ShantanuT01/DACTYL-Pretraining huggingface dataset:
While the Kobayashi--Maskawa single phase origin of CP violation passed its first crucial precision test in $B\to J/\psi K_S$, the chirality of weak $b$-quark couplings has not yet been carefully tested. We discuss recent proposals for studying the chiral and CP-violating structure of these couplings in radiative and in hadronic B decays.
We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained in a so-called uniform gauge which is related to the static gauge by a 2d duality transformation. The Hamiltonian is of the Nambu type and depends on two parameters: a single S^5 angular momentum J and the string tension \lambda. In the general case both parameters can be finite. The space of string states consists of short and long strings. In the sector of short strings the large J expansion with \lambda'=\lambda/J^2 fixed recovers the plane-wave Hamiltonian and higher-order corrections recently studied in the literature. In the strong coupling limit \lambda\to \infty, J fixed, the energy of short strings scales as \sqrt[4]{\lambda} while the energy of long strings scales as \sqrt{\lambda}. We further show that the gauge-fixed Hamiltonian is integrable by constructing the corresponding Lax representation. We discuss some general properties of the monodromy matrix, and verify that the asymptotic behavior of the quasi-momentum perfectly agrees with the one obtained earlier for some specific cases.
A multi-epoch X-ray spectral and variability analysis is conducted for the narrow-line Seyfert 1 (NLS1) active galactic nucleus (AGN) Mrk 478. All available X-ray data from XMM-Newton and Suzaku satellites, spanning from 2001 to 2017, are modelled with a variety of physical models including partial covering, soft-Comptonisation, and blurred reflection, to explain the observed spectral shape and variability over the 16 years. All models are a similar statistical fit to the data sets, though the analysis of the variability between data sets favours the blurred reflection model. In particular, the variability can be attributed to changes in flux of the primary coronal emission. Different reflection models fit the data equally well, but differ in interpretation. The use of reflionx predicts a low disc ionisation and power law dominated spectrum, while relxill predicts a highly ionised and blurred reflection dominated spectrum. A power law dominated spectrum might be more consistent with the normal X-ray-to-UV spectral shape (aox). Both blurred reflection models suggest a rapidly spinning black hole seen at a low inclination angle, and both require a sub-solar (~0.5) abundance of iron. All physical models require a narrow emission feature at 6.7 keV likely attributable to Fe xxv emission, while no evidence for a narrow 6.4 keV line from neutral iron is detected.
We study gaugino condensation in presence of an anomalous $U(1)$ gauge group and find that global supersymmetry is dynamically broken. An example of particular interest is provided by effective string models with 4-dimensional Green-Schwarz anomaly cancellation mechanism. The structure of the hidden sector is constrained by the anomaly cancellation conditions and the scale of gaugino condensation is shifted compared with the usual case. We explicitly compute the resulting soft supersymmetry breaking terms.
We study the large deviations of sums of correlated random variables described by a matrix product ansatz, which generalizes the product structure of independent random variables to matrices whose non-commutativity is the source of correlations. We show with specific examples that different large deviation behaviors can be found with this ansatz. In particular, it is possible to construct sums of correlated random variables that violate the Law of Large Numbers, the Central Limit Theorem, as well as sums that have nonconvex rate functions or rate functions with linear parts or plateaux.
The phase transition to a deconfined phase is studied and the consequences in the formation of neutron stars are investigated. We use the quark-meson-coupling model for the hadron matter and the MIT Bag model for the quark matter in order to build the appropriate equations of state for the hybrid stars. The properties of the stars are then calculated. The differences between unpaired and color-flavor locked quark matter are discussed.
We consider the Hall effect in a system of weakly coupled one-dimensional chains with Luttinger interaction within each chain. We construct a perturbation theory in the inter-chain hopping term and find that there is a power law dependence of the Hall conductivity on the magnetic field with an exponent depending on the interaction constant. We show that this perturbation theory becomes valid if the magnetic field is sufficiently large.
