ShantanuT01/DACTYL-Pretraining huggingface dataset:
After being destroyed by a binary supermassive black hole, a stellar density cusp can regrow at the center of a galaxy via energy exchange between stars moving in the gravitational field of the single, coalesced hole. We illustrate this process via high-accuracy N-body simulations. Regeneration requires roughly one relaxation time and the new cusp extends to a distance of roughly one-fifth the black hole's influence radius, with density rho ~ r^{-7/4}; the mass in the cusp is of order 10% the mass of the black hole. Growth of the cusp is preceded by a stage in which the stellar velocity dispersion evolves toward isotropy and away from the tangentially-anisotropic state induced by the binary. We show that density profiles similar to those observed at the center of the Milky Way and M32 can regenerate themselves in several Gyr following infall of a second black hole; the presence of density cusps at the centers of these galaxies can therefore not be used to infer that no merger has occurred. We argue that Bahcall-Wolf cusps are ubiquitous in stellar spheroids fainter than M_V ~ -18.5 that contain supermassive black holes, but the cusps have not been detected outside of the Local Group since their angular sizes are less than 0.1". We show that the presence of a cusp implies a lower limit of \~10^{-4} per year on the rate of stellar tidal disruptions, and discuss the consequences of the cusps for gravitational lensing and the distribution of dark matter on sub-parsec scales.
We rephrase the Wootters-Fields construction [Ann. Phys., {\bf 191}, 363 (1989)] of a full set of mutually unbiased bases in a complex vector space of dimensions $N=p^r$, where $p$ is an odd prime, in terms of the character vectors of the cyclic group $G$ of order $p$. This form may be useful in explicitly writing down mutually unbiased bases for $N=p^r$.
We propose and discuss a specific scheme allowing to realize a Quantum Cryptography qutrit protocol. This protocol exploits the polarization properties of single frequency and single spatial mode biphotons.
We consider the de Rham complex over scales of weighted isotropic and anisotropic H\"older spaces with prescribed asymptotic behaviour at the infinity. Starting from theorems on the solvability of the system of operator equations generated by the de Rham differential $d$ and the operator $d^*$ formally adjoint to it, a description of the cohomology groups of the de Rham complex over these scales was obtained. It was also proved that in the isotropic case the cohomology space is finite-dimensional, and in the anisotropic case the general form of an element from the cohomology space is presented.
In this paper, we try to probe whether a clean CMB map obtained from the raw satellite data using a cleaning procedure is sufficiently clean. Specifically we study if there are any foreground residuals still present in the cleaned data using a cross-correlation statistic. Residual contamination is expected to be present, primarily, in the galactic plane due to the high emission from our own galaxy. A foreground mask is applied conventionally to avoid biases in the estimated quantities of interest due to foreground leakage. Here, we map foreground residuals, if present, in the unmasked region i.e., outside a CMB analysis mask. Further locally extended foreground-contaminated regions, found eventually, are studied to understand them better. The few contaminated regions thus identified may be used to slightly extend the available masks to make them more stringent.
Various studies firmly establish the fact that gamma-ray observations can act as a unique probe to detect the possible cosmic ray (CR) sources, study the CR density distribution and explore the average properties of interstellar medium (ISM) such as the gas density profile of ISM. We use the DRAGON code to study different propagation models by incorporating realistic source distribution, Galactic magnetic field (GMF) and gas density profile, and finally obtain the proton distribution (both spatial and energy) in the Galaxy by fitting the locally observed CR spectra. The uncertainties in the model parameters used to study the CR propagation are also shown here. Our obtained proton distribution is then used to calculate the diffuse gamma-ray flux produced by proton-proton interactions in the Galactic halo. We compare our diffuse gamma-ray fluxes with the previous results and the isotropic gamma-ray background (IGRB) at sub -TeV energy regime measured by \textit{Fermi}-LAT. It is found to be much less than IGRB, which suggests IGRB is mostly of extragalactic origin. Finally, we use our obtained proton distribution to calculate gamma-ray fluxes from individual Galactic Molecular Clouds (GMCs) and those fluxes are compared with the \textit{Fermi}-LAT observations of GMCs.
