ShantanuT01/DACTYL-Pretraining huggingface dataset:
For the first time, the cumulant 2-body reduced density matrix (= 2-matrix) of the spin-unpolarized homogeneous electron gas (HEG) is considered. This $\gamma_{\rm c}$ proves to be the common source for both the momentum distribution $n(k)$ and the static structure factor $S(q)$. Within many-body perturbation theory, this $\gamma_{\rm c}$ is given by only {\it linked} diagrams (with 2 open particle-hole lines as well as with closed loops and interaction lines). Here it is worked out in detail, how the 1-body quantity $n(k)$ follows from the 2-body quantity $\gamma_{\rm c}$ - through a certain contraction procedure, cf Eqs.(2.25)-(2.28). In particular, this $\gamma_{\rm c}$ is developed for the high-density HEG. Its correctness is checked by deriving from it $n(k)$ and $S(q)$, known from the random-phase approximation (RPA). This study opens the way to a more sophisticated HEG description in terms of cumulant geminals or/and variational methods. Besides, the cumulant structure factor (CSF) of the exchange in lowest order is explicitly given and sum rules for the CSFs and their small- and large-$q$ behavior (beyond RPA) are systematically summarized within the plasmon sum rule, coalescing theorems, and the inflexion-point trajectory.
By utilizing the frequency anticorrelation of two-photon states produced via spontaneous parametric down conversion (SPDC), the working principle of a novel remote spectrometer is demonstrated. With the help of a local scanning monochromator, the spectral transmission function of an optical element (or atmosphere) at remote locations can be characterized for wide range of wavelengths with expected high resolution.
In perturbative QCD approach, we investigate the $B(B_{s})\rightarrow D_{(s)}(\bar{D}_{(s)})\,T$ and $D_{(s)}^{*}(\bar{D}_{(s)}^{*})\,T$ decays, which include the Cabibbo-Kobayashi-Maskawa (CKM) favored decays and the Cabibbo-Kobayashi-Maskawa-suppressed decays, where T denotes a light tensor meson. From our calculation, we find that the nonfactorizable emission diagrams and the annihilation type diagrams are important, especially for those color suppressed channels. For those decays with a tensor meson emitted, the factorizable emission diagrams vanish owing to the fact that a tensor meson can not be produced through the local (V-A) or tensor current. The numerical results show that the predictions for the branching ratios of considered charmed B decays are in the range of $10^{-4}$ to $10^{-6}$ for those CKM-favored decays (governed by $|V_{cb}|$) and in the range of $10^{-5}$ to $10^{-8}$ for those CKM-suppressed decays (governed by $|V_{ub}|$). We also predict large transverse polarization contributions in many of the $B(B_{s}) \rightarrow D_{(s)}^{\ast}(\bar{D}_{(s)}^{*})T$ decay channels.
The structure and evolution of the spiral arms of our Milky Way are basic but long-standing questions in astronomy. In particular, the lifetime of spiral arms is still a puzzle and has not been well constrained from observations. In this work, we aim to inspect these issues using a large catalogue of open clusters. We compiled a catalogue of 3794 open clusters based on Gaia EDR3. A majority of these clusters have accurately determined parallaxes, proper motions, and radial velocities. The age parameters for these open clusters are collected from references or calculated in this work. In order to understand the nearby spiral structure and its evolution, we analysed the distributions, kinematic properties, vertical distributions, and regressed properties of subsamples of open clusters. We find evidence that the nearby spiral arms are compatible with a long-lived spiral pattern and might have remained approximately stable for the past 80 million years. In particular, the Local Arm, where our Sun is currently located, is also suggested to be long-lived in nature and probably a major arm segment of the Milky Way. The evolutionary characteristics of nearby spiral arms show that the dynamic spiral mechanism might be not prevalent for our Galaxy. Instead, density wave theory is more consistent with the observational properties of open clusters.
Employing Brillouin spectroscopy, strong interfacial Dzyaloshinskii-Moriya interactions have been observed in an ultrathin Pt/CoFeB film. Our micromagnetic simulations show that spin-wave nonreciprocity due to asymmetric surface pinning is insignificant for the 0.8nmthick CoFeB film studied. The observed high asymmetry of the monotonic spin wave dispersion relation is thus ascribed to strong Dzyaloshinskii-Moriya interactions present at the Pt/CoFeB interface. Our findings should further enhance the significance of CoFeB as an important material for magnonic, spintronic and skyrmionic applications.
