NASA IRTF, to obtain a data cube with 1.5" spatial and 25 km/s spectral, resolution. Combining near-infrared, radio, and the [NeII] data shows that the extinction to the starburst is substantial, more than 2 magnitudes at K band, and that the neon abundance is less than half solar. We find that the star formation in the nuclear region is confined to a rotating ring or disk of 4.3" (~300 pc) diameter, inside the Inner Lindblad Resonance. This region is an intense concentration of mass, with a dynamical mass of ~3 x 10^9 solar masses, and of star formation. The young stars in the ring produce the [NeII] flux reported by Spitzer for the entire galaxy. The mysterious blue component of line emission detected in the near-infrared is also seen in [NeII]; it is not a normal AGN outflow.
In this work we study the generalization of twisted homology to geometric and non-geometric backgrounds. In the process we describe the necessary conditions to wrap a network of D-branes on twisted cycles. If the cycle is localized in time, we show how by an instantonic brane mediation, some D-branes transform into fluxes on different backgrounds including non-geometric fluxes. As a consequence, we show that in the case of a IIB six-dimensional torus compactification on a simple orientifold, the flux superpotential is not invariant by this brane-flux transition, allowing the connection among different Minkowski vacuum solutions. For the case in which non-geometric fluxes are turned on, we also discuss some topological restrictions for the transition to occur. In this context, we show that there are some vacuum solutions protected to change by a brane-flux transition.
In the context of the low energy effective theory, the exact Landau level spectrum of quasiparticles in twisted bilayer graphene with small twist angle is analytically obtained by spheroidal eigenvalues. We analyze the dependence of the Landau levels on the twist angle to find the points, where the two-fold degeneracy for twist angles is lifted in the nonzero modes and below/above which massive/massless fermion pictures become valid. In the perpendicular magnetic field of 10\,T, the degeneracy is removed at $\theta_{{\rm deg}}\sim 3^\circ$ %angles around 3 degrees for a few low levels, specifically, $\theta_{\rm deg}\simeq 2.56^\circ$ for the first pair of nonzero levels and $\theta_{\rm deg}\simeq 3.50^\circ$ for the next pair. Massive quasiparticle appears at $\theta<\theta_{{\rm c}}\simeq 1.17^\circ$ in 10\,T, %angles less than 1.17 degrees. which match perfectly with the recent experimental results. Since our analysis is applicable to the cases of arbitrary constant magnetic fields, we make predictions for the same experiment performed in arbitrary constant magnetic fields, e.g., for B=40\,T we get $\theta_{\rm c}\simeq 2.34^\circ$ and the sequence of angles $\theta_{\rm deg} = 5.11, 7.01, 8.42,...$ for the pairs of nonzero energy levels. The symmetry restoration mechanism behind the massive/massless transition is conjectured to be a tunneling (instanton) in momentum space.
We present Far Ultraviolet Spectroscopic Explorer observations of the star-forming galaxy Mrk 54 at z = 0.0448. The Lyman continuum radiation is not detected above the HI absorption edge in our Galaxy. An upper limit is evaluated by comparison with the background measured in regions of the detector adjacent to the observed spectrum. A spectral window of 16 A, reasonably free of additional HI Lyman series line absorption is used. No correction is needed for molecular hydrogen absorption in our Galaxy but a foreground extinction of 0.29 mag is accounted for. An upper limit of 6.15 10^{-16} erg/cm^2/s/A is obtained for the flux at ~ 900 A in the rest frame of Mrk 54. By comparison with the number of ionizing photons derived from the H-alpha flux, this limit translates into an upper limit of f_esc < 0.062 for the fraction of Lyman continuum photons that escape the galaxy without being absorbed by interstellar material. This limit compares with the limits obtained in three other nearby galaxies and is compatible with the escape fractions predicted by models.   The upper limits obtained in nearby galaxies contrasts with the detection of Lyman continuum flux in the composite spectrum of Lyman-break galaxies at z ~ 3.4. The difficulties and implications of a comparison are discussed.
