ShantanuT01/DACTYL-Pretraining huggingface dataset:
In a series of papers, Kempf and co-workers (J. Phys. A: Math. Gen. {\bf 30}, 2093, (1997); Phys. Rev. D {\bf52}, 1108, (1995); Phys. Rev. D {\bf55}, 7909, (1997)) introduced a D-dimensional $(\beta,\beta')$-two-parameter deformed Heisenberg algebra which leads to a nonzero minimal observable length. In this work, the Lagrangian formulation of an electrostatic field in three spatial dimensions described by Kempf algebra is studied in the case where $\beta'=2\beta$ up to first order over deformation parameter $\beta$. It is shown that there is a similarity between electrostatics in the presence of a minimal length (modified electrostatics) and higher derivative Podolsky's electrostatics. The important property of this modified electrostatics is that the classical self-energy of a point charge becomes a finite value. Two different upper bounds on the isotropic minimal length of this modified electrostatics are estimated. The first upper bound will be found by treating the modified electrostatics as a classical electromagnetic system, while the second one will be estimated by considering the modified electrostatics as a quantum field theoretic model. It should be noted that the quantum upper bound on the isotropic minimal length in this paper is near to the electroweak length scale $(\ell_{electroweak}\sim 10^{-18}\, m)$.
We adapt the non-linear $\sigma$ model to study the nonequilibrium critical dynamics of O(n) symmetric ferromagnetic system. Using the renormalization group analysis in $d=2+\epsilon$ dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scaling behavior almost immediately after the system starts to evolve while the correlation and response functions demonstrate scaling behavior which is typical for aging phenomena. The corresponding fluctuation-dissipation ratio is computed to first order in $\epsilon$ and the relation between transverse and longitudinal fluctuations is discussed.
Based on new ISO mid-infrared observations and ground based $H_\alpha$ and near-infrared observations, we report the detection of a bright starburst in the intragroup medium (IGM) of the famous compact group of galaxies Stephan's Quintet (Source A in Fig.1). We demonstrate that this starburst is caused by a collision between a high velocity ($\delta$V$\sim$ 1000 km/sec) intruder galaxy (NGC7318b) and the IGM of the group. While this is the only starburst known today that is induced by a galaxy/cold-intergalactic-medium collision, it provides new constraints to the theory for interaction-induced starbursts, and may hint at a new mechanism for the star formation excess seen in more distant clusters.
All-electrical and programmable manipulations of ferromagnetic bits are highly pursued for the aim of high integration and low energy consumption in modern information technology. Methods based on the spin-orbit torque switching in heavy metal/ferromagnet structures have been proposed with magnetic field, and recently are heading toward deterministic switching without external magnetic field. Here we demonstrate that an in-plane effective magnetic field can be induced by an electric field without breaking the symmetry of the structure of the thin film, and realize the deterministic magnetization switching in a hybrid ferromagnetic/ferroelectric structure with Pt/Co/Ni/Co/Pt layers on PMN-PT substrate. The effective magnetic field can be reversed by changing the direction of the applied electric field on the PMN-PT substrate, which fully replaces the controllability function of the external magnetic field. The electric field is found to generate an additional spin-orbit torque on the CoNiCo magnets, which is confirmed by macrospin calculations.
The Group V and VI transition metals share a common Fermi surface feature of hole ellipsoids at the N point in the Brillouin zone. In clear contrast to the other Fermi surface sheets, which are purely of d character, these arise from a band that has a significant proportion of p character. By performing local density approximation (LDA), generalized gradient approximation (GGA), strongly constrained and appropriately normed (SCAN) meta-GGA, and GW approximation calculations, we find that the p character part of this band (and therefore the Fermi surface) is particularly sensitive to the exchange-correlation approximation. LDA and GGA calculations inadequately describe this feature, predicting N hole ellipsoid sizes that are consistently too large in comparison to various experimental measurements, whereas quasiparticle self-consistent GW calculations predict a size that is slightly too small (and non-self-consistent GW calculations that use an LDA starting point predict a size that is much too small). Overall, for the metals tested here, SCAN provides the most accurate Fermi surface predictions, mostly correcting the discrepancies between measurements and calculations that were observed when LDA calculations were used. However, none of the tested exchange-correlation approximations succeeds in simultaneously bringing all of the measurable properties of these metals into good experimental agreement, particularly where magnetism is concerned. The SCAN calculations predict antiferromagnetic moments for Cr that are 3 times larger than the experimental value (1.90 $\mu_B$ compared to 0.62 $\mu_B$).
