ShantanuT01/DACTYL-Pretraining huggingface dataset:
Redshift space distortions caused by galaxy peculiar velocities provide a window onto the growth rate of large scale structure and a method for testing general relativity. We investigate through a comparison of N-body simulations to various extensions of perturbation theory beyond the linear regime, the robustness of cosmological parameter extraction, including the gravitational growth index, \gamma. We find that the Kaiser formula and some perturbation theory approaches bias the growth rate by 1-sigma or more relative to the fiducial at scales as large as k > 0.07 h/Mpc. This bias propagates to estimates of the gravitational growth index as well as \Omega_m and the equation of state parameter and presents a significant challenge to modelling redshift space distortions. We also determine an accurate fitting function for a combination of line of sight damping and higher order angular dependence that allows robust modelling of the redshift space power spectrum to substantially higher k.
We present in detail a class of solutions to the $4D SU(\infty)$ Moyal Anti Self Dual Yang Mills equations that are related to $reductions$ of the generalized Moyal Nahm quations using the Ivanova-Popov ansatz. The former yields solutions to the ASDYM/SDYM equations for arbitary gauge groups. A further dimensional reduction yields solutions to the Moyal Anti Self Dual Gravitational equations. The Self Dual Yang Mills /Self Dual Gravity case requires a separate study. SU(2) and $SU(\infty)$ (continuous) Moyal Toda equations are derived and solutions to the latter equations in $implicit$ form are proposed via the Lax-Brockett double commutator formalism . An explicit map taking the Moyal heavenly form (after a rotational Killing symmetry reduction) into the SU(2) Moyal Toda field is found. Finally, the generalized Moyal Nahm equations are conjectured that contain the continuous $SU(\infty)$ Moyal Toda equation after a suitable reduction. Three different embeddings of the three different types of Moyal Toda equations into the Moyal Nahm equations are discussed.
The widths of the decays $\rho^{-}\to\eta\pi^{-}$ and $\tau^{-}\to\eta(\eta')\pi^{-}\nu$ are calculated in the framework of the NJL model. It is shown that these decays are defined by the $u$ and $d$ quark mass difference. It leads to the suppression of these decays in comparison with the main decay modes. In the process $\rho^{-}\to\eta\pi^{-}$ the intermediate scalar $a_0^{-}$ state is taken into account. For the $\tau$ decays the intermediate states with $a_0^{-}$, $\rho^{-}(770)$ and $\rho^{-}(1450)$ mesons are used. Our estimates are compared with the results obtained in other works.
The problem of extraction of a single-mode quantum state from a high-Q cavity is studied for the case in which the time of preparation of the quantum state of the cavity mode is short compared with its decay time. The temporal evolution of the quantum state of the field escaping from the cavity is calculated in terms of phase-space functions. A general condition is derived under which the quantum state of the pulse built up outside the cavity is a nearly perfect copy of the quantum state the cavity field was initially prepared in. The results show that unwanted losses prevent the realization of a nearly perfect extraction of nonclassical quantum states from high-Q optical microcavities with presently available technology.
Hypervelocity stars (HVS) move so fast that they are unbound to the Galaxy. When they were first discovered in 2005, dynamical ejection from the supermassive black hole (SMBH) in the Galactic Centre (GC) was suggested as their origin. The two dozen HVSs known today are young massive B stars, mostly of 3-4 solar masses. Recently, 20 HVS candidates of low mass were discovered in the Segue G and K dwarf sample, but none of them originates from the GC. We embarked on a kinematic analysis of the Segue HVS candidate sample using the full 6D phase space information based on new proper motion measurements. Their orbital properties can then be derived by tracing back their trajectories in different mass models of our Galaxy. We present the results for 14 candidate HVSs, for which proper motion measurements were possible. Significantly lower proper motions than found in the previous study were derived. Considering three different Galactic mass models we find that all stars are bound to the Galaxy. We confirm that the stars do not originate from the GC. The distribution of their proper motions and radial velocities is consistent with predictions for runaway stars ejected from the Galactic disk by the binary supernova mechanism. However, their kinematics are also consistent with old disk membership. Moreover, most stars have rather low metallicities and strong $\alpha$-element enrichment as typical for thick disk and halo stars, whereas the metallicity of the three most metal-rich stars could possibly indicate that they are runaway stars from the thin disk. One star shows halo kinematics.