Recently, a class of Roche-lobe-filling binary systems consisting of hot subdwarf stars and white dwarfs with sub-hour periods has been discovered. At present, the hot subdwarf is in a shell He burning phase and is transferring some of its remaining thin H envelope to its white dwarf companion. As the evolution of the hot subdwarf continues, it is expected to detach, leaving behind a low mass C/O core white dwarf secondary with a thick He layer. Then, on a timescale of $\sim 10$ Myr, gravitational wave radiation will again bring the systems into contact. If the mass transfer is unstable and results in a merger and a catastrophic thermonuclear explosion is not triggered, it creates a remnant with a C/O-dominated envelope, but one still rich enough in He to support an R Corona Borealis-like shell burning phase. We present evolutionary calculations of this phase and discuss its potential impact on the cooling of the remnant white dwarf.
We have monitored photometrically the Y0 brown dwarf WISEP J173835.52+273258.9 (W1738) at both near- and mid-infrared wavelengths. This ~1 Gyr-old 400K dwarf is at a distance of 8pc and has a mass around 5 M_Jupiter. We observed W1738 using two near-infrared filters at lambda~1um, Y and J, on Gemini observatory, and two mid-infrared filters at lambda~4um, [3.6] and [4.5], on the Spitzer observatory. Twenty-four hours were spent on the source by Spitzer on each of June 30 and October 30 2013 UT. Between these observations, around 5 hours were spent on the source by Gemini on each of July 17 and August 23 2013 UT. The mid-infrared light curves show significant evolution between the two observations separated by four months. We find that a double sinusoid can be fit to the [4.5] data, where one sinusoid has a period of 6.0 +/- 0.1 hours and the other a period of 3.0 +/- 0.1 hours. The near-infrared observations suggest variability with a ~3.0 hour period, although only at a <~2 sigma confidence level. We interpret our results as showing that the Y dwarf has a 6.0 +/- 0.1 hour rotation period, with one or more large-scale surface features being the source of variability. The peak-to-peak amplitude of the light curve at [4.5] is 3%. The amplitude of the near-infrared variability, if real, may be as high as 5 to 30%. Intriguingly, this size of variability and the wavelength dependence can be reproduced by atmospheric models that include patchy KCl and Na_2S clouds and associated small changes in surface temperature. The small number of large features, and the timescale for evolution of the features, is very similar to what is seen in the atmospheres of the solar system gas giants.
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent $\nu$. The resulting values of the critical exponent $\nu$ in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. This is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.
The high frequency limits of the singular component $A(\omega)$ of the small wavevector expansion of the longitudinal (L) and transverse (T) components of the spin-resolved exchange-correlation kernel tensor $f_{xc,\sigma \sigma'}^{L,T}(q,\omega)=-v(q)G_{\sigma \sigma'}^{L,T}(q,\omega)$ in a two-dimensional isotropic electron liquid with arbitrary spin polarization are studied. Here $G_{\sigma \sigma'}^{L,T}(q,\omega)$ is the spin-resolved local field factor, $v(q)$ is the Coulomb interaction in momentum space, and $\sigma$ denotes spin. Particularly, the real part of $A(\omega)$ is found to be logarithmically divergent at large $\omega$. the large wavevetor structure of the corresponding spin-resolved static structure factor is also established.
In this paper we push forward and exploit an analogy between the morphologies of the X-ray cavities observed in some galaxy clusters, and the optically deficient point-symmetric bubbles occurring in some planetary nebulae (PNe). Point-symmetric PNe are thought to be shaped by stellar binary interactions; namely, the presence of a companion to the PN's progenitor star is required. We suggest that similar point-symmetric structures in the X-ray cavities of galaxy clusters might be associated with the presence of massive binary black holes. A systematic cataloguing of high-resolution images of the diffuse X-ray emission at the core of galaxy clusters might contribute to individuate massive binary black holes.
