ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study hybrid atom-molecule quantum walks in one-dimensional optical lattices with two interacting bosonic atoms which may be converted into a molecule. The hybrid atom-molecule energy bands include a continuum band and two isolated bands, which respectively correspond to scattering states and dressed bound states (DBS's). Because of the atom-molecule coupling, the DBS's may appear even in the absence of atom-atom interaction. From an initial state of two atoms occupying the same site, in addition to independent quantum walks which correspond to scattering states, correlated quantum walks appear as a signature of DBS's. Even if the atom-atom interaction and the atom-molecule coupling are much stronger than the tunneling strengths, independent quantum walks may still appear under certain resonant conditions. The correlated quantum walks show two light-cones with different propagation velocities, which can be analytically explained by the effective tunneling strengths of the two different DBS's. Furthermore, the effective nearest-neighbor tunneling of DBS's can be suppressed to zero, which can be explained by the destructive interference between the atomic pair and the molecule.
We analyze a sample of galaxies chosen to have F24>0.5 mJy and satisfy a certain IRAC color criterion. IRS spectra yield redshifts, spectral types, and PAH luminosities, to which we add multi-wavelength broadband photometry. Stellar population modeling and IRS spectra together demonstrate that the double criteria used to select this sample have efficiently isolated massive star-forming galaxies at z~1.9. This is the first starburst-dominated ULIRG sample at high redshift with total infrared luminosity measured directly from FIR and millimeter photometry, and as such gives us the first accurate view of broadband SEDs for starburst galaxies at extremely high luminosity and at all wavelengths. Similar broadband data are assembled for three other galaxy samples -- local starburst galaxies, local AGN/ULIRGS, and a second 24mu-luminous z~1.9 sample dominated by AGN. L(PAH)/L(IR) for the new z~1.9 starburst sample is the highest ever seen, some three times higher than in local starbursts, whereas in AGNs this ratio is depressed below the starburst trend, often severely. Several pieces of evidence imply that AGNs exist in this starburst dominated sample, except two of which even host very strong AGN, while they still have very strong PAH emission. The ACS images show most objects have very extended morphologies in the rest-frame UV band, thus extended distribution of PAH molecules. Such an extended distribution prevents further destruction PAH molecules by central AGNs. We conclude that objects in this sample are ULIRGs powered mainly by starburst; and the total infrared luminosity density contributed by this type of objects is 0.9-2.6x 10^7 Lsol/Mpc^3.
Some hypothetical particles are considered essentially undetectable because they are far too light and slow-moving to transfer appreciable energy or momentum to the normal matter that composes a detector. I propose instead directly detecting such feeble particles, like sub-MeV dark matter or even gravitons, through their uniquely distinguishable decoherent effects on quantum devices like matter interferometers. More generally, decoherence can reveal phenomena that have arbitrarily little classical influence on normal matter, giving new motivation for the pursuit of macroscopic superpositions.
In the Schr\"odinger-cat gedanken experiment a cat is in a quantum superposition of two macroscopically distinct states, alive and dead.The paradoxical interpretation of quantum mechanics is that the cat is not in one state or the other, alive or dead, immediately prior to its measurement. Because of this apparent defiance of macroscopic reality, quantum superpositions of states macroscopically distinct have generated much interest. Here we address the issue of proving a contradiction with macroscopic reality objectively, through the testable predictions of quantum mechanics. We consider the premises of macroscopic reality (that the ``cat'' is either ``dead'' or ``alive'', the measurement indicating which) and macroscopic locality (that simultaneous measurements some distance away cannot induce the macroscopic change, ``dead'' to ``alive'' and vice versa, to the ``cat''). The predictions of quantum mechanics for certain states, generated using states exhibiting continuous variable entanglement, are shown to be incompatible with the predictions of all theories based on this dual premise. Our proof is along the lines of Bell's theorem, but where all relevant measurements give macroscopically distinct results.