We investigate the contribution of the low-energy electronic excitations towards the Raman spectrum of bilayer graphene for the incoming photon energy Omega >> 1eV. Starting with the four-band tight-binding model, we derive an effective scattering amplitude that can be incorporated into the commonly used two-band approximation. Due to the influence of the high-energy bands, this effective scattering amplitude is different from the contact interaction amplitude obtained within the two-band model alone. We then calculate the spectral density of the inelastic light scattering accompanied by the excitation of electron-hole pairs in bilayer graphene. In the absence of a magnetic field, due to the parabolic dispersion of the low-energy bands in a bilayer crystal, this contribution is constant and in doped structures has a threshold at twice the Fermi energy. In an external magnetic field, the dominant Raman-active modes are the n_{-} to n_{+} inter-Landau-level transitions with crossed polarisation of in/out photons. We estimate the quantum efficiency of a single n_{-} to n_{+} transition in the magnetic field of 10T as I_{n_{-} to n_{+}}~10^{-12}.
We associate to each automorphism of the plane, a geometric construction with some properties, it is the {\it{canonical resolution}}.   We study the geometry of the canonical resolution, we deduce from it an upper bound for a geometric invariant (the ample index) linked to an automorphism of the affine plane and we link the structure of the effective cone of the surface we get to values of another geometric invariant (the effective index).
It is well-known that in order to make the action well defined, one may employ different kinds of boundary conditions (BCs) accompanied by the appropriate Gibbons-Hawking-York (GHY) terms. In this paper we investigate the role of the selected BC and the corresponding GHY terms on the black hole (BH) entropy. Our result shows, regardless of the kind of BC, the BH entropy in all cases is the same as one obtained under Dirichlet BC from Wald formula or semi-classical approximation method. We considered the Schwarzschild solution for $f(R)$-gravity and general relativity (GR) in standard dimensions as special models.
A major question in galaxy formation is how the gas supply that fuels activity in galaxies is modulated by their environment. We use spectroscopy of a set of well characterized clusters and groups at $0.4<z<0.8$ from the ESO Distant Cluster Survey (EDisCS) and compare it to identically selected field galaxies. Our spectroscopy allows us to isolate galaxies that are dominated by old stellar populations. Here we study a stellar-mass limited sample ($\log(M_*/M_\odot)>10.4$) of these old galaxies with weak [OII] emission. We use line ratios and compare to studies of local early type galaxies to conclude that this gas is likely excited by post-AGB stars and hence represents a diffuse gas component in the galaxies. For cluster and group galaxies the fraction with EW([OII])$>5$\AA\ is $f_{[OII]}=0.08^{+0.03}_{-0.02}$ and $f_{[OII]}=0.06^{+0.07}_{-0.04}$ respectively. For field galaxies we find $f_{[OII]}=0.27^{+0.07}_{-0.06}$, representing a 2.8$\sigma$ difference between the [OII] fractions for old galaxies between the different environments. We conclude that a population of old galaxies in all environments has ionized gas that likely stems from stellar mass loss. In the field galaxies also experience gas accretion from the cosmic web and in groups and clusters these galaxies have had their gas accretion shut off by their environment. Additionally, galaxies with emission preferentially avoid the virialized region of the cluster in position-velocity space. We discuss the implications of our results, among which is that gas accretion shutoff is likely effective at group halo masses (log~${\cal M}/$\msol$>12.8$) and that there are likely multiple gas removal processes happening in dense environments.
The details of the calculation of the two-boson exchange effects in the parity-violating elastic $ep$ scattering within a simple hadronic model, including both the nucleon and $\Delta(1232)$-resonance intermediate states, are presented. We examine the sensitivity of our results with respect to choice of form factors. We emphasize the importance to use correct relations relating N to $\Delta$ and $\Delta$ to N transition vertex functions. The $N\Delta$ Coulomb quadrupole transition is found to play important role at higher $Q^2\geq 3.0$ GeV$^2$. We also elucidate the relation between our results and the well-known result on the $\gamma ZE$ effect given by Marciano and Sirlin (MS). The effect of the nucleon contribution $\delta_N$ to parity-asymmetry $A_{PV}$, is found to be in general, larger than the corresponding $\Delta$ contribution $\delta_\Delta$ except at extreme forward angles. The corrections to the extracted values of the strange form factors $G^{s}_{E}+\beta G^{s}_{M}$ from the HAPPEX, A4, and G0 data are also presented. The total TBE corrections to the extracted values of $G^{s}_{E}+\beta G^{s}_{M}$ in recent experiments of HAPPEX G0, and A4 are, depending on kinematics, found to be small except in a few cases where they range from -20.6% to $48.3 %$.