We clarify the physical origin of the difference between gauge properties of conserved currents in abelian and nonabelian theories. In the latter, but not in the former, such currents can always be written on shell as gauge invariants modulo identically conserved, superpotential, terms. For the ``isotopic" vector and the stress tensor currents of spins 1 and 2 respectively, we explain this difference by the fact that the non-abelian theories are just the self-coupled versions of the abelian ones using these currents as sources. More precisely, we indicate how the self-coupling turns the non-invariantizable abelian conserved currents into (on-shell) superpotentials. The fate of other conserved currents is also discussed.
We report a theoretical study on the spin and electron transport in the nonlocal lateral spin valve with non-collinear magnetic configuration. The nonlocal magnetoresistance, defined as the voltage difference on the detection lead over the injected current, is derived analytically. The spin transfer torques on the detection lead are calculated. It is found that spin transfer torques are symmetrical for parallel and antiparallel magnetic configurations, which is different from that in conventional sandwiched spin valve.
Recent work on the Szekeres inhomogeneous cosmological models uncovered a surprising rotation effect. Hellaby showed that the angular $(\theta, \phi)$ coordinates do not have a constant orientation, while Buckley and Schlegel provided explicit expressions for the rate of rotation from shell to shell, as well as the rate of tilt when the 3-space is embedded in a flat 4-d Euclidean space. We here investigate some properties of this embedding, for the quasi-spherical recollapsing case, and use it to show that the two sets of results are in complete agreement. We also show how to construct Szekeres models that are closed in the 'radial' direction, and hence have a 'natural' embedded torus topology. Several explicit models illustrate the embedding as well as the shell rotation and tilt effects.
The galactic halo likely grew over time in part by assembling smaller galaxies, the so-called building blocks. We investigate if the properties of these building blocks are reflected in the halo white dwarf (WD) population in the Solar neighborhood. Furthermore, we compute the halo WD luminosity functions (WDLFs) for four major building blocks of five cosmologically motivated stellar haloes. We couple the SeBa binary population synthesis model to the Munich-Groningen semi-analytic galaxy formation model, applied to the high-resolution Aquarius dark matter simulations. Although the semi-analytic model assumes an instantaneous recycling approximation, we model the evolution of zero-age main sequence stars to WDs, taking age and metallicity variations of the population into account. Although the majority of halo stars is old and metal-poor and therefore the WDs in the different building blocks have similar properties (including present-day luminosity), we find in our models that the WDs originating from building blocks that have young and/or metal-rich stars can be distinguished from WDs that were born in other building blocks. In practice however, it will be hard to prove that these WDs really originate from different building blocks, as the variations in the halo WD population due to binary WD mergers result in similar effects. The five joined stellar halo WD populations that we modelled result in WDLFs that are very similar to each other. We find that simple models with a Kroupa or Salpeter initial mass function (IMF) fit the observed luminosity function slightly better, since the Chabrier IMF is more top-heavy, although this result is dependent on our choice of the stellar halo mass density in the Solar neighborhood.
Gas response to the underlying stellar spirals is explored for M81 using unmagnetized hydrodynamic simulations. Constrained within the uncertainty of observations, 18 simulations are carried out to study the effects of selfgravity and to cover the parameter space comprising three different sound speeds and three different arm strengths. The results are confronted with those data observed at wavelengths of 8 $\mu$m and 21 cm. In the outer disk, the ring-like structure observed in 8 $\mu$m image is consistent with the response of cold neutral medium with an effective sound speed 7 km s$^{-1}$, while for the inner disk, the presence of spiral shocks can be understood as a result of 4:1 resonances associated with the warm neutral medium with an effective sound speed 19 km s$^{-1}$. Simulations with single effective sound speed alone cannot simultaneously explain the structures in the outer and inner disks. This justifies the coexistence of cold and warm neutral media in M81. The anomalously high streaming motions observed in the northeast arm and the outward shifted turning points in the iso-velocity contours seen along the southwest arm are interpreted as signatures of interactions with companion galaxies. The level of simulated streaming motions narrows down the uncertainty of observed arm strength toward larger amplitudes.