A popular derivation of the apparent temperature of the particle transverse momentum spectra and its inconsistency are considered. An improved formula for the apparent temperature is discussed. It is shown that recent results on transverse mass spectra of $J/\psi$ and $\psi^{\prime}$ mesons support a hypothesis of statistical production of charmonia at hadronization and suggest the early thermal freeze-out of these mesons. Using the apparent temperature formula the collective transverse velocity of the hadronizing quark gluon plasma is extracted to be $<v_T > \approx 0.2$. Predictions for transverse mass spectra of hidden and open charm mesons along with bottomonium at SPS and RHIC energies are discussed.
Using density functional theory with the inclusion of van der Waals (vdW) interaction, we have investigated electronic energy bands, density of states, effective masses of charge carriers, and photo absorption coefficients of pseudo-cubic CH$_3$NH$_3$PbX$_3$ (X=I, Br). Our results confirm the direct bandgap of 1.49 (1.92) eV for X=I (Br) in the pseudo-cubic $Pm$ phase with lattice constant of 6.324 (5.966) \AA, being agreed well with experiment and indicating the necessity of vdW correction. The calculated photo absorption coefficients for X=I (Br) have the onset at red (orange) color and the first peak around violet (ultraviolet) color in overall agreement with the experiment.
In this thesis we study algebraic structures in M-theory, in particular the exceptional Lie algebras arising in dimensional reduction of its low energy limit, eleven-dimensional supergravity. We focus on e8 and its infinite-dimensional extensions e9 and e10. We review the dynamical equivalence, up to truncations on both sides, between eleven-dimensional supergravity and a geodesic sigma model based on the coset E10/K(E10), where K(E10) is the maximal compact subgroup. The description of e10 as a graded Lie algebra is crucial for this equivalence. We study generalized Jordan triple systems, which are closely related to graded Lie algebras, and which may also play a role in the description of M2-branes using three-dimensional superconformal theories.
From many fewer acquired measurements than suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that, a signal can be reconstructed with high probability when it exhibits sparsity in some domain. Most of the conventional CS recovery approaches, however, exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a signal, which are irrespective of the non-stationarity of natural signals and cannot achieve high enough degree of sparsity, thus resulting in poor CS recovery performance. In this paper, we propose a new framework for image compressive sensing recovery using adaptively learned sparsifying basis via L0 minimization. The intrinsic sparsity of natural images is enforced substantially by sparsely representing overlapped image patches using the adaptively learned sparsifying basis in the form of L0 norm, greatly reducing blocking artifacts and confining the CS solution space. To make our proposed scheme tractable and robust, a split Bregman iteration based technique is developed to solve the non-convex L0 minimization problem efficiently. Experimental results on a wide range of natural images for CS recovery have shown that our proposed algorithm achieves significant performance improvements over many current state-of-the-art schemes and exhibits good convergence property.
We show that the common singularities present in generic modified gravity models governed by actions of the type $S=\int d^4x \sqrt{-g}f(R,\phi,X)$, with $X= -{1/2}g^{ab}\partial_a\phi\partial_b\phi$, are essentially the same anisotropic instabilities associated to the hypersurface $F(\phi)=0$ in the case of a non-minimal coupling of the type $F(\phi)R$, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface $\frac{\partial f}{\partial R}=0$ exists. Some examples are explicitly discussed.
