ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present an implementation of the Atiyah-Bott residue formula for $\overline{M}_{0,m}(\mathbb{P}^{n},d)$. We use this implementation to compute a large number of Gromov-Witten invariants of genus $0$, including intersection numbers of rational curves on general complete intersections. We also compute some numbers of rational contact curves satisfying suitable Schubert conditions. Our computations confirm known predictions made by Mirror Symmetry. The code we developed for these problems is publicly available and can also be used for other types of computations.
In this paper we establish a generalization of Bombieri-Vinogradov theorem for primes represented by a fixed positive definite binary quadratic form. Then we apply this theorem to generalize a result of Vatwani on bounded gap between Gaussian primes.
Current-induced spin torques in layered magnetic heterostructures have many commonalities across broad classes of magnetic materials. These include not only collinear ferromagnets, ferrimagnets, and antiferromagnets, but also more complex noncollinear spin systems. We develop a general Lagrangian-Rayleigh approach for studying the role of dissipative torques, which can pump energy into long-wavelength magnetic dynamics, causing dynamic instabilities. While the Rayleigh structure of such torques is similar for different magnetic materials, their consequences depend sensitively on the nature of the order and, in particular, on whether there is a net magnetic moment. The latter endows the system with a unipolar switching capability, while magnetically compensated materials tend to evolve towards limit cycles, at large torques, with chirality dependent on the torque sign. Apart from the ferromagnetic and antiferromagnetic cases, we discuss ferrimagnets, which display an intricate competition between switching and limit cycles. As a simple case for compensated noncollinear order, we consider isotropic spin glasses, as well as a scenario of their coexistence with a collinear magnetic order.
This article establishes an algebraic error estimate for the stochastic homogenization of fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media. The approach is similar to that of Armstrong and Smart in the study of quantitative stochastic homogenization of uniformly elliptic equations.
We show that a bound system in momentum space can be treated like a gas of free elementary constituents and a collective excitation of a background field which represents the countless quantum fluctuations generating the binding potential. The distribution function of the internal momenta in the bound system at rest is given by the projection of the solution of a relativistic bound state equation on the free wave functions of the elementary constituents. The 4-momentum carried by the collective excitation is the difference between the bound state 4-momentum and the sum of the free 4-momenta. This definiton ensures the explicit fulfilment of Lorentz covariance, mass-shell constraints and single particle normalizability of the bound state function. The discussion is made for a two particle bound state and can be easily generalized to the case of three or more particles.
We present the X-ray and optical properties of the galaxy groups selected in the Chandra X-Bo\"otes survey. Our final sample comprises 32 systems at \textbf{$z<1.75$}, with 14 below $z = 0.35$. For these 14 systems we estimate velocity dispersions ($\sigma_{gr}$) and perform a virial analysis to obtain the radii ($R_{200}$ and $R_{500}$) and total masses ($M_{200}$ and $M_{500}$) for groups with at least five galaxy members. We use the Chandra X-ray observations to derive the X-ray luminosity ($L_X$). We examine the performance of the group properties $\sigma_{gr}$, $L_{opt}$ and $L_X$, as proxies for the group mass. Understanding how well these observables measure the total mass is important to estimate how precisely the cluster/group mass function is determined. Exploring the scaling relations built with the X-Bo\"otes sample and comparing these with samples from the literature, we find a break in the $L_X$-$M_{500}$ relation at approximately $M_{500} = 5\times10^{13}$ M$_\odot$ (for $M_{500} > 5\times10^{13}$ M$_\odot$, $M_{500} \propto L_X^{0.61\pm0.02}$, while for $M_{500} \leq 5\times10^{13}$ M$_\odot$, $M_{500} \propto L_X^{0.44\pm0.05}$). Thus, the mass-luminosity relation for galaxy groups cannot be described by the same power law as galaxy clusters. A possible explanation for this break is the dynamical friction, tidal interactions and projection effects which reduce the velocity dispersion values of the galaxy groups. By extending the cluster luminosity function to the group regime, we predict the number of groups that new X-ray surveys, particularly eROSITA, will detect. Based on our cluster/group luminosity function estimates, eROSITA will identify $\sim$1800 groups ($L_X = 10^{41}-10^{43}$ ergs s$^{-1}$) within a distance of 200 Mpc. Since groups lie in large scale filaments, this group sample will map the large scale structure of the local universe.