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the previous one.
In this paper we consider the barotropic compressible quantum Navier-Stokes equations with a linear density dependent viscosity and its limit when the scaled Planck constant vanish. Following recent works on degenerate compressible Navier-Stokes equations, we prove the global existence of weak solutions by the use of a singular pressure close to vacuum. With such singular pressure, we can use the standard definition of global weak solutions which also allows to justify the limit when the scaled Planck constant denoted by $\epsilon$ tends to 0.
Computing the clique number and chromatic number of a general graph are well-known NP-Hard problems. Codenotti et al. (Bruno Codenotti, Ivan Gerace, and Sebastiano Vigna. Hardness results and spectral techniques for combinatorial problems on circulant graphs. \emph{Linear Algebra Appl.}, 285(1-3): 123--142, 1998) showed that computing clique number and chromatic number are still NP-Hard problems for the class of circulant graphs. We show that computing clique number is NP-Hard for the class of Cayley graphs for the groups $G^n$, where $G$ is any fixed finite group (e.g., cubelike graphs). We also show that computing chromatic number cannot be done in polynomial time (under the assumption $\text{P}\neq \text{NP}$) for the same class of graphs. Our presentation uses free Cayley graphs. The proof combines free Cayley graphs with quotient graphs and Goppa codes.
We use the integral form of the Boltzmann equation which allows us to take into account the memory effects using the initial condition that selects the solutions going to the local equilibrium Maxwell distribution in the $t \to -\infty$ limit. Implementing the relaxation-time approximation for the collision integral (BGK-equation) we present the derivation of the hyperbolic Navier-Stokes and the hyperbolic heat conduction equations in the first order approximation. It is shown that the relaxation time in the obtained hyperbolic equations is the Maxwellian relaxation time. As special case we obtain the telegraph equation for the heat propagation in static medium and estimate the relaxation time for the heat conduction in some materials.
In a stationary axisymmetric spacetime, the angular velocity of a stationary observer that Fermi-Walker transports its acceleration vector is also the angular velocity that locally extremizes the magnitude of the acceleration of such an observer, and conversely if the spacetime is also symmetric under reversing both t and phi together. Thus a congruence of Nonrotating Acceleration Worldlines (NAW) is equivalent to a Stationary Congruence Accelerating Locally Extremely (SCALE). These congruences are defined completely locally, unlike the case of Zero Angular Momentum Observers (ZAMOs), which requires knowledge around a symmetry axis. The SCALE subcase of a Stationary Congruence Accelerating Maximally (SCAM) is made up of stationary worldlines that may be considered to be locally most nearly at rest in a stationary axisymmetric gravitational field. Formulas for the angular velocity and other properties of the SCALEs are given explicitly on a generalization of an equatorial plane, infinitesimally near a symmetry axis, and in a slowly rotating gravitational field, including the weak-field limit, where the SCAM is shown to be counter-rotating relative to infinity. These formulas are evaluated in particular detail for the Kerr-Newman metric. Various other congruences are also defined, such as a Stationary Congruence Rotating at Minimum (SCRAM), and Stationary Worldlines Accelerating Radially Maximally (SWARM), both of which coincide with a SCAM on an equatorial plane of reflection symmetry. Applications are also made to the gravitational fields of maximally rotating stars, the Sun, and the Solar System.