Let $r\geq 3$ be an integer and $G$ be a graph. Let $\delta(G), \Delta(G)$, $\alpha(G)$ and $\mu(G)$ denotes minimum degree, maximum degree, independence number and matching number of $G$, respectively. Recently, Caro, Davila and Pepper proved $\delta(G)\alpha(G)\leq \Delta(G)\mu(G)$. Mohr and Rautenbach characterized the extremal graphs for non-regular graphs and 3-regular graphs. In this note, we characterize the extremal graphs for all $r$-regular graphs in term of Gallai-Edmonds Structure Theorem, which extends Mohr and Rautenbach's result.
We analytically and numerically study quasinormal frequencies (QNFs) of neutral and charged scalar fields in the charged anti-de Sitter (AdS) black holes and discuss the stability of the black holes in terms of the QNFs. We focus on the range of the mass squared $\mu^2$ of the scalar fields for which the Robin boundary condition parametrised by $\zeta$ applies at the conformal infinity. We find that if the black hole of radius $r_{+}$ and charge $Q$ is much smaller than the AdS length $\ell$, the instability of the charged scalar field can be understood in terms of superradiance in the reflective boundary condition. Noting that the s-wave normal frequency in the AdS spacetime is a decreasing function of $\zeta$, we find that if $|eQ|\ell/r_{+}$ is greater than $(3+\sqrt{9+4\mu^2\ell^2})/2$, where $e$ is the charge of the scalar field, the black hole is superradiantly unstable irrespectively of $\zeta$. On the other hand, if $|eQ|\ell/r_{+}$ is equal to or smaller than this critical value, the stability crucially depends on $\zeta$ and there appears a purely oscillating mode at the onset of the instability. We argue that as a result of the superradiant instability, the scalar field gains charge from the black hole and energy from its ambient electric field, while the black hole gives charge to the scalar field and gains energy from the scalar field but decreases its asymptotic mass parameter.
Let $\mathcal{F}$ be a family of graphs. The Tur\'{a}n number $ex(n;\mathcal{F})$ is defined to be the maximum number of edges in a graph of order $n$ that is $\mathcal{F}$-free. In 1959, Erd\H{o}s and Gallai determined the Tur\'an number of $M_{k+1}$ (a matching of size $k+1$) as follows: \[ ex(n;M_{k+1})= \max\left\{\binom{2k+1}{2},\binom{n}{2}-\binom{n-k}{2}\right\}. \] Since then, there has been a lot of research on Tur\'an number of linear forests.   A linear forest is a graph whose connected components are all paths or isolated vertices. Let $\mathcal{L}_{n,k}$ be the family of all linear forests of order $n$ with $k$ edges. In this paper, we prove that \[ ex(n;\mathcal{L}_{n,k})= \max \left\{\binom{k}{2},\binom{n}{2}-\binom{n-\left\lfloor \frac{k-1}{2}\right \rfloor}{2}+ c \right\}, \] where $c=0$ if $k$ is odd and $c=1$ otherwise. This determines the maximum number of edges in a non-Hamiltonian graph with given Hamiltonian completion number and also solves two open problems in \cite{WY} as special cases.   Moreover, we show that our main theorem implies Erd\H{o}s-Gallai Theorem and also gives a short new proof for it by the closure and counting techniques. Finally, we generalize our theorem to a conjecture which implies the famous Erd\H{o}s Matching Conjecture.
We indicate the progress of experimental gravity, present an outlook in this field, and summarise the Observational/Experimental Parallel Session together with a related plenary talk on gravitational waves of the 2nd LeCosPA Symposium.
We study the transport properties of low-energy (quasi)particles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We consider four different geometrical setups and focus on the dependence of transport on the strength of an applied magnetic field. By solving the classical equations of motion for each setup we calculate the magnetoconductance in terms of transmission and reflection coefficients for both the normal and Andreev versions of the billiard, calculating in the latter the critical field value above which the outgoing current of holes becomes zero.