We present result from DECam SDSS i PSF photometry of the radial stellar density profiles of the Large Magellanic Cloud (LMC) old globular clusters (GCs) NGC1841, 2210, Hodge11 and Reticulum, which extent out of ~ 380 pc from their centres. We found that the studied LMC GCs would not seem to exhibit extended stellar structures like those frequently seen in Galactic globular clusters (GGCs), which could suggest that the LMC gravitational field has not been efficient in stripping stars off its GCs. The concentration parameter $c$ of the studied LMC GCs would seem to depend on both the internal dynamics and the position of the GC in the galaxy, as the Jacobi-to-cluster radius ratio does. When comparing them with GGCs with similar masses and age-to-half-mass relaxation times ratios, the studied LMC GCs would seem to have the smallest concentration parameter $c$ values and step aside of the GGC relationship in the core-to-half-light radius ratio ($r_c/r_h$) vs half-light-to-tidal radius ratio ($r_h/r_t$) plane. These observational differences could suggest that other conditions, like the gravitational potential of the host galaxy and/or the orbital parameters (e.g. halo- or disc- like orbits), could play some role in the evolution of the structural parameters of these two GC populations.
We outline the science case for extended radio emission and polarization in galaxy clusters which would be a scientifically important area of research for an upcoming Jansky Very Large Array Sky Survey. The survey would provide a major contribution in three key areas of the physics of clusters: 1) the active galactic nucleus population and the impact of feedback on the evolution of the intra-cluster medium, 2) the origin and evolution of diffuse cluster radio sources to probe the physics of mergers with implications for cosmology, and 3) the origin and role of magnetic fields in the ICM and in large scale structures. Considering all three areas, a survey must have sufficient spatial resolution to study the tailed galaxies which trace the cluster weather as well as the radio lobes driving energy into the cluster from the central AGN. The survey must also have sensitivity to low surface brightness emission and large angular scales to probe radio halos and relics as well as the WHIM residing in the large scale structure filaments. Finally, we note that full polarization information would be a highly valuable tool to probe a number of cluster-related issues. Due to the general steep spectral index of the emission we consider the survey is best suited to this science when conducted in P, L, or S bands. We conclude that the choices of S Band + D Configuration, L Band + C Configuration, and P Band + B Configuration offer optimal resolutions for constraining galactic interactions and feedback in cluster environments, while still probing large scale structure and the bulk cluster environment itself. While the push to probe higher redshifts and lower mass limits strongly favors a narrow and deep (or even targeted) survey strategy, we note that a wide survey covering roughly 1/4-2/3 of the sky will have significant scientific return, discovery potential, and archival value.
In the black-box model, problems constrained by a `promise' are the only ones that admit a quantum exponential speedup over the best classical algorithm in terms of query complexity. The most prominent example of this is the Deutsch-Jozsa algorithm. More recently, Wim van Dam put forward an algorithm for unstructured problems (i.e., those without a promise). We consider the Deutsch-Jozsa algorithm with a less restrictive (or `broken') promise and study the transition to an unstructured problem. We compare this to the success of van Dam's algorithm. These are both compared with a standard classical sampling algorithm. The Deutsch-Jozsa algorithm remains good as the problem initially becomes less structured, but the van Dam algorithm can be adapted so as to become superior to the Deutsch-Jozsa algorithm as the promise is weakened.
For any given real number $\alpha$ with bounded partial quotients, we construct explicitly continuum many real numbers $\beta$ with bounded partial quotients for which the pair $(\alpha, \beta)$ satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.
