ShantanuT01/DACTYL-Pretraining huggingface dataset:
An analysis of the solutions for the field equations of generalized scalar-tensor theories of gravitation is performed through the study of the geometry of the phase space and the stability of the solutions, with special interest in the Brans-Dicke model. Particularly, we believe to be possible to find suitable forms of the Brans-Dicke parameter omega and potential V of the scalar field, using the dynamical systems approach, in such a way that they can be fitted in the present observed scenario of the Universe.
This paper explores the moduli-dependent coefficients of higher derivative interactions that appear in the low-energy expansion of the four-graviton amplitude of maximally supersymmetric string theory compactified on a d-torus. These automorphic functions are determined for terms up to order D^6R^4 and various values of d by imposing a variety of consistency conditions. They satisfy Laplace eigenvalue equations with or without source terms, whose solutions are given in terms of Eisenstein series, or more general automorphic functions, for certain parabolic subgroups of the relevant U-duality groups. The ultraviolet divergences of the corresponding supergravity field theory limits are encoded in various logarithms, although the string theory expressions are finite. This analysis includes intriguing representations of SL(d) and SO(d,d) Eisenstein series in terms of toroidally compactified one and two-loop string and supergravity amplitudes.
We generalize holographic bit threads to bulk theories with a gravitational action containing higher-curvature terms. Bit threads are a reformulation of holographic entanglement entropy, where the entropy is given by the maximum number of threads emanating from a boundary region into the bulk. We show that the addition of higher-curvature terms adds corrections to the bit thread thickness that depend on the local geometry and thread orientation. Two different methods are given: determination of the density bound by requiring the maximum number of threads through a given surface to reproduce the entanglement entropy functional on that surface, and application of Lagrange dualization. The results of the two methods are applied to Gauss-Bonnet gravity as the simplest non-trivial example.
We present an exhaustive class of states with quantum backflow -- the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. They are characterized by a general function of momenta subject to very weak conditions. Such a family of states is of interest in the light of a recent experimental proposal to measure backflow. We find one particularly simple state which has surprisingly large backflow -- about 41 percent of the lower bound on flux derived by Bracken and Melloy. We study the eigenstates of a regularized current operator and we show how some of these states, in a certain limit, lead to our class of backflow states. This limit also clarifies the correspondence between the spectrum of the regularized current operator, which has just two non-zero eigenvalues in our chosen regularization, and the usual current operator.
We present the matching condition for the strong coupling contant alpha_s at a heavy quark threshold to four loops in the modified minimal subtraction scheme. Our results lead to further decrease of the theoretical uncertainty of the evolution of the strong coupling constant through heavy quark thresholds. Using a low energy theorem we furthermore derive the effective coupling of the Higgs boson to gluons (induced by a virtual heavy quark) in four- and (partially) through five-loop approximation.
We study (higher order) asymptotic behaviour near branch points of stationary $n$-dimensional two-valued $C^{1, \mu}$ graphs in an open subset of ${\mathbb R}^{n+m}$. Specifically, if $M$ is the graph of a two-valued $C^{1, \mu}$ function $u$ on an open subset $\Omega \subset {\mathbb R}^{n}$ taking values in the space of un-ordered pairs of points in ${\mathbb R}^{m}$, and if the integral varifold $V = (M, \theta),$   where the multiplicity function $\theta \, : \, M \rightarrow \{1, 2\}$ is such that $\theta =2$ on the set where the two values of $u$ agree and $\theta =1$ otherwise, is stationary in $\Omega \times {\mathbb R}^{m}$ with respect to the mass functional, we show that at ${\mathcal H}^{n-2}$-a.e.\ point $Z$ along its branch locus $u$ decays asymptotically, modulo its single valued average, to a unique non-zero two-valued cylindrical harmonic tangent function $\varphi^{(Z)}$ which is homogeneous of some degree $\geq 3/2$. As a corollary, we obtain that the branch locus of $u$ is countably $(n-2)$-rectifiable, and near points $Z$ where the degree of homogeneity of $\varphi^{(Z)}$ is equal to $3/2$, the branch locus is an embedded real analytic submanifold of dimension $n-2$. These results, combined with the recent works \cite{M} and \cite{MW}, imply a stratification theorem for the (relatively open) set of density $< 3$ points of a stationary codimension 1 integral $n$-varifold with stable regular part and no triple junction singularities.
The process of quantum creation of a qusihomogeneous inflationary universe near a cosmological singularity is considered. It is shown that during the evolution quantum fluctuations of spatial topologies increase and the universe acquires homogeneous and isotropic character on arbitrary large distances.