Schroedinger's disentanglement [E. Schroedinger, Proc. Cambridge Phil. Soc. 31, 555 (1935)], i. e., remote state decomposition, as a physical way to study entanglement, is carried one step further with respect to previous work in investigating the qualitative side of entanglement in any bipartite state vector. Remote measurement (or, equivalently, remote orthogonal state decomposition) from previous work is generalized to remote linearly-independent complete state decomposition both in the non-selective and the selective versions. The results are displayed in terms of commutative square diagrams, which show the power and beauty of the physical meaning of the (antiunitary) correlation operator inherent in the given bipartite state vector. This operator, together with the subsystem states (reduced density operators), constitutes the so-called correlated subsystem picture. It is the central part of the antilinear representation of a bipartite state vector, and it is a kind of core of its entanglement structure. The generalization of previously elaborated disentanglement expounded in this article is a synthesis of the antilinear representation of bipartite state vectors, which is reviewed, and the relevant results of Cassinelli et al. [J. Math. Analys. and Appl., 210, 472 (1997)] in mathematical analysis, which are summed up. Linearly-independent bases (finite or infinite) are shown to be almost as useful in some quantum mechanical studies as orthonormal ones. Finally, it is shown that linearly-independent remote pure-state preparation carries the highest probability of occurrence. This singles out linearly-independent remote influence from all possible ones.
We study the spatial structure of 1/4 BPS solitons in 4 dimensional N=4 gauge theory. A weak binding approximation is used where the soliton is made of several "ingredient" particles. Some spatial moduli are described which are not accounted for in the (p,q) web picture. These moduli are counted and their effect on the solutions is demonstrated. The potential for off BPS configurations is estimated by a simple expression and is found to agree with previous expressions. We discuss the fermionic zero modes of the solitons, and find agreement with web predictions.
The initial mass function (IMF) succinctly characterizes a stellar population, provides a statistical measure of the end result of the star-formation process, and informs our under- standing of the structure and dynamical evolution of stellar clusters, the Milky Way, and other galaxies. Detecting variations in the form of the IMF could provide powerful insights into the processes that govern the formation and evolution of stars, clusters, and galaxies. In this contribution, we review measurements of the IMF in resolved stellar populations, and critically assess the evidence for systematic IMF variations. Studies of the field, local young clusters and associations, and old globular clusters suggest that the vast majority were drawn from a "universal" IMF, suggesting no gross systematic variations in the IMF over a range of star formation environments, and much of cosmic time. We conclude by highlighting the complimentary roles that Gaia and the Large Synoptic Survey Telescope will play in future studies of the IMF in Galactic stellar populations.
We study a superconducting quantum point contact made of a narrow In$_{0.75}% $Ga$_{0.25}$As channel with Nb proximity electrodes. The narrow channel is formed in a gate-fitted constriction of InGaAs/InAlAs/InP heterostructure hosting a two-dimensional electron gas. When the channel opening is varied with the gate, the Josephson critical current exhibits a discretized variation that arises from the quantization of the transverse momentum in the channel. The quantization of Josephson critical current persists down to the single-channel regime, providing an unambiguous demonstration of a semiconductor--superconductor hybrid Josephson junction involving only a single ballistic channel.
Let G be a graph with a distribution of pebbles on its vertices. A pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The optimal pebbling number of G is the smallest number of pebbles which can placed on the vertices of G such that, for any vertex v of G, there is a sequence of pebbling moves resulting in at least one pebble on v. We determine the optimal pebbling number for several classes of induced subgraphs of the square grid, which we call staircase graphs.
We test how metallicity variation (a background gradient and fluctuations) affects the physics of local thermal instability using analytical calculations and idealized, high-resolution 1D hydrodynamic simulations. Although the cooling function ($\Lambda[T,Z]$) and the cooling time ($t_{\rm cool}$) depend on gas temperature and metallicity, we find that the growth rate of thermal instability is explicitly dependent only on the derivative of the cooling function relative to temperature ($\partial \ln \Lambda/\partial \ln T$) and not on the metallicity derivative ($\partial \ln \Lambda/ \partial \ln Z$). For most of $10^4~{\rm K} \lesssim T \lesssim 10^7~{\rm K}$, both the isobaric and isochoric modes (occurring at scales smaller and larger than the sonic length covered in a cooling time [$c_s t_{\rm cool}$], respectively) grow linearly, and at higher temperatures ($\gtrsim 10^7~{\rm K}$) the isochoric modes are stable. We show that even the nonlinear evolution depends on whether the isochoric modes are linearly stable or unstable. For the stable isochoric modes, we observe the growth of small-scale isobaric modes but this is distinct from the nonlinear fragmentation of a dense cooling region. For unstable isochoric perturbations we do not observe large density perturbations at small scales. While very small clouds ($\sim {\rm min}[c_st_{\rm cool}]$) form in the transient state of nonlinear evolution of the stable isochoric thermal instability, most of them merge eventually.