In this paper we compute the pullback of divisor classes under the Prym map (extended to the boundary), and apply this result to get a lower bound on the slope of effective divisors on the perfect cone compactification of the moduli space of principally polarized abelian fivefolds.   In the appendix by Klaus Hulek, the notion of slope for arbitrary toroidal compactifications is discussed, and the slope bound is shown to hold in general.
We discuss the use of information geometry in black hole physics and present the outcomes. The type of information geometry we utilize in this approach is the thermodynamic (Ruppeiner) geometry defined on the state space of a given thermodynamic system in equilibrium. The Ruppeiner geometry can be used to analyze stability and critical phenomena in black hole physics with results consistent with those from the Poincare stability analysis for black holes and black rings. Furthermore other physical phenomena are well encoded in the Ruppeiner metric such as the sign of specific heat and the extremality of the solutions. The black hole families we discuss in particular in this manuscript are the Myers-Perry black holes.
The Fermi Large Area Telescope (LAT) has observed more than a hundred of gamma-ray pulsars, about one third of which are radio-quiet, i.e. not detected at radio frequencies. The most of radio-loud pulsars are detected by Fermi LAT by using the radio timing models, while the radio-quiet ones are discovered in a blind search. The difference in the techniques introduces an observational selection bias and, consequently, the direct comparison of populations is complicated. In order to produce an unbiased sample, we perform a blind search of gamma-ray pulsations using Fermi-LAT data alone. No radio data or observations at optical or X-ray frequencies are involved in the search process. We produce a gamma-ray selected catalog of 25 non-recycled gamma-ray pulsars found in a blind search, including 16 radio-quiet and 9 radio-loud pulsars. This results in the direct measurement of the fraction of radio-quiet pulsars $\varepsilon_{RQ} = 64\pm 10\%$, which is in agreement with the existing estimates from the population modeling in the outer magnetosphere model. The Polar cap models are disfavored due to a lower expected fraction and the prediction of age dependence. The age, gamma-ray energy flux, spin-down luminosity and sky location distributions of the radio-loud and radio-quiet pulsars from the catalog do not demonstrate any statistically significant difference. The results indicate that the radio-quiet and radio-loud pulsars belong to one and the same population. The catalog shows no evidence for the radio beam evolution.
A colored space is the pair $(X,r)$ of a set $X$ and a function $r$ whose domain is $\binom{X}{2}$. Let $(X,r)$ be a finite colored space and $Y,Z\subseteq X$. We shall write $Y\simeq_r Z$ if there exists a bijection $f:Y\to Z$ such that $r(U)=r(f(U))$ for each $U\in\binom{Y}{2}$. We denote the numbers of equivalence classes with respect to $\simeq_r$ contained in $\binom{X}{2}$ and $\binom{X}{3}$ by $a_2(r)$ and $a_3(r)$, respectively. In this paper we prove that $a_2(r)\leq a_3(r)$ when $5\leq |X|$, and show what happens when the equality holds.
The X-ray/radio transient superluminal jet source GRO J1655-40 was recently suggested to contain a black hole from optical observations. Being a relatively close-by system (d \sim 3.2 kpc), it can likely provide us with rich information about the physics operating in both galactic and extragalactic jet sources. We present the first simultaneous broad band high energy observations of GRO J1655-40 during the 1995 July-August outburst by three instruments: ASCA, WATCH/GRANAT and BATSE/CGRO, in the energy band from 1 keV to 2 MeV. Our observations strengthen the interpretation that GRO J1655-40 contains a black hole. We detected a two-component energy spectrum, commonly seen from other galactic black hole binaries, but never detected from a neutron star system. Combining our results with the mass limits derived from optical radial velocity and orbital period measurements, we further constrain the mass of the central object to be between 3.3 and 5.8 M$_{\sun}$, above the well-established mass upper limit of 3.2 M$_{\sun}$ for a neutron star (the optical mass function for GRO J1655-40 is 3.16$\pm$0.2 M$_{\sun}$). This system is therefore the first galactic superluminal jet source for which there is strong evidence that the system contains a stellar mass black hole. The inclination angle of the binary system is constrained to be between 76 and 87 degrees, consistent with estimates obtained from optical light curves and radio jet kinematics.
