ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we generalize the construction of locally boosted black brane space time to higher derivative gravities. We consider the Gauss-Bonnet term (with coefficient $\alpha'$) as a toy example. We find the solution to the $\alpha'$ corrected Einstein equations to first order in the boundary derivative expansion. This allows us to find the $\alpha'$ corrections to the boundary stress tensor in the presence of the Gauss-Bonnet term in the bulk action. We therefore obtain the ratio of shear viscosity to entropy which agrees with other methods of computation in the literature.
Recent experiment by Zhinden et al (Phys. Rev {\bf A} 63 02111, 2001) purports to test compatibility between relativity and quantum mechanics in the classic EPR setting. We argue that relativity has no role in the EPR argument based solely on non-relativistic quantum formalism. It is suggested that this interesting experiment may have significance to address fundamental questions on quantum probability.
We present a morphological study of the galaxy population of the luminous X-ray cluster MS1054-03 at z=0.83. The sample consists of 81 spectroscopically confirmed cluster members in a 3 x 2 Mpc area imaged in F606W and F814W with WFPC2. We find thirteen ongoing mergers in MS1054-03, comprising 17% of the L > L* cluster population. Most of these mergers will likely evolve into luminous (\sim 2 L*) elliptical galaxies, and some may evolve into S0 galaxies. Assuming the galaxy population in MS1054-03 is typical for its redshift it is estimated that \sim 50% of present-day cluster ellipticals experienced a major merger at z < 1. The mergers are preferentially found in the outskirts of the cluster, and probably occur in small infalling clumps. Morphologies, spectra, and colors of the mergers show that their progenitors were typically E/S0s or early-type spirals with mean stellar formation redshifts z* \gtrsim 1.7. The red colors of the merger remnants are consistent with the low scatter in the color-magnitude relation in rich clusters at lower redshift. The discovery of a high fraction of mergers in this young cluster is direct evidence against formation of ellipticals in a single ``monolithic'' collapse at high redshift, and in qualitative agreement with predictions of hierarchical models for structure formation.
As an essential application of quantum mechanics in classical cryptography, quantum secret sharing has become an indispensable component of quantum internet. Recently, a differential phase shift quantum secret sharing protocol using a twin field has been proposed to break the linear rate-distance boundary. However, this original protocol has a poor performance over channels with asymmetric transmittances. To make it more practical, we present a differential phase shift quantum secret sharing protocol with asymmetric source intensities and give the security proof of our protocol against individual attacks. Taking finite-key effects into account, our asymmetric protocol can theoretically obtain the key rate two orders of magnitude higher than that of the original protocol when the difference in length between Alice's channel and Bob's is fixed at 14 km. Moreover, our protocol can provide a high key rate even when the difference is quite large and has great robustness against finite-key effects. Therefore, our work is meaningful for the real-life applications of quantum secret sharing.
High-mass microquasars are binary systems composed by a massive star and a compact object from which relativistic jets are launched. Regarding the companion star, observational evidence supports the idea that winds of hot stars are formed by clumps. Then, these inhomogeneities may interact with the jets producing a flaring activity. In the present contribution we study the interaction between a jet and a clump of the stellar wind in a high-mass microquasar. This interaction produces a shock in the jet, where particles may be accelerated up to relativistic energies. We calculate the spectral energy distributions of the dominant non-thermal processes: synchrotron radiation, inverse Compton scattering, and proton-proton collisions. Significant levels of X- and gamma-ray emission are predicted, with luminosities in the different domains up to ~ 10^{34} - 10^{35} erg/s on a timescale of about ~ 1 h. Finally, jet-clump interactions in high-mass microquasars could be detectable at high energies. These phenomena may be behind the fast TeV variability found in some high-mass X-ray binary systems, such as Cygnus X-1, LS 5039 and LS I+61 303. In addition, our model can help to derive information on the properties of jets and clumpy winds.
Boson stars are descendants of the so-called geons of Wheeler, except that they are built from scalar particles instead of electromagnetic fields. If scalar fields exist in nature, such localized configurations kept together by their self-generated gravitational field can form within Einstein's general relativity. In the case of complex scalar fields, an absolutely stable branch of such non-topological solitons with conserved particle number exists. Our present surge stems from the speculative possibility that these compact objects could provide a considerable fraction of the non-baryonic part of dark matter. In any case, they may serve as a convenient "laboratory" for studying numerically rapidly rotating bodies in general relativity and the generation of gravitational waves.
In this paper we consider the Euler-Poisson system (describing a plasma made of ions with a negligible ion temperature) on the Sobolev spaces $H^s(\R^3)$, $s > 5/2$. Using a geometric approach we show that for any time $T > 0$ the corresponding solution map, $(\rho_0,u_0) \mapsto (\rho(T),u(T))$, is nowhere locally uniformly continuous. On the other hand it turns out that the trajectories of the ions are analytic curves in $\R^3$.