There exist simple single-charge and multi-charge BPS p-brane solutions in the D-dimensional maximal supergravities. From these, one can fill out orbits in the charge vector space by acting with the global symmetry groups. We give a classification of these orbits, and the associated cosets that parameterise them.
We find pp wave solutions in string theory with null-like linear dilatons. These provide toy models of big bang cosmologies. We formulate Matrix String Theory in these backgrounds. Near the big bang ``singularity'', the string theory becomes strongly coupled but the Yang-Mills description of the matrix string is weakly coupled. The presence of a second length scale allows us to focus on a specific class of non-abelian configurations, viz. fuzzy cylinders, for a suitable regime of parameters. We show that, for a class of pp waves, fuzzy cylinders which start out big at early times dynamically shrink into usual strings at sufficiently late times.
In this article we show that the form $x^2 + iy^2 + z^2 + iw^2$ represents all gaussian integers. The main tools used in this proof are Fermat's little theorem (over finite field extensions), the Mordell-Niven theorem (representation of some gaussians), and the generalized Euler-identity over finite field extensions.
We study the stress tensor multiplet four-point function in the 6d maximally supersymmetric $(2,0)$ $A_{N-1}$ and $D_N$ theories, which have no Lagrangian description, but in the large $N$ limit are holographically dual to weakly coupled M-theory on $AdS_7\times S^4$ and $AdS_7\times S^4/\mathbb{Z}_2$, respectively. We use the analytic bootstrap to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity $R$ and the first higher derivative correction $R^4$ vertices, which is the first 1-loop correction computed for a non-Lagrangian theory. We then take the flat space limit and find precise agreement with the corresponding terms in the 11d M-theory S-matrix, some of which we compute for the first time using two-particle unitarity cuts.
Photoionization by the high-redshift ultraviolet radiation background heats low density gas before it falls into dark matter potential wells, and it eliminates the neutral hydrogen and singly ionized helium that dominate cooling of primordial gas at temperatures of $10^4-10^5$K. We investigate the influence of photoionization on galaxy formation using high-resolution simulations with a 1-dimensional, spherically symmetric, Lagrangian hydrodynamics/gravity code. We find that the presence of a photoionizing background suppresses the formation of galaxies with circular velocities $v_{circ} \simlt 30\,$\kms\ and substantially reduces the mass of cooled baryons in systems with circular velocities up to $v_{circ} \sim 50\,$\kms. Above $v_{circ} \sim 75\,$\kms, photoionization has no significant effect. Photoionization exerts its influence primarily by heating gas before collapse; the elimination of line cooling processes is less important. We discuss the implications of these results for hierarchical theories of galaxy formation.
We generalize Greenberger-Horne-Zeilinger (GHZ) theorem to an arbitrary number of D-dimensional systems. Contrary to conventional approaches using compatible composite observables, we employ incompatible and concurrent observables, whose common eigenstate is still a generalized GHZ state. It is these concurrent observables which enable to prove a genuinely N-partite and D-dimensional GHZ theorem. Our principal idea is illustrated for a four-partite system with D which is an arbitrary multiple of 3. By extending to N qudits, we show that GHZ theorem holds as long as N is not divisible by all nonunit divisors of D, smaller than N.
Close binary systems undergoing mass transfer or common envelope interactions can account for the morphological properties of some planetary nebulae. The search for close binary companions in planetary nebulae is hindered by the difficulty of detecting cool, late-type, main sequence companions in binary systems with hot pre-white dwarf primaries. However, models of binary PN progenitor systems predict that mass accretion or tidal interactions can induce rapid rotation in the companion, leading to X-ray-emitting coronae. To test such models, we have searched for, and detected, X-ray emission from three binary central stars within planetary nebulae: the post-common envelope close binaries in HFG 1 and DS 1 consisting of O-type subdwarfs with late-type, main sequence companions, and the binary system in LoTr 5 consisting of O-type subdwarf and rapidly rotating, late-type giant companion. The X-ray emission in each case is best characterized by spectral models consisting of two optically-thin thermal plasma components with characteristic temperatures of about 10 MK and 15-40 MK, and total X-ray luminosities about 10^30 erg/s. We consider the possible origin of the X-ray emission from these binary systems and conclude that the most likely origin is, in each case, a corona around the late-type companion, as predicted by models of interacting binaries.