We review two definitions of temperature in statistical mechanics, $T_B$ and $T_G$, corresponding to two possible definitions of entropy, $S_B$ and $S_G$, known as surface and volume entropy respectively. We restrict our attention to a class of systems with bounded energy and such that the second derivative of $S_B$ with respect to energy is always negative: the second request is quite natural and holds in systems of obvious relevance, i.e. with a number $N$ of degrees of freedom sufficiently large (examples are shown where $N \sim 100$ is sufficient) and without long-range interactions. We first discuss the basic role of $T_B$, even when negative, as the parameter describing fluctuations of observables in a sub-system. Then, we focus on how $T_B$ can be measured dynamically, i.e. averaging over a single long experimental trajectory. On the contrary, the same approach cannot be used in a generic system for $T_G$, since the equipartition theorem may be spoiled by boundary effects due to the limited energy. These general results are substantiated by the numerical study of a Hamiltonian model of interacting rotators with bounded kinetic energy. The numerical results confirm that the kind of configurational order realized in the regions at small $S_B$, or equivalently at small $|T_B|$, depends on the sign of $T_B$.
We report a comprehensive investigation of the lattice dynamics of URu$_2$Si$_2$ as a function of temperature using Raman scattering, optical conductivity and inelastic neutron scattering measurements as well as theoretical {\it ab initio} calculations. The main effects on the optical phonon modes are related to Kondo physics. The B$_{1g}$ ($\Gamma_3$ symmetry) phonon mode slightly softens below $\sim$100~K, in connection with the previously reported softening of the elastic constant, $C_{11}-C_{12}$, of the same symmetry, both observations suggesting a B$_{1g}$ symmetry-breaking instability in the Kondo regime. Through optical conductivity, we detect clear signatures of strong electron-phonon coupling, with temperature dependent spectral weight and Fano line shape of some phonon modes. Surprisingly, the line shapes of two phonon modes, E$_u$(1) and A$_{2u}$(2), show opposite temperature dependencies. The A$_{2u}$(2) mode loses its Fano shape below 150 K, whereas the E$_u$(1) mode acquires it below 100~K, in the Kondo cross-over regime. This may point out to momentum-dependent Kondo physics. By inelastic neutron scattering measurements, we have drawn the full dispersion of the phonon modes between 300~K and 2~K. No remarkable temperature dependence has been obtained including through the hidden order transition. {\it Ab initio} calculations with the spin-orbit coupling are in good agreement with the data except for a few low energy branches with propagation in the (a,b) plane.
We propose and investigate a procedure to measure, at least in principle, a positive quantum version of the local kinetic energy density. This procedure is based, under certain idealized limits, on the detection rate of photons emitted by moving atoms which are excited by a localized laser beam. The same type of experiment, but in different limits, can also provide other non positive-definite versions of the kinetic energy density. A connection with quantum arrival time distributions is discussed.
In this paper it is shown that if $\Omega \subset \mathbb{R}^N$ is an open, bounded Lipschitz set, and if $f: \Omega \times \mathbb{R}^{d \times N \times N} \rightarrow [0, \infty)$ is a continuous function with $f(x, \cdot)$ of linear growth for all $x \in \Omega$, then the relaxed functional in the space of functions of Bounded Hessian of the energy \[ F[u] = \int_{\Omega} f(x, \nabla^2u(x)) dx \] for bounded sequences in $W^{2,1}$ is given by \[ {\cal F}[u] = \int_\Omega {\cal Q}_2f(x, \nabla^2u) dx + \int_\Omega ({\cal Q}_2f)^{\infty}\bigg(x, \frac{d D_s(\nabla u)}{d |D_s(\nabla u)|} \bigg) d |D_s(\nabla u) |. \] This result is obtained using blow-up techniques and establishes a second order version of the $BV$ relaxation theorems of Ambrosio and Dal Maso and Fonseca and M\"uller. The use of the blow-up method is intended to facilitate future study of integrands which include lower order terms and applications in the field of second order structured deformations.