After reformulate the incompressible Euler-$\alpha$ equations in 3D smooth domain with Drichlet data, we obtain the unique classical solutions to Euler-$\alpha$ equations exist in uniform time interval independent of $\alpha$. We also show the solution of the Euler-$\alpha$ converge to the corresponding solution of Euler equation in $L^2$ in space, uniformly in time. In the sequel, it follows that the $H^s$ $(s>\frac{n}{2}+1)$ solutions of Euler-$\alpha$ equations exist in any fixed sub-interval of the maximum existent interval for the Euler equations provided that initial is regular enough and $\alpha$ is small sufficiently.
The coalescence of double neutron star (NS-NS) and black hole (BH)-NS binaries are prime sources of gravitational waves (GW) for Advanced LIGO/Virgo and future ground-based detectors. Neutron-rich matter released from such events undergo rapid neutron capture (r-process) nucleosynthesis as it decompresses into space, enriching our universe with rare heavy elements like gold and platinum. Radioactive decay of these unstable nuclei powers a rapidly evolving, approximately isotropic thermal transient known as a ``kilonova', which probes the physical conditions during the merger and its aftermath. Here I review the history and physics of kilonovae, leading to the current paradigm of day-timescale emission at optical wavelengths from lanthanide-free components of the ejecta, followed by week-long emission with a spectral peak in the near-infrared (NIR). These theoretical predictions, as compiled in the original version of this review, were largely confirmed by the transient optical/NIR counterpart discovered to the first NS-NS merger, GW170817, discovered by LIGO/Virgo. Using a simple light curve model to illustrate the essential physical processes and their application to GW170817, I then introduce important variations about the standard picture which may be observable in future mergers. These include ~hours-long UV precursor emission, powered by the decay of free neutrons in the outermost ejecta layers or shock-heating of the ejecta by a delayed ultra-relativistic outflow; and enhancement of the luminosity from a long-lived central engine, such as an accreting BH or millisecond magnetar. Joint GW and kilonova observations of GW170817 and future events provide a new avenue to constrain the astrophysical origin of the r-process elements and the equation of state of dense nuclear matter.
In a recent paper, Moshe Jarden proposed a conjecture, later named the Kuykian conjecture, which states that if A is an abelian variety defined over a Hilbertian field K, then every intermediate field of K(A_{tor})/K is Hilbertian. We prove that the conjecture holds for Galois extensions of K in K(A_{tor}).
One of the most promising approaches for unsupervised learning is combining deep representation learning and deep clustering. Some recent works propose to simultaneously learn representation using deep neural networks and perform clustering by defining a clustering loss on top of embedded features. However, these approaches are sensitive to imbalanced data and out-of-distribution samples. As a consequence, these methods optimize clustering by pushing data close to randomly initialized cluster centers. This is problematic when the number of instances varies largely in different classes or a cluster with few samples has less chance to be assigned a good centroid. To overcome these limitations, we introduce a new unsupervised framework for joint debiased representation learning and image clustering. We simultaneously train two deep learning models, a deep representation network that captures the data distribution, and a deep clustering network that learns embedded features and performs clustering. Specifically, the clustering network and learning representation network both take advantage of our proposed statistics pooling block that represents mean, variance, and cardinality to handle the out-of-distribution samples and class imbalance. Our experiments show that using these representations, one can considerably improve results on imbalanced image clustering across a variety of image datasets. Moreover, the learned representations generalize well when transferred to the out-of-distribution dataset.
We prove a strengthening of Mui\'c's integral non-vanishing criterion for Poincar\'e series on unimodular locally compact Hausdorff groups and use it to prove a result on non-vanishing of L-functions associated to cusp forms of half-integral weight.
We investigate the degree of the polar transformations associated to a certain class of multi-valued homogeneous functions. In particular we prove that the degree of the pre-image of generic linear spaces by a polar transformation associated to a homogeneous polynomial $F$ is determined by the zero locus of $F$. For zero dimensional-dimensional linear spaces this was conjecture by Dolgachev and proved by Dimca-Papadima using topological arguments. Our methods are algebro-geometric and rely on the study of the Gauss map of naturally associated logarithmic foliations.
We discuss a question which appears in [S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bous Marie- Th\'eorie des topos et cohomologie \'etale des sch\'emas, Expos\'e XII, Remarks 6.13] concerning proper base change. In particular, we propose a solution in a particular non-affine case.