We extend the `moment transport method' for calculating the statistics of inflationary perturbations to the quantum phase of evolution on sub-horizon scales. The quantum transport equations form a set of coupled ordinary differential equations for the evolution of quantum correlation functions during inflation, which are valid on sub- and super-horizon scales, and reduce to the known classical transport equations after horizon crossing. The classical and quantum equations follow directly from the field equations of cosmological perturbation theory. In this paper, we focus on how the evolution equations arise, and explore how transport methods relate to other approaches, and in particular how formal integral solutions to the transport equations connect to those of the In-In formalism.
A link is established between the observed (approximate) geometric mass hierarchy of quarks and leptons and the triangular structure of their tenable flavor representations. This singles out SU(3) as the horizontal flavor group, thereby linking the Fermi mass hierarchy with the threefold family replication. These linkages are exploited within a flavor-chiral SU(3) model, with fermions and Higgs bosons in the 3+6* representation. The model is Left-Right symmetric and utilizes the universal see-saw mechanism with a geometric mass suppression pattern. Given certain assumptions, the model produces successful mass-ratio (rather than square-mass-ratio) mixing angle relations and fixes the light quark mass ratio.
For about a decade, spectro-polarimetry of HeI 10830 has been applied to the magnetic diagnostics of the solar chromosphere. This resonance line is very versatile, as it is visible both on disk and in off-limb structures, and it has a good sensitivity to both the weak-field Hanle effect and the strong-field Zeeman effect. Recent observations of an active-region filament showed that the linear polarization was dominated by the transverse Zeeman effect, with very little or no hint of scattering polarization. This is surprising, since the HeI levels should be significantly polarized in a conventional scattering scenario. To explain the observed level of atomic depolarization by collisional or radiative processes, one must invoke plasma densities larger by several orders of magnitude than currently known values for prominences. We show that such depolarization can be explained quite naturally by the presence of an unresolved, highly entangled magnetic field, which averages to give the ordered field inferred from spectro-polarimetric data, over the typical temporal and spatial scales of the observations. We present a modeling of the polarized HeI 10830 in this scenario, and discuss its implications for the magnetic diagnostics of prominences and spicules, and for the general study of unresolved magnetic field distributions in the solar atmosphere.
We construct natural maps (the Klein and Wirtinger maps) from moduli spaces of vector bundles on an algebraic curve $X$ to affine spaces, as quotients of the nonabelian theta linear series. We prove a finiteness result for these maps over generalized Kummer varieties (moduli of torus bundles), leading us to conjecture that the maps are finite in general. The conjecture provides canonical explicit coordinates on the moduli space. The finiteness results give low--dimensional parametrizations of Jacobians (in $\Pp^{3g-3}$ for generic curves), described by $2\Theta$ functions or second logarithmic derivatives of theta.   We interpret the Klein and Wirtinger maps in terms of opers on $X$. Opers are generalizations of projective structures, and can be considered as differential operators, kernel functions or special bundles with connection. The matrix opers (analogues of opers for matrix differential operators) combine the structures of flat vector bundle and projective connection, and map to opers via generalized Hitchin maps. For vector bundles off the theta divisor, the Szeg\"o kernel gives a natural construction of matrix oper. The Wirtinger map from bundles off the theta divisor to the affine space of opers is then defined as the determinant of the Szeg\"o kernel. This generalizes the Wirtinger projective connections associated to theta characteristics, and the assoicated Klein bidifferentials.
For every odd prime number p, we give examples of non-constant smooth families of genus 2 curves over fields of characteristic p which have pro-Galois (pro-\'etale) covers of infinite degree with geometrically connected fibers. The Jacobians of the curves are isomorphic to products of elliptic curves.