Medium resolution J-band spectroscopy of individual red supergiant stars is a promising tool to investigate the chemical composition of the young stellar population in star forming galaxies. As a continuation of recent work on iron and titanium, detailed non-LTE calculations are presented to investigate the influence of NLTE on the formation of silicon lines in the J-band spectra of red supergiants. Substantial effects are found resulting in significantly stronger absorption lines of neutral silicon in non-LTE. As a consequence, silicon abundances determined in non-LTE are significantly smaller than in LTE with the non-LTE abundance corrections varying smoothly between -0.4 dex to -0.1 dex for effective temperatures between 3400K to 4400K. The effects are largest at low metallicity. The physical reasons behind the non-LTE effects and the consequences for extragalactic J-band abundance studies are discussed.
We present a new dynamical picture that identifies the formation of the exotic $\bar c c$-containing states $XY \! Z$ with the confinement-induced hadronization of a rapidly separating pair of a compact diquark and antidiquark. This picture combines the advantages of diquark-based models, which can accommodate much of the known $XY \! Z$ spectrum, with the experimental fact that such states are both relatively narrow and are produced promptly. It also naturally explains the preference of some of the exotic states to decay to $\psi(2S)$, rather than $J/\psi$, in terms of a simple wave-function overlap effect.
A molecular solid C$_{50}$Cl$_{10}$ with possible crystalline structures, including the hexagonal-close-packed (hcp) phase, the face-centered cubic (fcc) phase, and a hexagonal monolayer, is predicted in terms of first-principles calculation within the density functional theory. The stable structures are determined from the total-energy calculations, where the hcp phase is uncovered more stable than the fcc phase and the hexagonal monolayer in energy per molecule. The energy bands and density of states for hcp and fcc C$_{50}$Cl$_{10}$ are presented. The results show that C$_{50}$Cl% $_{10}$ molecules can form either a hcp or fcc indirect-gap band insulator or an insulating hexagonal monolayer.
We present an analytical result for the ratio of the physical correlation length in a 2D Heisenberg antiferromagnet on a square lattice, and the one which is actually computed in numerical simulations. This last correlation length is deduced from the second moment of the structure factor at the antiferromagnetic momentum Q. We show that the ratio is very close to one in agreement with previously obtained numerical result of the 1/N expansion.
The frequencies of kHz Quasi-Periodic Oscillations in the bright Low-Mass X-ray Binary Sco X-1 have been reported to appear preferentially in a 3:2 ratio. We show that a proper statistical analysis of those RXTE data upon which the claim is based indicated a 2.4 sigma deviation from a constant distribution in ratios. The analysis of a much larger RXTE/PCA dataset shows that there is no sharp concentration around a 3:2 ratio, but that the ratios are broadly distributed over the range 820-1150 Hz.
We prove an upper bound on sums of squares of minors of {+1, -1} matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin (2009), but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices, and generalise a result of Turan on determinants of random {+1,-1} matrices.
It is now straightforward to carry out S-matrix to potential inversion over a very wide range of energies and for a wide range of projectile-target combinations. Inversion is possible in many cases involving spin. IP inversion also permits direct scattering data-to-potential inversion and furnishes powerful tools for the phenomenological analysis of nuclear scattering. The resulting single particle potentials exhibit various generic properties which challenge fundamental reaction theories as well as yield information on densities, provide input for reaction calculations. S-matrix to potential inversion is also a powerful tool for directly investigating theoretical processes which contribute to inter-nuclear potentials. Various studies have given insight into contributions to the dynamic polarisation potential (DPP) due to breakup processes and due to collective and reaction channel coupling and have also illuminated the role played by exchange processes in leading to non-locality and parity dependence of the potentials. A case study involving d + He-4 is a model for ways in which inversion applied jointly to theory and experiment might illuminate the scattering of exotic nuclei.
We prove that any symplectic resolution of the closure of a nilpotent orbit in a semi-simple complex Lie algebra is isomorphic to the collapsing of the cotangent bundle of a projective homogenous variety. Then we give a complete characterization of those nilpotent orbits whose closure admit a symplectic resolution.
The initial condition at the matching scale $\mu_W = O(M_W)$ for the Wilson coefficient of the magnetic photon-penguin operator in the decay $B\to X_s \gamma$ is calculated in the next-to-leading-order approximation. The technical details of the necessary two-loop calculation in the full theory are described and the matching with the corresponding result in the effective theory is discussed in detail. Our outcome for the initial condition confirms the final results of Adel and Yao and Greub and Hurth. We show that --- contrary to the claims in the second of these papers --- the matching procedure can be properly performed for infrared divergent amplitudes, i.e. independently of contributions from gluon bremsstrahlung.