Understanding the physical mechanisms behind thermal effects in phosphors is crucial for white light-emitting diodes (WLEDs) applications, as thermal quenching of their photoluminescence might render them useless. The two chemically close Eu-doped \Hosta and \Hostb crystals are typical phosphors studied for WLEDs. The first one sustains efficient light emission at 100$^{\circ}$C while the second one emits very little light at that temperature. Herein, we analyze from first principles their electronic structure and atomic geometry, before and after absorption/emission of light. Our results, in which the Eu-5d levels are obtained inside the band gap thanks to the removal of an electron from the 4f$^7$ shell, attributes the above-mentioned experimental difference to an auto-ionization model of the thermal quenching, based on the energy difference between Eu$_{\text{5d}}$ and the conduction band minimum. For both Eu-doped phosphors, we identify the luminescent center, and we show that the atomic relaxation in their excited state is of crucial importance for a realistic description of the emission characteristics.
The problematic divergence of the $q$-partition function of the harmonic oscillator recently considered in \cite{plastino} is a particular case of the non-normalizabilty of the distribution function of classical Hamiltonian systems in non-extensive thermostatistics as discussed previously in \cite{lutsko-boon}.
We investigate the structure of smooth projective 3-folds X with -K_X nef and K_X^3=0.
An automorphism of order $n$ of a K3 surface is called purely non-symplectic if it multiplies the holomorphic symplectic form by a primitive $n$-th root of unity. We give the classification of purely non-symplectic automorphisms with $\varphi(n)\geq 12$ where $\varphi$ denotes the Euler totient function.
We present the theory for ultracold atomic gases in an optical lattice near a Feshbach resonance. In the single-band approximation the theory describes atoms and molecules which can both tunnel through the lattice. Moreover, an avoided crossing between the two-atom and the molecular states occurs at every site. We determine the microscopic parameters of the generalized Hubbard model that describes this physics, using the experimentally known parameters of the Feshbach resonance in the absence of the optical lattice. As an application we also calculate the zero-temperature phase diagram of an atomic Bose gas in an optical lattice.
In this paper we study Jackiw-Rebbi model, in which a massless fermion is coupled to the kink of $\lambda \phi^4$ theory through a Yukawa interaction. In the original Jackiw-Rebbi model the soliton is prescribed. However, we are interested in the back-reaction of the fermion on the soliton besides the effect of the soliton on the fermion. Also, as a particular example, we consider a minimal supersymmetric kink model, $\mathcal{N}=1$, in ($1+1$) dimensions. In this case, the bosonic self-coupling, $\lambda$, and the Yukawa coupling between fermion and soliton, $g$, have specific relation, $g=\sqrt{\lambda/2}$. As the set of coupled equations of motion of the system is not analytically solvable, we use a numerical method to solve it self-consistently. We obtain the bound energy spectrum, bound states of the system and the corresponding shape of the soliton using a relaxation method, except for the zero mode fermionic state and threshold energies which are analytically solvable. With the aid of these results we are able to show how the soliton is affected in general and supersymmetric cases. The results we obtain are consistent with the ones in the literature, considering the soliton as background.