The deviations of non-linear perturbations of black holes from the linear case are important in the context of ringdown signals with large signal-to-noise ratio. To facilitate a comparison between the two we derive several results of linear perturbation theory in coordinates which may be adopted in numerical work. Specifically, our results are derived in Kerr-Schild coordinates adjusted by a general height function. In the first part of the paper we address the questions: for an initial configuration of a massless scalar field, what is the amplitude of the excited quasinormal mode (QNM) for any observer outside outside the event horizon, and furthermore what is the resulting tail contribution? This is done by constructing the full Green's function for the problem with exact solutions of the confluent Heun equation satisfying appropriate boundary conditions. In the second part of the paper, we detail new developments to our pseudospectral numerical relativity code bamps to handle scalar fields. In the linear regime we employ precisely the Kerr-Schild coordinates treated by our previous analysis. In particular, we evolve pure QNM type initial data along with several other types of initial data and report on the presence of overtone modes in the signal.
We determine the independence number of the orthogonality graph on $2^k$-dimensional hypercubes. This answers a question by Galliard from 2001 which is motivated by a problem in quantum information theory. Our method is a modification of a rank argument due to Frankl who showed the analogous result for $4p^k$-dimensional hypercubes, where $p$ is an odd prime.
We show that a general one-dimensional (1D) lattice with nonlinear inter-particle interactions can always be thermalized for arbitrarily small nonlinearity in the thermodynamic limit, thus proving equipartition hypothesis in statistical physics for an important class of systems. Particularly, we find that in the lattices of interaction potential $V(x)=x^2/2+\lambda x^n/n$ with $n\geq4$, there is \textit{a universal scaling law} for the thermalization time $T^{eq}$, i.e., $T^{eq}\propto\lambda^{-2}\epsilon^{-(n-2)}$, where $\epsilon$ is the energy density. Numerical simulations confirm that it is accurate for an even $n$. A slight correction is needed for an odd $n$, which is due to the Chirikov overlap occurring in the weakly nonlinear regime between extra vibration modes excited by the asymmetry of potential. Based on this scaling law, as well as previous prediction for the case of $n=3$, a universal formula for the thermalization time for a 1D lattice with a general interaction potential is obtained.
The purpose of this paper is to go further into the study of the quadratic Szeg{\"o} equation, which is the following Hamiltonian PDE : $i \partial\_t u = 2J\Pi(|u|^2)+\bar{J}u^2$, $u(0, \cdot)=u\_0$, where $\Pi$ is the Szeg{\"o} projector onto nonnegative modes, and $J = J(u)$ is the complex number given by $J=\int\_\mathbb{T}|u|^2u$. We exhibit an infinite set of new conservation laws $\{\ell\_k \}$ which are in involution. These laws give us a better understanding of the "turbulent" behavior of certain rational solutions of the equation : we show that if the orbit of a rational solution is unbounded in some $H^s$, $s > 1/2$, then one of the $\ell\_k$'s must be zero. As a consequence, we characterize growing solutions which can be written as the sum of two solitons.
This article fills a gap in the mathematical analysis of Adaptive Biasing algorithms, which are extensively used in molecular dynamics computations. Given a reaction coordinate, ideally, the bias in the overdamped Langevin dynamics would be given by the gradient of the associated free energy function, which is unknown. We consider an adaptive biased version of the overdamped dynamics, where the bias depends on the past of the trajectory and is designed to approximate the free energy.   The main result of this article is the consistency and efficiency of this approach. More precisely we prove the almost sure convergence of the bias as time goes to infinity, and that the limit is close to the ideal bias, as an auxiliary parameter of the algorithm goes to $0$.   The proof is based on interpreting the process as a self-interacting dynamics, and on the study of a non-trivial fixed point problem for the limiting flow obtained using the ODE method.
Exemplar-based class-incremental learning is to recognize new classes while not forgetting old ones, whose samples can only be saved in limited memory. The ratio fluctuation of new samples to old exemplars, which is caused by the variation of memory capacity at different environments, will bring challenges to stabilize the incremental optimization process. To address this problem, we propose a novel self-paced imbalance rectification scheme, which dynamically maintains the incremental balance during the representation learning phase. Specifically, our proposed scheme consists of a frequency compensation strategy that adjusts the logits margin between old and new classes with the corresponding number ratio to strengthen the expression ability of the old classes, and an inheritance transfer strategy to reduce the representation confusion by estimating the similarity of different classes in the old embedding space. Furthermore, a chronological attenuation mechanism is proposed to mitigate the repetitive optimization of the older classes at multiple step-wise increments. Extensive experiments on three benchmarks demonstrate stable incremental performance, significantly outperforming the state-of-the-art methods.