The modified measure theories recommend themselves as a good possibility to go beyond the standard formulation to solve yet unsolved problems. The Galileon measure that is constructed in the way to be invariant under the Galileon shift symmetry is considered in the context of superstring theory. The translation invariance of the vacuum holds up to a Galileon transformations. The supersymmetric action is presented with all terms, including the tension, being derived from the equations of motion.
This paper discusses prime numbers that are (resp. are not) congruent numbers. Particularly the only case not fully covered by earlier results, namely primes of the form $p=8k+1$, receives attention.
Recently in \cite{Anderson:2013zia, Anderson:2013ila}, it was shown that global de Sitter space is unstable even to the massive particle creation with no self-interactions. In this paper we study the instability by making use of the coordinate-independent plane wave in de Sitter space, within this formalism, we show that the previous results of instability of de Sitter space due to the particle creation can be generalized to higher-spin fields in a straightforward way. The so-called plane wave are defined globally in de Sitter space and de Sitter invariance is manifest since such modes are deduced from the group theoretical point of view by the means of the Casimir operators. In fact, we employ the underling symmetry of embedding space namely the $4+1$ dimensional flat space to write the field equations and the solutions can be obtained in terms of the plane wave in embedding space.
This paper consists of two parts. In the first part we describe the recent works on the inverse problems for the wave equation in $(n+1)$-dimensional space equipped with pseudo-Riemannian metric with Lorentz signature. We study the conditions of the existence of black (or white) holes for these wave equations. In the second part we prove energy type estimates on a finite time interval in the presence of black or white holes. We use these estimates to prove the nonuniqueness of the inverse problems.
We report measurements of hard diffractive processes performed by the CDF collaboration in proton-antiproton collisions at the Fermilab Tevatron collider at $\sqrt{s}$=1960 GeV. The characteristics of the diffractive structure function from diffractive dijet production studies are presented. The results of exclusive dijet production in double pomeron exchange are discussed in the context of exclusive Higgs production at the LHC.
In this paper, we discuss the maximum principle for a time-fractional diffusion equation $$ \partial_t^\alpha u(x,t) = \sum_{i,j=1}^n \partial_i(a_{ij}(x)\partial_j u(x,t)) + c(x)u(x,t) + F(x,t),\ t>0,\ x \in \Omega \subset {\mathbb R}^n$$ with the Caputo time-derivative of the order $\alpha \in (0,1)$ in the case of the homogeneous Dirichlet boundary condition. Compared to the already published results, our findings have two important special features. First, we derive a maximum principle for a suitably defined weak solution in the fractional Sobolev spaces, not for the strong solution. Second, for the non-negative source functions $F = F(x,t)$ we prove the non-negativity of the weak solution to the problem under consideration without any restrictions on the sign of the coefficient $c=c(x)$ by the derivative of order zero in the spatial differential operator. Moreover, we prove the monotonicity of the solution with respect to the coefficient $c=c(x)$.