We report on the first application of the Alcock-Paczynski test to stacked voids in spectroscopic galaxy redshift surveys.We use voids from the Sutter et al. (2012) void catalog, which was derived from the Sloan Digital Sky Survey Data Release 7 main sample and luminous red galaxy catalogs. The construction of that void catalog removes potential shape measurement bias by using a modified version of the ZOBOV algorithm and by removing voids near survey boundaries and masks. We apply the shape-fitting procedure presented in Lavaux & Wandelt (2012) to ten void stacks out to redshift z=0.36. Combining these measurements, we determine the mean cosmologically induced "stretch" of voids in three redshift bins, with 1-sigma errors of 5-15%. The mean stretch is consistent with unity, providing no indication of a distortion induced by peculiar velocities. While the statistical errors are too large to detect the Alcock-Paczynski effect over our limited redshift range, this proof-of-concept analysis defines procedures that can be applied to larger spectroscopic galaxy surveys at higher redshifts to constrain dark energy using the expected statistical isotropy of structures that are minimally affected by uncertainties in galaxy velocity bias.
We construct a vector bundle $E$ on a smooth complex projective surface $X$ with the property that the restriction of $E$ to any smooth closed curve in $X$ admits an algebraic connection while $E$ does not admit any algebraic connection.
Measurements of the lateral distribution of Cherenkov photons with the wide-angle atmospheric Cherenkov light detector array AIROBICC and of the charged particle lateral distribution with the scintillator matrix of the HEGRA air-shower detector complex in air showers are reported. With the atmospheric shower-front sampling technique these detectors measure the electromagnetic component of an extensive air shower via the lateral density distribution of the shower particles and of the Cherenkov photons. The data are compared with events generated with the CORSIKA program package with the QGSJET hadronic-event generator. Consistency checks performed with primary energy-reconstruction methods based on different shower observables indicate satisfactory agreement between these extensive air shower simulations and the experimental data. The energy spectrum features a so called ``knee'' at an energy of E_knee = 3.98 (+4.66) (-0.83) (stat) +- 0.53 (syst) PeV. Power law fits to the differential energy spectrum yield indices of -2.72 (+0.02)(-0.03) (stat) +- 0.07 (syst) below, and -3.22 (+0.47) (-0.59) (stat) +- 0.08 (syst)} above the knee. The best-fit elongation rate for the whole energy range is determined to 78.3 +- 1.0 (stat) +- 6.2 (syst) g/cm^2. At the highest energies it seems to decrease slightly.The best-fit fraction of light nuclei decreases from 37 (+28) (-21) % (combined statistical and systematic) to 8 (+32) (-8) % (combined statistical and systematic) in the energy range discussed here. A detailed study of the systematic errors reveals that a non-changing composition cannot be excluded.
These lecture notes are a concise introduction of recent techniques to prove local spectral universality for a large class of random matrices. The general strategy is presented following the recent book with H.T. Yau. We extend the scope of this book by focusing on new techniques developed to deal with generalizations of Wigner matrices that allow for non-identically distributed entries and even for correlated entries. This requires to analyze a system of nonlinear equations, or more generally a nonlinear matrix equation called the Matrix Dyson Equation (MDE). We demonstrate that stability properties of the MDE play a central role in random matrix theory. The analysis of MDE is based upon joint works with J. Alt, O. Ajanki, D. Schr\"oder and T. Kr\"uger that are supported by the ERC Advanced Grant, RANMAT 338804 of the European Research Council.   The lecture notes were written for the 27th Annual PCMI Summer Session on Random Matrices held in 2017. The current edited version will appear in the IAS/Park City Mathematics Series, Vol. 26.
We study existence and regularity of the density for the solution $u(t,x)$ (with fixed $t > 0$ and $x \in D$) of the heat equation in a bounded domain $D \subset \mathbb R^d$ driven by a stochastic inhomogeneous Neumann boundary condition with stochastic term. The stochastic perturbation is given by a fractional Brownian motion process. Under suitable regularity assumptions on the coefficients, by means of tools from the Malliavin calculus, we prove that the law of the solution has a smooth density with respect to the Lebesgue measure in $\mathbb R$.