I discuss some aspects of the moduli space of hyper-K{\"a}hler four-fold compactifications of type II and ${\cal M}$- theories. The dimension of the moduli space of these theories is strictly bounded from above. As an example I study Hilb$^2(K3)$ and the generalized Kummer variety $K^2(T^4)$. In both cases RR-flux (or $G$-flux in ${\cal M}$-theory) must be turned on, and we show that they give rise to vacua with ${\cal N}=2$ or ${\cal N}=3$ supersymmetry upon turning on appropriate fluxes. An interesting subtlety involving the symmetric product limit $S^2(K3)$ is pointed out.
Blazars are a class of AGN, one of their jets is pointed towards the earth. Here, we report about the multi-wavelength study for blazar S5 1803+78 between MJD 58727 to MJD 59419. We analysed $\gamma$-ray data collected by Fermi-LAT, X-ray data collected by Swift-XRT \& NuSTAR, optical photons detected by Swift-UVOT \& TUBITAK observatory in Turkey. Three flaring states are identified by analysing the $\gamma$-ray light curve. A day scale variability is observed throughout the flares with the similar rise and decay times suggesting a compact emission region located close to the central engine. Cross-correlation studies are carried out between $\gamma$-ray, radio, and X-ray bands, and no significant correlation is detected. The $\gamma$-ray and optical emission are significantly correlated with zero time lag suggesting a co-spatial origin of them. A significant positive correlation between the R-I index and the V magnitude is observed. The broadband spectral energy distributions (SEDs) modeling was performed for all the flaring episodes as well as for one quiescent state for comparison. SEDs are best fitted with the synchrotron-self Compton (SSC) model under a one-zone leptonic scenario. The SED modeling shows that to explain the high flaring state strong Doppler boosting is required.
This paper concerns what Background Independence itself is (as opposed to some particular physical theory that is background independent). The notions presented mostly arose from a layer-by-layer analysis of the facets of the Problem of Time in Quantum Gravity. Part of this coincides with two relational postulates which are thus identified as classical precursors of two of the facets of the Problem of Time. These are furthemore tied to the forms of each of the GR Hamiltonian and momentum constraints. Other aspects of Background Independence include the algebraic closure of these constraints, expressing physics in terms of beables, foliation independence as implemented by refoliation invariance, the reconstruction of spacetime from space. The final picture is that Background Independence - a philosophically desirable and physically implementable feature for a theory to have - has the facets of the Problem of Time among its consequences. Thus these arise naturally and are problems to be resolved, as opposed to avoided `by making one's physics background-dependent in order not to have these problems'. This serves as a selection criterion that limits the use of a number of model arenas and physical theories.
This paper has been removed by arXiv administrators because it plagiarizes gr-qc/0011027, "Viscous cosmologies in scalar-tensor theories for Kasner type metrics," by M. Cataldo, S. del Campo and P. Salgado; and gr-qc/0404108, "Energy and Momentum Densities Associated with Solutions Exhibiting Directional Type Singularities," by Ragab M. Gad.
We consider topologically twisted N=4 supersymmetric Yang-Mills theory on a four-manifold of the form V = W \times R_+ or V = W \times I, where W is a Riemannian three-manifold. Different kinds of boundary conditions apply at infinity or at finite distance. We verify that each of these conditions defines a `middle-dimensional' subspace of the space of all bulk solutions. Taking the two boundaries of V into account should thus generically give a discrete set of solutions. We explicitly find the spherically symmetric solutions when W = S^3 endowed with the standard metric. For widely separated boundaries, these consist of a pair of solutions which coincide for a certain critical value of the boundary separation and disappear for even smaller separations.
We prove radial symmetry of singular solutions to an overdetermined boundary value problem for a class of degenerate quasilinear elliptic equations.