We consider generic MQCD configurations with matter described by semi-infinte D4-branes and softly broken supersymmetry. We show that the matter sector does not introduce supersymmetry breaking parameters so that the most relevant supersymmetry breaking operator at low energies is the gaugino mass term. By studying the run-away properties of these models in the decoupling limit of the adjoint matter, we argue that these softly broken MQCD configurations fail to capture the infrared physics of QCD at scales below the gaugino mass scale.
We propose a closed expression for the three loop anomalous dimension of a class of twist-3 operators built with gauge fields and covariant derivatives. To this aim, we solve the long-range Bethe Ansatz equations at finite spin and provide a consistent analytical formula obtained assuming maximal transcendentality violation as suggested by the known one-loop anomalous dimension. The final result reproduces the universal cusp anomalous dimension and obeys recursion relations inspired by the principle of reciprocity invariance.
A few characteristic exponents describing power law behaviors of roughness, coherence and persistence in stochastic time series are compared to each other. Relevant techniques for analyzing such time series are recalled in order to distinguish how the various exponents are measured, and what basic differences exist between each one. Financial time series, like the JPY/DEM and USD/DEM exchange rates are used for illustration, but mathematical ones, like (fractional or not) Brownian walks can be used also as indicated.
A permutation sigma in Sn is a k-derangement if for any subset X = {a1, . . ., ak} \subseteq [n], {sigma(a1), . . ., sigma(ak)} is not equal to X. One can form the k-derangement graph on the set of permutations of Sn by connecting two permutations sigma and tau if sigma(tau)^-1 is a k-derangement. We characterize when such a graph is connected or Eulerian. For n an odd prime power, we determine the independence, clique and chromatic number of the 2-derangement graph.
The close relationship between mergers and the reorientation of the spin for galaxies and their host dark haloes is investigated using a cosmological hydrodynamical simulation (Horizon-AGN). Through a statistical analysis of merger trees, we show that spin swings are mainly driven by mergers along the filamentary structure of the cosmic web, and that these events account for the preferred perpendicular orientation of massive galaxies with respect to their nearest filament. By contrast, low-mass galaxies (M_s<10^10 M_sun at redshift 1.5) undergoing very few mergers, if at all, tend to possess a spin well aligned with their filament. Haloes follow the same trend as galaxies but display a greater sensitivity to smooth anisotropic accretion. The relative effect of mergers on spin magnitude is qualitatively different for minor and major mergers: mergers (and diffuse accretion) generally increase the magnitude of the angular momentum, but the most massive major mergers also give rise to a population of objects with less spin left. Without mergers secular accretion builds up the spin of galaxies but not that of haloes. It also (re)aligns galaxies with their filament.
We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting the parameter of the exponential time tend to zero it is seen that these results connect to the corresponding results for excursions of stationary diffusions (in stationary state). We characterize also the laws of the diffusion prior and posterior to the last zero before the exponential time. It is proved using Krein's representations that, e.g., the law of the length of the excursion straddling an exponential time is infinitely divisible. As an illustration of the results we discuss Ornstein-Uhlenbeck processes.
In this paper we classify non-symplectic automorphisms of order 8 on complex K3 surfaces in case that the fourth power of the automorphism has only rational curves in its fixed locus. We show that the fixed locus is the disjoint union of a rational curve and 10 isolated points or it consists in 4 isolated fixed points. We give examples corresponding to the case with a rational curve in the fixed locus and to the case with only isolated points in the fixed locus.
A new duality relation is derived for the Potts model in one dimension. It is shown that the partition function is self-dual with the nearest-neighbor interaction and the external field appearing as dual parameters. Zeroes of the partition function are analyzed. Particularly, we show that the new duality relation implies a circle theorem in the complex temperature plane for the one-dimensional Ising model.
The thermodynamic, kinetic and magnetic properties of the hydrogen monomer on doped graphene layers were studied by ab initio simulations. Electron doping was found to heighten the diffusion potential barrier, while hole doping lowers it. However, both kinds of dopings heighten the desorption potential barrier. The underlying mechanism was revealed by investigating the effect of doping on the bond strength of graphene and on the electron transfer and the coulomb interaction between the hydrogen monomer and graphene. The kinetic properties of H and D monomers on doped graphene layers during both the annealing process (annealing time $t_0 =$300 s) and the constant-rate heating process (heating rate $\alpha =$1.0 K/s) were simulated. Both electron and hole dopings were found to generally increase the desorption temperatures of hydrogen monomers. Electron doping was found to prevent the diffusion of hydrogen monomers, while the hole doping enhances their diffusion. Macroscopic diffusion of hydrogen monomers on graphene can be achieved when the doping-hole density reaches $5.0\times10^{13}$ cm$^{-2}$. The magnetic moment and exchange splitting were found to be reduced by both electron and hole dopings, which was explained by a simple exchange model. The study in this report can further enhance the understanding of the interaction between hydrogen and graphene and is expected to be helpful in the design of hydrogenated-graphene-based devices.