Image reconstruction is likely the most predominant auxiliary task for image classification, but we would like to think twice about this convention. In this paper, we investigated "approximating the Fourier Transform of the input image" as a potential alternative, in the hope that it may further boost the performances on the primary task or introduce novel constraints not well covered by image reconstruction. We experimented with five popular classification architectures on the CIFAR-10 dataset, and the empirical results indicated that our proposed auxiliary task generally improves the classification accuracy. More notably, the results showed that in certain cases our proposed auxiliary task may enhance the classifiers' resistance to adversarial attacks generated using the fast gradient sign method.
Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting parameter via a local recursion defined directly on the limit of the graph sequence. Interestingly, the recursion may admit multiple solutions, implying non-trivial long-range dependencies between the covered vertices. We overcome this lack of correlation decay by introducing a perturbative parameter (temperature), which we let progressively go to zero. This allows us to uniquely identify the correct solution. In the important case where the graph limit is a unimodular Galton-Watson tree, the recursion simplifies into a distributional equation that can be solved explicitly, leading to a new asymptotic formula that considerably extends the well-known one by Karp and Sipser for Erd\"os-R\'enyi random graphs.
In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multidimensional rotator is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere.
Deep sub-millimetre observations using SCUBA are presented of the central regions of four high redshift clusters which have been extensively studied optically: CL0023+0423 (z=0.84), J0848+4453 (z=1.27), CL1604+4304 (z=0.90) and CL1604+4321 (z=0.92). 10 sub-millimetre sources are securely detected towards these four clusters at 850 microns, with two further tenuous detections; the raw 850 micron source counts exceed those determined from blank-field surveys by a factor of 3-4. In particular, towards CL1604+4304, 6 sources are detected with S(850) > 4 mJy making this the richest sub-mm field discovered to date. Corrections for gravitational lensing by these high redshift clusters reduce these excess sources counts, but are unlikely to account for more than about half of the excess, with the remainder presumably directly associated with cluster galaxies. The 450 to 850 micron flux density ratios of the detected sources are systematically higher (at a significance level > 98%) than those determined for blank-field selected sources, consistent with them being at the cluster redshifts. If subsequent identifications confirm cluster membership, these results will demonstrate that the optical Butcher-Oemler effect is also observed at sub-mm wavelengths.
We determine the smooth locus and the locus of canonical singularities in the Cornalba compactification \bar S_g of the moduli space S_g of spin curves, i.e., smooth curves of genus g with a theta characteristic. Moreover, the following lifting result for pluricanonical forms is proved: Every pluricanonical form on the smooth locus of \bar S_g extends holomorphically to a desingularisation of \bar S_g.
Assuming that the neutrino mass matrix is diagonalized by the TBM, we looked for the charged lepton mass matrix textures which render a lepton mixing matrix consistent with data. We were interested in the textures with the maximum number of zeros, so, we explored the cases of real matrices with three (and also four zeros) and found which of them provide solutions in agreement with data. We present the successful Yukawa textures and obtained the relative sizes of their non-zero entries. We found some interesting relations among the entries of these textures in terms of the charged lepton masses.
We use data from the Multi-Unit Spectroscopic Explorer (MUSE), recently commissioned at the Very Large Telescope (VLT), to study the kinematics and stellar population content of NGC 4371, an early-type massive barred galaxy in the core of the Virgo cluster. We integrate this study with a detailed structural analysis using imaging data from the Hubble and Spitzer space telescopes, which allows us to perform a thorough investigation of the physical properties of the galaxy. We show that the rotationally supported inner components in NGC 4371, an inner disc and a nuclear ring - which, according to the predominant scenario, are built with stars formed from gas brought to the inner region by the bar - are vastly dominated by stars older than 10 Gyr. Our results thus indicate that the formation of the bar occurred at a redshift of about $z=1.8^{+0.5}_{-0.4}$ (error bars are derived from 100 Monte Carlo realisations). NGC 4371 thus testifies to the robustness of bars. In addition, the mean stellar age of the fraction of the major disc of the galaxy covered by our MUSE data is above 7 Gyr, with a small contribution from younger stars. This suggests that the quenching of star formation in NGC 4371, likely due to environmental effects, was already effective at a redshift of about $z=0.8^{+0.2}_{-0.1}$. Our results point out that bar-driven secular evolution processes may have an extended impact in the evolution of galaxies, and thus on the properties of galaxies as observed today, not necessarily restricted to more recent cosmic epochs.