Samples of pristine Solar System material found in meteorites and interplanetary dust particles are highly enriched in (15)N. Conspicuous nitrogen isotopic anomalies have also been measured in comets, and the (14)N/(15)N abundance ratio of the Earth is itself larger than the recognised pre-solar value by almost a factor of two. Ion--molecules, low-temperature chemical reactions in the proto-solar nebula have been repeatedly indicated as responsible for these (15)N-enhancements. We have searched for (15)N variants of the N2H+ ion in L1544, a prototypical starless cloud core which is one of the best candidate sources for detection owing to its low central core temperature and high CO depletion. The goal is the evaluation of accurate and reliable (14)N/(15)N ratio values for this species in the interstellar gas. A deep integration of the (15)NNH+ (1-0) line at 90.4 GHz has been obtained with the IRAM 30 m telescope. Non-LTE radiative transfer modelling has been performed on the J=1-0 emissions of the parent and (15)N-containing dyazenilium ions, using a Bonnor--Ebert sphere as a model for the source. A high-quality fit of the N2H+ (1--0) hyperfine spectrum has allowed us to derive a revised value of the N2H+ column density in L1544. Analysis of the observed N(15)NH+ and (15)NNH+ spectra yielded an abundance ratio N[N(15)NH+]/N[(15)NNH+] = 1.1 +/- 0.3. The obtained (14)N/(15)N ratio is ~ 1000 +/- 200, suggestive of a sizeable (15)N depletion in this molecular ion. Such a result is not consistent with the prediction of present nitrogen chemical models. As chemical models predict large (15)N fractionation of N2H+, we suggest that (15)N(14)N, or (15)N in some other molecular form, is preferentially depleted onto dust grains.
We formulate and study an extension of gerbe duality to relative Gromov-Witten theory.
The effect of the recently obtained 2nd post-Newtonian corrections on the accuracy of estimation of parameters of the gravitational-wave signal from a coalescing binary is investigated. It is shown that addition of this correction degrades considerably the accuracy of determination of individual masses of the members of the binary. However the chirp mass and the time parameter in the signal is still determined to a very good accuracy. The possibility of estimation of effects of other theories of gravity is investigated. The performance of the Newtonian filter is investigated and it is compared with performance of post-Newtonian search templates introduced recently. It is shown that both search templates can extract accurately useful information about the binary.
We studied finite Fibonacci sequence of Co and Py stripes aligned side-by-side and in direct contact with each other. Calculations based on continuous model including exchange and dipole interactions were performed for structures feasible for fabrication and characterization of main properties of magnonic quasicrystals. We have shown the fractal structure of the magnonic spectrum with a number of magnonics gaps of different width. Also localization of spin waves in quasicrystals and existence of surface spin waves in finite quaiscrystal structure is demonstrated.
We use the excited coherent states built over the initial non-de Sitter modes, to study the modification of spectra of primordial scalar fluctuation. Non-de Sitter modes are actually the asymptotic solution of the inflaton field equation[JHEP 09(2014) 020]. We build excited coherent states over the non-de Sitter modes and despite the lack of interactions in the Lagrangian, we find a non-zero one-point function. It is shown that the primordial non-Gaussianity resulting from excited-de Sitter modes depend both of time and background space-time. It is very tiny of order $(\leq{10}^{-24})$, at the Planck initial fixed time that confirmed by resent observations for single field inflation but it grows in the present epoch. Moreover, our results at the leading order are similar to what obtained with general initial states and in the dS limit leads to standard results [JCAP 1202(2012) 005]. We will show that the non-dS modes and its resulting spectrum are more usable for far past time limit.
This is the third part of a four-paper sequence, which establishes the Threshold Conjecture and the Soliton-Bubbling vs.~Scattering Dichotomy for the energy critical hyperbolic Yang--Mills equation in the $(4+1)$-dimensional Minkowski space-time. This paper provides basic tools for considering the dynamics of the hyperbolic Yang--Mills equation in an arbitrary topological class at an optimal regularity. We generalize the standard notion of a topological class of connections on $\mathbb R^{d}$, defined via a pullback to the one-point compactification $\mathbb S^{d} = \mathbb R^{d} \cup \{\infty\}$, to rough connections with curvature in the critical space $L^{\frac{d}{2}}(\mathbb R^{d})$. Moreover, we provide excision and extension techniques for the Yang--Mills constraint (or Gauss) equation, which allow us to efficiently localize Yang--Mills initial data sets. Combined with the results in the previous paper \cite{OTYM2}, we obtain local well-posedness of the hyperbolic Yang--Mills equation on $\mathbb R^{1+d}$ $(d \geq 4)$ in an arbitrary topological class at optimal regularity in the temporal gauge (where finite speed of propagation holds). In addition, in the energy subcritical case $d = 3$, our techniques provide an alternative proof of the classical finite energy global well-posedness theorem of Klainerman--Machedon \cite{KlMa2}, while also removing the smallness assumption in the temporal-gauge local well-posedness theorem of Tao \cite{TaoYM}.   Although this paper is a part of a larger sequence, the materials presented in this paper may be of independent and general interest. For this reason, we have organized the paper so that it may be read separately from the sequence.