We present an automated system for detecting, tracking, and cataloging emerging active regions throughout their evolution and decay using SOHO Michelson Doppler Interferometer (MDI) magnetograms. The SolarMonitor Active Region Tracking (SMART) algorithm relies on consecutive image differencing to remove both quiet-Sun and transient magnetic features, and region-growing techniques to group flux concentrations into classifiable features. We determine magnetic properties such as region size, total flux, flux imbalance, flux emergence rate, Schrijver's R-value, R* (a modified version of R), and Falconer's measurement of non-potentiality. A persistence algorithm is used to associate developed active regions with emerging flux regions in previous measurements, and to track regions beyond the limb through multiple solar rotations. We find that the total number and area of magnetic regions on disk vary with the sunspot cycle. While sunspot numbers are a proxy to the solar magnetic field, SMART offers a direct diagnostic of the surface magnetic field and its variation over timescale of hours to years. SMART will form the basis of the active region extraction and tracking algorithm for the Heliophysics Integrated Observatory (HELIO).
Some instanton corrections to the universal hypermultiplet moduli space metric of the type-IIA string theory compactified on a Calabi-Yau threefold arise due to multiple wrapping of BPS membranes and fivebranes around certain cycles of Calabi-Yau. The classical universal hypermultipet metric is locally equivalent to the Bergmann metric of the symmetric quaternionic space SU(2,1)/U(2), whereas its generic quaternionic deformations are governed by the integrable SU(infinity) Toda equation. We calculate the exact (non-perturbative) UH metrics in the special cases of (i) the D-instantons (the wrapped D2-branes) in the absence of fivebranes, and (ii) the fivebrane instantons with vanishing charges, in the absence of D-instantons. The solutions of the first type preserve the U(1)xU(1) classical symmetry, while they can be interpreted as the gravitational dressing of the hyper-K"ahler D-instanton solutions. The second type solution preserves the non-abelian SU(2) classical symmetry, while it can be interpreted as a gradient flow in the universal hypermultiplet moduli space.
Several platforms are being considered as hardware for quantum technologies. For quantum computing (QC), superconducting qubits and artificially trapped ions are among the leading platforms, but many others also show promise, e.g. photons, cold atoms, defect centers including Rare-Earth (RE) ions. So far, results are limited to the regime of noisy intermediate scale qubits (NISQ), with a small number of qubits and a limited connectivity, and it is likely that future QC hardware will utilize several existing platforms in different ways. Thus, it currently makes sense to invest resources broadly and explore the full range of promising routes to quantum technology. Rare-earth ions in solids constitute one of the most versatile platforms for future quantum technology. One advantage is good coherence properties even when confined in strong natural traps inside a solid-state matrix. This confinement allows very high qubit densities and correspondingly strong ion-ion couplings. In addition, although their fluorescence is generally weak, cavity integration can enhance the emission greatly and enable very good connections to photonic circuits, including at the telecom wavelengths, making them promising systems for long-term scalability. The primary aim of this roadmap is to provide a complete picture of what components a RE quantum computer would consist of, to describe the details of all parts required to achieve a scalable system, and to discuss the most promising paths to reach it. In brief, we find that clusters of 50-100 single RE ions can act as high fidelity qubits in small processors, occupying only about (10 nm)^3. Due to the high capacity for integration of the RE systems, they be optically read out and connected to other such clusters for larger scalability. We make suggestions for future improvements, which could allow the REQC platform to be a leading one.
This paper has been removed by arXiv administrators because it plagiarizes gr-qc/0404032 and others.
This is the write-up of my lectures at the NATO Summer School held in Salamanca in June 1992. The paper deals with the problem of time in quantum gravity. All the major schemes are reviewed. Please note that the paper is in two parts for ease of email transmission; this is part 1. The mailer from gr-qc may further subdivide these two sections.