We investigate two chemical abundance calibrations for the narrow-line-region (NLR) of active galaxies in terms of three easily observable optical emission-line ratios, namely, [OIII]$\lambda\lambda$4959,5007/H$\beta$, [NII]$\lambda\lambda$6548,84/H$\alpha$ and [OII]$\lambda3727/$[OIII]$\lambda\lambda$4959,5007. The calibrations are obtained from a grid of models on the assumption that the main process responsible for the production of these lines is photoionization by a ``typical'' active galactic nucleus continuum. The chemical elements vary their abundance together with oxygen, except nitrogen, which is assumed to be a product of secondary nucleosynthesis. The calibrations are calculated for the range $8.4 \le 12+log(O/H) \le 9.4$, and tested using NLR data for a sample of Seyfert's and LINER's having HII regions in the vicinity of the nucleus. The gaseous abundances of these HII regions have been determined in previous works, and the NLR abundances are obtained on the assumption that they can be extrapolated from those of the HII regions. The calibrations work very well for the Seyfert's, giving abundance values which agree with those obtained from the HII regions, and can thus be used for quick estimates of the chemical abundances of the NLR's. For the LINER's, the calibrations give lower values than those derived from the corresponding HII regions, suggesting that the assumptions of the models do not apply for them, and that there are different physical processes at work in the NLR of the LINER's.
We prove that any smooth complex projective variety with generic vanishing index bigger or equal than 2 has birational bicanonical map. Therefore, if X is a smooth complex projective variety X with maximal Albanese dimension and non-birational bicanonical map, then the Albanese image of X is fibered by subvarieties of codimension at most 1 of an abelian subvariety of Alb X.
The far infrared background is a sink for the hidden aspects of galaxy formation. At optical wavelengths, ellipticals and spheroids are old, even at $z \sim 1.$ Neither the luminous formation phase nor their early evolution is seen in the visible. We infer that ellipticals and, more generally, most spheroids must have formed in dust-shrouded starbursts. In this article, we show how separate tracking of disk and spheroid star formation enables us to infer that disks dominate near the peak in the cosmic star formation rate at $z \lapproxeq 2$ and in the diffuse ultraviolet/optical/infrared background, whereas spheroid formation dominates the submillimetre background.
We study a class of systems of quasilinear differential inequalities associated to weakly coercive differential operators and power reaction terms. The main model cases are given by the $p$-Laplacian operator as well as the mean curvature operator in non parametric form. We prove that if the exponents lie under a certain curve, then the system has only the trivial solution. These results hold without any restriction provided the possible solutions are more regular. The underlying framework is the classical Euclidean case as well as the Carnot groups setting.
For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from zero. The basis of our method is the establishment of a Nash inequality, followed either by a comparison with the simple random walk or by a more direct analysis based on a martingale decomposition. As an example of application, we show that under certain conditions, our results imply an estimate of the speed of convergence of the mean square displacement of the walk towards its limit.
We present three-dimensional hydrodynamical simulations of buoyant gas in a typical cluster environment. The hot matter was injected continuously into a small region off-set from the cluster centre. In agreement with previous analytic estimates we found that the bubbles evolve very differently depending on their luminosity. Using tracer particles we computed radio maps of the bubbles based on different assumptions about the magnetic field. In the radio band the bubbles closely resemble FRI sources. For the bubbles to be detectable for long enough to account for FRI sources, we found that reacceleration has to take place. The bubbles are generally difficult to detect, both, in the radio and in the X-ray band. Thus it is possible to hide a significant amount of energy in the form of bubbles in clusters. Finally, we compute the efficiency of the bubbles to stir the ICM and find that recurrent low-power sources may be fairly effective in mixing the inner cluster region.
Two fundamental empirical laws have been established in the analysis of galaxy space distribution. First, recent analyses have revealed that the three dimensional distribution of galaxies and clusters is characterized by large scale structures and huge voids: such a distribution shows fractal correlations up to the limits of the available samples. This has confirmed the earlier de Vaucouleurs power-law density - distance relation, now corresponding to a fractal structure with dimension $D \approx 2$, at least, in the range of scales $ \sim 1 \div 200 Mpc$ ($H_0 = 55 km/sec/Mpc$). An eventual cut-off towards homogenization has not been yet identified. Second, since Hubble's discovery, the linear redshift-distance law has been well established within $200 Mpc$ and also much deeper. The co-existence of these laws within the same scales is a challenge for the standard cosmology where the linear Hubble law is a strict consequence of homogeneity of the expanding universe. This puzzle is now sufficiently strong to raise doubts for the standard cosmology.