For a curve $X$ of genus $>1$ defined over a finite field, we present a criterion which allows us to state the non existence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the automorphism group of some modular curves of high genus.
Let $X$ be a projective variety and let $C$ be a rational normal curve on $X$. We compute the normal bundle of $C$ in a general complete intersection of hypersurfaces of sufficiently large degree in $X$. As a result, we establish the separable rational connectedness of a large class of varieties, including general Fano complete intersections of hypersurfaces of degree at least three in flag varieties, in arbitrary characteristic. In addition, we give a new way of computing the normal bundle of certain rational curves in products of varieties in terms of their restricted tangent bundles and normal bundles on each factor.
We have combined direct nanofabrication by local anodic oxidation with conventional electron-beam lithography to produce a parallel double quantum dot based on a GaAs/AlGaAs heterostructure. The combination of both nanolithography methods allows to fabricate robust in-plane gates and Cr/Au top gate electrodes on the same device for optimal controllability. This is illustrated by the tunability of the interdot coupling in our device. We describe our fabrication and alignment scheme in detail and demonstrate the tunability in low-temperature transport measurements.
The spin-1/2 XXZ diamond chain is considered within the Jordan-Wigner fermionization. The fermionized Hamiltonian contains the interacting terms which are treated within the Hartree-Fock approximation. We obtain the ground-state magnetization curve of the model for some particular cases and compare the results with the exact diagonalization data for finite chains of 30 spins and known exact results. We also analyze the validity of the suggested approximation.
Stellar ages are extremely difficult to determine and often subject to large uncertainties, especially for field low-mass stars. We plan to carry out a calibration of the decrease in high-energy emissions of low-mass GKM stars with time, and therefore precise age determination is a key ingredient. The overall goal of our research is to study the time evolution of these high-energy emissions as an essential input to studing exoplanetary atmospheres.   We propose to determine stellar ages with a methodology based on wide binaries. We are interested in systems composed of a low-mass star and a white dwarf (WD), where the latter serves as a stellar chronometer for the system. We aim at obtaining reliable ages for a sample of late-type stars older than 1 Gyr.   We selected a sample of wide binaries composed by a DA type WD and a GKM companion. High signal-to-noise, low-resolution spectroscopic observations were obtained for most of the WD members of the sample. Atmospheric parameters were determined by fitting the spectroscopic data to appropiate WD models. The total ages of the systems were derived by using cooling sequences, an initial-final mass relationship and evolutionary tracks, to account for the progenitor life.   The spectroscopic observations have allowed us to determine ages for the binary systems using WDs as cosmochronometers. We obtained reliable ages for 27 stars between 1 and 5 Gyr, which is a range where age determination becomes difficult for field objects.
The empirical HOD model of Wang et al. 2006 fits, by construction, both the stellar mass function and correlation function of galaxies in the local Universe. In contrast, the semi-analytical models of De Lucia & Blazoit 2007 (DLB07) and Guo et al. 2011 (Guo11), built on the same dark matter halo merger trees than the empirical model, still have difficulties in reproducing these observational data simultaneously. We compare the relations between the stellar mass of galaxies and their host halo mass in the three models, and find that they are different. When the relations are rescaled to have the same median values and the same scatter as in Wang et al., the rescaled DLB07 model can fit both the measured galaxy stellar mass function and the correlation function measured in different galaxy stellar mass bins. In contrast, the rescaled Guo11 model still over-predicts the clustering of low-mass galaxies. This indicates that the detail of how galaxies populate the scatter in the stellar mass -- halo mass relation does play an important role in determining the correlation functions of galaxies. While the stellar mass of galaxies in the Wang et al. model depends only on halo mass and is randomly distributed within the scatter, galaxy stellar mass depends also on the halo formation time in semi-analytical models. At fixed value of infall mass, galaxies that lie above the median stellar mass -- halo mass relation reside in haloes that formed earlier, while galaxies that lie below the median relation reside in haloes that formed later. This effect is much stronger in Guo11 than in DLB07, which explains the over-clustering of low mass galaxies in Guo11. Our results illustrate that the assumption of random scatter in the relation between stellar and halo mass as employed by current HOD and abundance matching models may be problematic in case a significant assembly bias exists in the real Universe.
We prove the existence of canonical scrolls; that is, scrolls playing the role of canonical curves. First of all, they provide the geometrical version of Riemann Roch Teorem: any special scroll is the projection of a canonical scroll and they allow to understand the classification of special scrolls in P3. Canonical scrolls correspond to the projective model of canonical geometrically ruled surfaces over a smooth curve. We also prove that the generic canonical scroll is projectively normal except in the hyperelliptic case and for very particular cases in the nonhyperelliptic situation.