We study the Likelihood function of data given f_NL for the so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linear function, local in real space, of a Gaussian random field. We compute the Cramer-Rao bound for f_NL and show that for small values of f_NL the 3-point function estimator saturates the bound and is equivalent to calculating the full Likelihood of the data. However, for sufficiently large f_NL, the naive 3-point function estimator has a much larger variance than previously thought. In the limit in which the departure from Gaussianity is detected with high confidence, error bars on f_NL only decrease as 1/ln Npix rather than Npix^-1/2 as the size of the data set increases. We identify the physical origin of this behavior and explain why it only affects the local type of non-Gaussianity, where the contribution of the first multipoles is always relevant. We find a simple improvement to the 3-point function estimator that makes the square root of its variance decrease as Npix^-1/2 even for large f_NL, asymptotically approaching the Cramer-Rao bound. We show that using the modified estimator is practically equivalent to computing the full Likelihood of f_NL given the data. Thus other statistics of the data, such as the 4-point function and Minkowski functionals, contain no additional information on f_NL. In particular, we explicitly show that the recent claims about the relevance of the 4-point function are not correct. By direct inspection of the Likelihood, we show that the data do not contain enough information for any statistic to be able to constrain higher order terms in the relation between the Gaussian field and the curvature perturbation, unless these are orders of magnitude larger than the size suggested by the current limits on f_NL.
We have performed a systematic study of Gamma-Ray Bursts (GRBs), which have various values in the peak energy of the ${\nu}F_{\nu}$ spectrum of the prompt emission, $E_{{\rm peak}}$, observed by \textsl{Swift}/BAT and \textsl{Fermi}/GBM, investigating their prompt and X-ray afterglow emissions. We cataloged the long-lasting GRBs observed by the \textsl{Swift} between 2004 December and 2014 February in 3 categories according to the classification by \citet{2008ApJ...679..570S}: X-Ray Flashes (XRFs), X-Ray Rich GRBs (XRRs), and Classical GRBs (C-GRBs). We then derived $E^{{\rm obs}}_{{\rm peak}}$, as well as $E^{{\rm src}}_{{\rm peak}}$ if viable, of the \textsl{Swift} spectra of their prompt emission. We also analyzed their X-Ray afterglows and found the trend that the GRB events with a lower $E_{{\rm peak}}^{{\rm src}}$, i.e. softer GRBs, are fainter in the 0.3--10 keV X-ray luminosity and decay more slowly than harder GRBs. The intrinsic event rates of the XRFs, XRRs, and C-GRBs were calculated, using the \textsl{Swift}/BAT trigger algorithm. That of either of the XRRs and XRFs is larger than that of the C-GRBs. If we assume that the observational diversity of $E_{{\rm peak}}$ is explained with the off-axis model \citep{2002ApJ...571L..31Y,2004ApJ...607L..103Y}, these results yield the jet half-opening angle of $\Delta\theta\sim 0.3^\circ$, and the variance of the observing angles $\theta_{{\rm obs}} \lesssim0.6^{\circ}$. This implies that the tiny variance of the observing angles of $\lesssim0.6^{\circ}$ would be responsible for the $E_{{\rm peak}}$ diversity observed by \textsl{Swift}/BAT, which is unrealistic. Therefore, we conclude that the $E_{{\rm peak}}$ diversity is not explained with the off-axis model, but is likely to originate from some intrinsic properties of the jets.
Gravitational-wave detectors on earth have detected gravitational waves from merging compact objects in the local Universe. In future we will detect gravitational waves from higher-redshift sources, which trace the high-redshift structure formation history. That is, by observing high-redshift gravitational-wave events we will be able to probe structure formation history. This will provide additional insight into the early Universe when primordial fluctuations are generated and also into the nature of dark matter.
AGN with double-peaked narrow lines (DPAGN) may be caused by kiloparsec scale binary AGN, bipolar outflows, or rotating gaseous disks. We examine the class of DPAGN in which the two narrow line components have closely similar intensity as being especially likely to involve disks or jets. Two spectroscopic indicators support this likelihood. For DPAGN from Smith et al. (2010), the "equal-peaked" objects (EPAGN) have [Ne V]/[O III] ratios lower than for a control sample of non-double peaked AGN. This is unexpected for a pair of normal AGN in a galactic merger, but may be consistent with [O III] emission from a rotating ring with relatively little gas at small radii. Also, [O III]/H-beta ratios of the redshifted and blueshifted systems in the EPAGN are more similar to each other than in a control sample, suggestive of a single ionizing source and inconsistent with the binary interpretation.