We consider a measure of the peculiar velocity field derived from the Mark III compilation of 2900 spiral galaxies (Willick \etal 1996b), using an analysis that is substantially free of bias (Nusser and Davis 1995). We expand the velocity field in a set of orthogonal, smooth modes, reducing the data to a set of 56 coefficients fitted to a maximum redshift of 6000 km/s, and maximum spherical harmonic of l=3. Equivalent mode coefficients can be computed for the gravity field derived from any whole-sky redshift catalog of galaxies, such as the \iras 1.2 Jy survey (Fisher \etal 1995). Detailed intercomparison shows the two independent fields to be remarkably aligned in general. There are, however, systematic discrepancies in the fields that lead to coherence in the residuals between them. These residuals take the form of a dipole field in the LG frame that grows with distance; it is not consistent with a bulk flow residual.   A chi-squared analysis of the mode-mode comparison designed to determine which value of $\beta\equiv \Omega^{0.6}/b$ for the \iras gravity field best fits the Mark III velocity field shows instead that no value of $\beta$ is acceptable. This is in contrast to the simulated catalogs, and suggests that there must be some systematic discrepancy between the two fields.
We study the nature of the ground state of the frustrated J1-J2 model and the J1-J3 model using a variational algorithm based on projected entangled-pair states (PEPS). By investigating spin-spin correlation functions, we observe a separation in regions with long-range and short-range order. A direct comparison with exact diagonalizations in the subspace of short-range valence bond singlets reveals that the system is well described by states within this subset in the short-range order regions. We discuss the question whether the system forms a spin-liquid, a plaquette valence bond crystal or a columnar dimer crystal in these regions.
The Dumont differential system on the Jacobi elliptic functions was introduced by Dumont (Math Comp, 1979, 33: 1293--1297) and was extensively studied by Dumont, Viennot, Flajolet and so on. In this paper, we first present a labeling scheme for the cycle structure of permutations. We then introduce two types of Jacobi-pairs of differential equations. We present a general method to derive the solutions of these differential equations. As applications, we present some characterizations for several permutation statistics.
We give an explicit prescription for experimentally determining the evolution operators which completely describe the dynamics of a quantum mechanical black box -- an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible, and illustrate the general theory by considering specifically one and two quantum bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication, and computation systems.
We perform a simplified analysis of the edge excitations of the canted antiferromagnetic (CAF) phase of the $\nu=0$ quantum Hall state in both monolayer and bilayer graphene. Namely, we calculate, within the framework of quantum Hall ferromagnetism, the mean-field quasiparticle spectrum of the CAF phase neglecting the modification of the order parameter at the edge. We demonstrate that, at a fixed perpendicular component $B_\perp$ of the magnetic field, the gap $\Delta_\text{edge}$ in the edge excitation spectrum gradually decreases upon increasing the parallel component $B_\parallel$, as the CAF phase continuously transforms to the fully spin-polarized ferromagnetic (F) phase. The edge gap closes completely ($\Delta_\text{edge}=0$) once the F phase, characterized by gapless counter-propagating edge excitations, is reached at some finite $B_\perp$-dependent value $B_\parallel^*$ and remains closed upon further increase of $B_\parallel$. This results in an gradual insulator-metal transition, in which the conductance $G \sim (e^2/h) \exp(-\Delta_\text{edge}/T)$ grows exponentially with $B_\parallel$ in the range $0<B_\parallel<B_\parallel^*$, while in the gapped CAF phase, and saturates to a metallic value $G \sim e^2/h$ in the F phase at $B_\parallel>B_\parallel^*$. This unique transport feature of the CAF phase provides a way to identify and distinguish it from other competing phases of the $\nu=0$ quantum Hall state in a tilted-field experiment.
We give a short proof of a strong form of Weyl's law for $\text{SO}(N)$ using well known facts of the theory of modular forms. The exponent of the error term is sharp when the rank is at least~$4$. We also discuss the cases with smaller rank improving previous results.
A semiclassical theory based on the Boltzmann transport equation for a two-dimensional electron gas modulated along one direction with weak electrostatic or magnetic modulations is proposed. It is shown that oscillations of the magnetoresistivity $ \rho_{||} $ corresponding to the current driven along the modulation lines observed at moderately low magnetic fields, can be explained as classical geometric resonances reflecting the commensurability of the period of spatial modulations and the cyclotron radius of electrons.