Recently Kamath et al. (2021) analysed Gaia EDR3 data of eighteen post-AGB supergiants with overabundance of s-process elements. For some of these stars in their sample they find unusually very low absolute luminosities which is not in agreement with the s-process nucleosynthesis on the AGB stage of evolution. It appears that they have not taken into account the RUWE values of these stars. I have taken a look at the RUWE values of these eighteen post-AGB stars with over abundance of s-process elements. Of the eighteen stars thirteen have RUWE values much greater than 1.4 and hence their distances (absolute luminosities) are not reliable. As per the study of Stassun and Torres (2021) stars with Gaia EDR3 RUWE values greater than 1.4 are most likely unresolved binaries in Gaia data base. Thus some of the s-process rich post-AGB stars are most likely contain unresolved low-mass binary companions. Only five stars (IRAS 07134+1005, IRAS 08143-4406, IRAS 12360-5740, IRAS 19500-1709 and IRAS 22272+5435) of these eighteen s-process rich stars have accurate Gaia EDR3 parallaxes and RUWE values less than 1.4 and their absolute luminosities are in agreement with the post-AGB evolutionary tracks.
The Markov commutator associated to a finite Markov kernel P is the convex semigroup consisting of all Markov kernels commuting with P. Its interest comes from its relation with the hypergroup property and with the notion of Markovian duality by intertwining. In particular, it is shown that the discrete analogue of the Achour-Trim{\`e}che's theorem, asserting the preservation of non-negativity by the wave equations associated to certain Metropolis birth and death transition kernels, cannot be extended to all convex potentials. But it remains true for symmetric and monotone convex potentials. Keywords: finite Markov kernels, Markov commutator, symmetry group of a Markov kernel, hypergroup property, duality by intertwining, Achour-Trim{\`e}che theorem, birth and death chains, Metropolis algorithms, one-dimensional discrete wave equations.
Each voter $i \in I$ has $\alpha_i$ cards that (s)he distributes among the candidates $a \in A$ as a measure of approval. One (or several) candidate(s) who received the maximum number of cards is (are) elected. We provide polynomial algorithms to recognize voting forms and voting correspondences generated by such voting schemes in cases when either the number of candidates or the number of voters is equal to $2$. We prove that for two voters, if $\alpha_2 \geq \alpha_1-2\geq 0$ then the unique voting correspondence has distinct rows. We also characterize voting forms with distinct rows.
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the paper, simulations between quantum branching programs and nonuniform quantum Turing machines are presented which allow to transfer lower and upper bound results between the two models. In the second part of the paper, different variants of quantum OBDDs are compared with their deterministic and randomized counterparts. In the third part, quantum branching programs are considered where the performed unitary operation may depend on the result of a previous measurement. For this model a simulation of randomized OBDDs and exponential lower bounds are presented.
We consider the spatially inhomogeneous quantum Boltzmann equation for bosons with a singular collision kernel, the weak-coupling limit of a large system of Bose-Einstein particles interacting through inverse power law. Global well-posedness of the corresponding Cauchy problem is proved in a periodic box near equilibrium for initial data satisfying high temperature condition.
A recently published paper by Nielsen, Guffanti and Sarkar argues that the evidence for cosmic acceleration is marginal and that a coasting universe - the Milne Universe - fits the same supernovae data in a Hubble diagram nearly as well. The Milne Universe has negative spatial curvature. Nevertheless, we confirm that the Milne model fits the data just as well as LCDM. We show that this unexpected result points to a weakness in the Hubble diagram rather than to a flaw in LCDM. It seems the Hubble diagram is insensitive to spatial curvature. Here we present the data and both models in a scale factor vs. cosmological time plot.This plot is exquisitely sensitive to spatial curvature because one of three unique transformations, for each of curvatures 0,+1,-1, is applied to transform from the Hubble diagram. Although the Milne negative curvature did not matter much in the Hubble diagram, it matters critically in the scale factor plot. Given that space is flat as measured by precise CMB observations, we find that when the SNe data, the LCDM model and the Milne model are plotted as scale factor vs. cosmological time the two resulting curves separate at 2 sigma above the noise- ten times their separation above the noise in the Hubble diagram. The transformed data fit to the LCDM model confirms, at a 95% confidence level, that the universe is accelerating and the Milne coasting universe is ruled out.