We provide an explicit construction of classical strings that have endpoints on the horizons of the 2D Lorentzian black hole. We argue that this is a dual description of geodesics that are localized around the horizon which are the Lorentzian counterparts of the winding strings of the Euclidean black hole (the cigar geometry). Identifying these with the states of the black hole, we can expect that issues of black hole information loss can be posed sharply in terms of a fully quantizable string theory.
Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting, exponential-like structure ---in contrast with the case of flat spacetime where it coincides with the classical potential. Several possible cosmological applications, as curvature-induced phase transitions and modifications of the values of the gravitational and cosmological constants, are briefly discussed.
In this paper we present an improved fitting formula for the dark matter bispectrum motivated by the previous phenomenological approach of Scoccimarro & Couchman (2001). We use a set of LCDM simulations to calibrate the fitting parameters in the k-range of 0.03 h/Mpc<k<0.4 h/Mpc and in the redshift range of 0<z<1.5. This new proposed fit describes well the BAO-features although it was not designed to. The deviation between the simulations output and our analytic prediction is typically less than 5% and in the worst case is never above 10%. We envision that this new analytic fitting formula will be very useful in providing reliable predictions for the non-linear dark matter bispectrum for LCDM models.
CaFe2O4 is a highly anisotropic antiferromagnet reported to display two spin arrangements with up-up-down-down (phase A) and up-down-up-down (phase B) configurations. The relative stability of these phases is ruled by the competing ferromagnetic and antiferromagnetic interactions between Fe3+ spins arranged in two different environments, but a complete understanding of the magnetic structure of this material does not exist yet. In this study we investigate epitaxial CaFe2O4 thin films grown on TiO2 (110) substrates by means of Pulsed Laser Deposition (PLD). Structural characterization reveals the coexistence of two out-of-plane crystal orientations and the formation of three in-plane oriented domains. The magnetic properties of the films, investigated macroscopically as well as locally, including highly sensitive Mossbauer spectroscopy, reveal the presence of just one order parameter showing long-range ordering below T = 185 K and the critical nature of the transition. In addition, a non-zero in-plane magnetization is found, consistent with the presence of uncompensated spins at phase or domain boundaries, as proposed for bulk samples.
Optimal transport from the volume measure to a convex combination of Dirac measures yields a tessellation of a Riemannian manifold into pieces of arbitrary relative size. This tessellation is studied for the cost functions $c_p(z,y)=\frac{1}{p}d^p(z,y)$ and $1\leq p<\infty$. Geometric descriptions of the tessellations for all $p$ is obtained for compact subsets of the Euclidean space. For $p=2$ this approach yields Laguerre tessellations. For $p=1$ it induces Johnson Mehl diagrams for all compact Riemannian manifolds.
I summarize some of the key questions to have emerged during the 1994 conference on ``Strongly Correlated Electron Systems'', held in Amsterdam, August 1994. Issues addressed include: Hunds rule interactions and how they renormalize; the Luttinger sum rule and metamagnetism; heavy fermion insulators, the nature of the charge gap, spectral weight transfer in the optical conductivity; non-Fermi liquid behavior in transition and heavy fermion metals; order parameter symmetry and the unusual nature of quasiparticle excitations in heavy fermion superconductors.
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions. Algebraic results are discussed and analysis is performed to deduce new results concerning rational arithmetical functions.
We study the rank 4 linear matroid $M(H_4)$ associated with the 4-dimensional root system $H_4$. This root system coincides with the vertices of the 600-cell, a 4-dimensional regular solid. We determine the automorphism group of this matroid, showing half of the 14,400 automorphisms are geometric and half are not. We prove this group is transitive on the flats of the matroid, and also prove this group action is primitive. We use the incidence properties of the flats and the {\it orthoframes} of the matroid as a tool to understand these automorphisms, and interpret the flats geometrically.
We present a rigorous, regularization independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass $\mu\ne0$ which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field at fixed cosmic time, in which the expectation value of the renormalized energy-momentum tensor is independent of the space coordinate and is of the perfect fluid form $g_{\mu,\nu}\rho_{vac}$ with $\rho_{vac}>0$, thus providing a quantum field theoretic foundation of the Cosmological constant. Using some values of $\mu$ suggested in the literature for the hypothetical axion particle, there results a model for dark energy which is consistent with past and future evolution and is also in good agreement with experimental data.