By carrying out Monte Carlo simulations based on the two-species atomic-scale kinetic growth model of GaAs(001) homoepitaxy and comparing the results with scanning tunneling microscope images, we show that initial growing islands undergo the structural transformation before adopting the proper beta2(2x4) reconstruction.
We discuss the Giardin\`a-Kurchan-Peliti population dynamics method for evaluating large deviations of time averaged quantities in Markov processes [Phys. Rev. Lett. \textbf{96}, 120603 (2006)]. This method exhibits systematic errors which can be large in some circumstances, particularly for systems with weak noise, with many degrees of freedom, or close to dynamical phase transitions. We show how these errors can be mitigated by introducing control forces within the algorithm. These forces are determined by an iteration-and-feedback scheme, inspired by multicanonical methods in equilibrium sampling. We demonstrate substantially improved results in a simple model and we discuss potential applications to more complex systems.
Consider exponential Carmichael function $\lambda^{(e)}$ such that $\lambda^{(e)}$ is multiplicative and $\lambda^{(e)}(p^a) = \lambda(a)$, where $\lambda$ is usual Carmichael function. We discuss the value of $\sum \lambda^{(e)}(n)$, where $n$ runs over certain subsets of $[1,x]$, and provide bounds on the error term, using analytic methods and especially estimates of $\int_1^T \bigl| \zeta(\sigma+it) \bigr|^m dt$.
We present the simplest model that permits a largely analytical exploration of the m=1 counter-rotating instability in a "hot" nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using WKB. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian disc must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.
We first formulate, in the framework of effective Lagrangian, the general form of the effective interactions of the lightest Higgs boson h and a heavier neutral Higgs boson H in a multi-Higgs system taking account of Higgs mixing effect. We regard h as the discovered Higgs boson which has been shown to be consistent with the standard model (SM) Higgs boson. The obtained effective interactions contain extra parameters reflecting the Higgs mixing effect. Next, We study the constraints on the anomalous coupling constants of H from both the requirement of the unitarity of the S matrix and the exclusion bounds on the SM Higgs boson obtained from the experimental data at the 7--8 TeV LHC. From this we obtain the available range of the anomalous coupling constants of H, with which H is not excluded by the yet known theoretical and experimental constraints. We then study the signatures of H at the 14 TeV LHC. In this paper, we suggest taking weak-boson scattering and pp to VH* to VVV as sensitive processes for probing H model independently at the 14 TeV LHC. We take several examples with the anomalous HVV coupling constants in the available ranges to do the numerical study. a full tree-level calculation at the hadron level is given with signals and backgrounds carefully calculated. We impose a series of proper kinematic cuts to effectively suppress the backgrounds. It is shown that, in both the VV scattering and the pp to VH* to VVV processes, H boson can be discovered from the invariant mass distributions of the final state particles with reasonable integrated luminosity. Especially, in the pp to VH* to VVV process, the invariant mass distribution of the final state jets can show a clear resonance peak of H. Finally, we propose several physical observables from which the values of the anomalous coupling constants f_W and f_{WW} can be measured experimentally.
The questions of whether a photon can be localized in an arbitrarily small volume and what is the allowable strength of that localization (the decrease with distance of the functional form) are questions of current interest. We propose a measure of localization for the single photon that is the expectation values of the electromagnetic field strength components in a coherent wavepacket state of mean photon number unity. As such, we deal with real quantities that have a physical meaning rather than complex amplitudes. It is seen that the real parts of complex amplitudes proposed previously as measures of localization are equal to our field expectations. With this measure, we examine two test states. The first has a well-resolved momentum. The field expectations show Gaussian (quadratic exponential) localization in all directions, although the localization length scale is much larger than the mean wavelength. For the other test state, with a spherically symmetric momentum distribution, we find almost exponential localization in all directions at t = 0. The profiles are scale invariant, so choosing the momentum width very large would make the localization length arbitrarily small. We conclude that there is no lower bound on the localization length scale of a photon as determined by this measure.
In the last ten years significant advances have been made in our understanding and ability to compute and predict properties of ferroelectrics and piezoelectrics using fundamental physics. Phase diagrams, electromechanical and elastic properties, and effects of defects and surfaces are now amenable to computation. Most importantly, new techniques have been developed, and new understanding of the meaning of polarization in dielectrics has been developed. Prospects for the future are discussed.
This paper presents an overview of the topology of D-Wave's next-generation quantum processors. It provides examples of minor embeddings and discusses performance of embedding algorithms for the new topology compared to the existing Chimera topology. It also presents some initial performance results for simple, standard Ising model classes of problems.