The purpose of this paper is to construct of the unification q-extension Genocchi polynomials. We give some interesting relations of this type of polynomials. Finally, we derive the q-extensions of Hurwitz-zeta type functions from the Mellin transformation of this generating function which interpolates the unification of q-extension of Genocchi polynomials.
We present a simple introduction to the techniques of effective field theory (EFT) and their application to QCD. For problems with more than one energy scale, the EFT approach is a useful alternative to more traditional model-building strategies. The most relevant such problem for this discussion is that of making contact between QCD and the hadronic phase of matter. As a simple example, an EFT calculation of the bound states of hydrogen within QED is sketched. A more significant demonstration of the power of EFTs, the construction of the chiral Lagrangian and chiral perturbation theory, is also included. The results provide us with the road map to a complete QCD-based theory of nuclear matter at nonzero temperatures and densities, a vital component to a quantitative understanding of the phase transition from hadron gas to quark-gluon plasma.
We study a complex Dirac field in the chiral representation minimally coupled to gravity in 3+1 dimensions in the context of Einstein-Cartan theory. Generically the matter content gravitates in two different ways: On the one hand, the energy-momentum induces spacetime curvature; on the other hand, the presence of spin acts as a source for the spacetime torsion, which does not propagate. In this setup we consider the most general stationary spherically symmetric ansatz and we find an analytic black hole solution that supports a nontrivial spinor configuration. The spinor field affects the geometry by inducing spacetime torsion, though, remarkably, it does not alter the black hole metric, which retains its Schwarzschild form. We find solutions both in asymptotically flat and asymptotically (Anti) de Sitter spaces. Additionally, we consider how the solution gets deformed when the so-called Holst term is included in the gravity action. We discuss possible observational effects due to the coupling of fermions in the nonvanishing torsion background. Additionally we include a Maxwell field into the problem and find that it forces the spinor field to be zero. Finally, nonminimal couplings of the spinor with spacetime curvature are considered, obtaining any effect on the spherically symmetric solutions.
For a nondegenerate quadratic form phi on a vector space V of dimension 2n + 1, let X_d be the variety of d-dimensional totally isotropic subspaces of V. We give a sufficient condition for X_2 to be 2-incompressible, generalizing in a natural way the known sufficient conditions for X_1 and X_n. Key ingredients in the proof include the Chernousov-Merkurjev method of motivic decomposition as well as Pragacz and Ratajski's characterization of the Chow ring of (X_2)_E, where E is a field extension splitting phi.
We develop a partial trace formula which circumvents some technical difficulties in computing the Selberg trace formula for the quotient $SL_3({\Z})\backslash SL_3({\R})/SO_3({\R})$. As applications, we establish the Weyl asymptotic law for the discrete Laplace spectrum and prove that almost all of its cusp forms are tempered at infinity. The technique shows there are non-lifted cusp forms on $SL_3({\Z})\backslash SL_3({\R})/SO_3({\R})$ as well as non-self-dual ones. A self-contained description of our proof for $SL_2({\Z})\backslash \U$ is included to convey the main new ideas. Heavy use is made of truncation and the Maass-Selberg relations.
We consider the $q$-deformed Schr\"odinger equation of the harmonic oscillator on the $N$-dimensional quantum Euclidian space. The creation and annihilation operator are found, which systematically produce all energy levels and eigenfunctions of the Schr\"odinger equation. In order to get the $q$-series representation of the eigenfunction, we also give an alternative way to solve the Schr\"odinger equation which is based on the $q$-analysis. We represent the Schr\"odinger equation by the $q$-difference equation and solve it by using $q$-polynomials and $q$-exponential functions.