We present a new form of the multi-boson reduction of KP hierarchy with Lax operator written in terms of boson fields abelianizing the second Hamiltonian structure. This extends the classical Miura transformation and the Kupershmidt-Wilson theorem from the (m)KdV to the KP case. A remarkable relationship is uncovered between the higher Hamiltonian structures and the corresponding Miura transformations of KP hierarchy, on one hand, and the discrete integrable models living on {\em refinements} of the original lattice connected with the underlying multi-matrix models, on the other hand. For the second KP Hamiltonian structure, worked out in details, this amounts to finding a series of representations of the nonlinear $\hWinf$ algebra in terms of arbitrary finite number of canonical pairs of free fields.
Lazard showed in his seminal work "Groupes analytiques $p$-adiques" that for rational coefficients continuous group cohomology of $p$-adic Lie-groups is isomorphic to Lie-algebra cohomology. We refine this result in two directions: firstly we extend his isomorphism under certain conditions to integral coefficients and secondly, we show that for algebraic groups, his isomorphism can be realized by differentiating locally analytic cochains.
Lanczos-Lovelock theories of gravity, in its first order version, are studied on asymptotically locally anti de Sitter spaces. It is shown that thermodynamics satisfies the standard behavior and an expression for entropy is found for this formalism. Finally a short analysis of the algebra of conserved charges is displayed.
All crucial features of the recently observed real-world weighted networks are obtained in a model where the weight of a link is defined with a single non-linear parameter $\alpha$ as $w_{ij}=(s_is_j)^\alpha$, $s_i$ and $s_j$ are the strengths of two end nodes of the link and $\alpha$ is a continuously tunable positive parameter. In addition the definition of strength as $s_i= \Sigma_j w_{ij}$ results a self-organizing link weight dynamics leading to a self-consistent distribution of strengths and weights on the network. Using the Barab\'asi-Albert growth dynamics all exponents of the weighted networks which are continuously tunable with $\alpha$ are obtained. It is conjectured that the weight distribution should be similar in any scale-free network.
We study the minimal supersymmetric standard model (MSSM) with minimal flavor violation (MFV), imposing constraints from flavor physics observables and MSSM Higgs searches, in light of the recent discovery of a 125 GeV Higgs boson by ATLAS and CMS. We analyze the electroweak vacuum stability conditions to further restrict the MSSM parameter space. In addition, a connection to ultraviolet physics is shown via an implementation of renormalization group running, which determines the TeV-scale spectrum from a small set of minimal supergravity parameters. Finally, we investigate the impact from dark matter direct detection searches. Our work highlights the complementarity of collider, flavor and dark matter probes in exploring the MSSM, and shows that even in a MFV framework, flavor observables constrain the MSSM parameter space well beyond the current reach of direct SUSY particle searches.
The paper analyzes the rotation averaging problem as a minimization problem for a potential function of the corresponding gradient system. This dynamical system is one generalization of the famous Kuramoto model on special orthogonal group SO(3), which is known as the non-Abelian Kuramoto model. We have proposed a novel method for finding weighted and unweighted rotation average. In order to verify the correctness of our algorithms, we have compared the simulation results with geometric and projected average using real and random data sets. In particular, we have discovered that our method gives approximately the same results as geometric average.
We present dynamical properties of linear waves and null geodesics valid for Kerr and Kerr-de Sitter black holes and their stationary perturbations. The two are intimately linked by the geometric optics approximation. For the nullgeodesic flow the key property is the r-normal hyperbolicity of the trapped set and for linear waves it is the distribution of quasi-normal modes: the exact quantization conditions do not hold for perturbations but the bounds on decay rates and the statistics of frequencies are still valid.
We present the BOSS Lyman-alpha (Lya) Forest Sample from SDSS Data Release 9, comprising 54,468 quasar spectra with zqso > 2.15 suitable for Lya forest analysis. This data set probes the intergalactic medium with absorption redshifts 2.0 < z_alpha < 5.7 over an area of 3275 square degrees, and encompasses an approximate comoving volume of 20 h^-3 Gpc^3. With each spectrum, we have included several products designed to aid in Lya forest analysis: improved sky masks that flag pixels where data may be unreliable, corrections for known biases in the pipeline estimated noise, masks for the cores of damped Lya systems and corrections for their wings, and estimates of the unabsorbed continua so that the observed flux can be converted to a fractional transmission. The continua are derived using a principal component fit to the quasar spectrum redwards of restframe Lya (lambda > 1216 Ang), extrapolated into the forest region and normalized by a linear function to fit the expected evolution of the Lya forest mean-flux. The estimated continuum errors are ~5% rms. We also discuss possible systematics arising from uncertain spectrophotometry and artifacts in the flux calibration; global corrections for the latter are provided. Our sample provides a convenient starting point for users to analyze clustering in BOSS Lya forest data, and it provides a fiducial data set that can be used to compare results from different analyses of baryon acoustic oscillations in the Lya forest. The full data set is available from the SDSS-III DR9 web site.
We study the effects of accretion environment (gas density, temperature and angular momentum) at large radii ($\sim 10$pc) on luminosity of hot accretion flows. The radiative feedback effects from the accretion flow on the accretion environment are also self-consistently taken into account. We find that the slowly rotating flows at large radii can significantly deviate from Bondi accretion when radiation heating and cooling are considered. We further find that when the temperature of environment gas is low (e.g. $T=2\times 10^7$K), the luminosity of hot accretion flows is high. When the temperature of gas is high (e.g. $T\geq4\times 10^7$K), the luminosity of hot accretion flow significantly deceases. The environment gas density can also significantly influence the luminosity of accretion flows. When density is higher than $\sim 4\times 10^{-22}\text{g} \text{cm}^{-3}$ and temperature is lower than $2\times 10^7$K, hot accretion flow with luminosity lower than $2\%L_{\text{Edd}}$ is not present. Therefore, the pc-scale environment density and temperature are two important parameters to determine the luminosity. The results are also useful for the sub-grid models adopted by the cosmological simulations.
For an elliptic curve $E$ defined over a number field $K$, the heuristic density of the set of primes of $K$ for which $E$ has cyclic reduction is given by an inclusion-exclusion sum $\delta_{E/K}$ involving the degrees of the $m$-division fields $K_m$ of $E$ over $K$. This density can be proved to be correct under assumption of GRH.   For $E$ without complex multiplication (CM), we show that $\delta_{E/K}$ is the product of an explicit non-negative rational number reflecting the finite entanglement of the division fields of $E$ and a universal infinite Artin-type product. For $E$ admitting CM over $K$ by a quadratic order ${\mathcal{O}}$, we show that $\delta_{E/K}$ admits a similar `factorization' in which the Artin type product also depends on ${\mathcal{O}}$.   For $E$ admitting CM over $\bar K$ by an order ${\mathcal{O}}\not\subset K$, which occurs for $K={\bf Q}$, the entanglement of division fields over $K$ is non-finite. In this case we write $\delta_{E/K}$ as the sum of two contributions coming from the primes of $K$ that are split and inert in ${\mathcal{O}}$. The split contribution can be dealt with by the previous methods, the inert contribution is of a different nature.   We determine the ways in which the density can vanish, and provide numerical examples of the different kinds of densities.
We report on the application of a feedback-controlled electromigration technique for the formation of nanometer-sized gaps in mesoscopic gold wires and rings. The effect of current density and temperature, linked via Joule heating, on the resulting gap size is investigated. Experimentally, a good thermal coupling to the substrate turned out to be crucial to reach electrode spacings below 10 nm and to avoid overall melting of the nanostructures. This finding is supported by numerical calculations of the current-density and temperature profiles for structure layouts subjected to electromigration. The numerical method can be used for optimizing the layout so as to predetermine the location where electromigation leads to the formation of a gap.