Percolation properties of the dead leaves model, also known as confetti percolation, are considered. More precisely, we prove that the critical probability for confetti percolation with square-shaped leaves is 1/2. This result is related to a question of Benjamini and Schramm concerning disk-shaped leaves and can be seen as a variant of the Harris-Kesten theorem for bond percolation. The proof is based on techniques developed by Bollob\'as and Riordan to determine the critical probability for Voronoi and Johnson-Mehl percolation.
The black hole mass and accretion rate in Ultraluminous X-ray sources (ULXs) in external galaxies, whose X-ray luminosities exceed those of the brightest black holes in our Galaxy by hundreds and thousands of times$^{1,2}$, is an unsolved problem. Here we report that all ULXs ever spectroscopically observed have about the same optical spectra apparently of WNL type (late nitrogen Wolf-Rayet stars) or LBV (luminous blue variables) in their hot state, which are very scarce stellar objects. We show that the spectra do not originate from WNL/LBV type donors but from very hot winds from the accretion discs with nearly normal hydrogen content, which have similar physical conditions as the stellar winds from these stars. The optical spectra are similar to that of SS 433, the only known supercritical accretor in our Galaxy$^{3}$, although the ULX spectra indicate a higher wind temperature. Our results suggest that ULXs with X-ray luminosities of $\sim 10^{40}$ erg s$^{-1}$ must constitute a homogeneous class of objects, which most likely have supercritical accretion discs.
We study the asymptotic behaviour of random walks in i.i.d. random environments on $\Z^d$. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when it exists) for any 2-valued environment, and show that this does not hold for 3-valued environments without additional assumptions. We give a proof of directional transience and the existence of positive speeds under strong, but non-trivial conditions on the distribution of the environment. Our results include generalisations (to the non-elliptic setting) of 0-1 laws for directional transience, and in 2-dimensions the existence of a deterministic limiting velocity.
We study analytically, in one dimension, the survival probability $P_{s}(t)$ up to time $t$ of an immobile target surrounded by mutually noninteracting traps each performing a continuous-time random walk (CTRW) in continuous space. We consider a general CTRW with symmetric and continuous (but otherwise arbitrary) jump length distribution $f(\eta)$ and arbitrary waiting time distribution $\psi(\tau)$. The traps are initially distributed uniformly in space with density $\rho$. We prove an exact relation, valid for all time $t$, between $P_s(t)$ and the expected maximum $E[M(t)]$ of the trap process up to time $t$, for rather general stochastic motion $x_{\rm trap}(t)$ of each trap. When $x_{\rm trap}(t)$ represents a general CTRW with arbitrary $f(\eta)$ and $\psi(\tau)$, we are able to compute exactly the first two leading terms in the asymptotic behavior of $E[M(t)]$ for large $t$. This allows us subsequently to compute the precise asymptotic behavior, $P_s(t)\sim a\, \exp[-b\, t^{\theta}]$, for large $t$, with exact expressions for the stretching exponent $\theta$ and the constants $a$ and $b$ for arbitrary CTRW. By choosing appropriate $f(\eta)$ and $\psi(\tau)$, we recover the previously known results for diffusive and subdiffusive traps. However, our result is more general and includes, in particular, the superdiffusive traps as well as totally anomalous traps.
This article characterizes the singularities of very weak solutions of 3D stationary Navier-Stokes equations in a punctured ball which are sufficiently small in weak $L^3$.
Experimental results for sequential transport through a lateral quantum dot in the regime of spin blockade induced by spin dependent tunneling are compared with theoretical results obtained by solving a master equation for independent electrons. Orbital and spin effects in electron tunneling in the presence of a perpendicular magnetic field are identified and discussed in terms of the Fock-Darwin spectrum with spin. In the nonlinear regime, a regular pattern of negative differential conductances is observed. Electrical asymmetries in tunnel rates and capacitances must be introduced in order to account for the experimental findings. Fast relaxation of the excited states in the quantum dot have to be assumed, in order to explain the absence of certain structures in the transport spectra.
We investigate the exclusive rare baryonic $\Lambda_{b}\to\Lambda\ell^{+}\ell^{-}$ in a family non-universal $Z^{\prime}$ model, which is one of the natural extension of standard model. Using transition form factors, calculated in the framework of light cone QCD sum rules, we analyze the effects of polarized and unpolarized CP violation asymmetries for the said decay. Our results indicate that the value of unpolarized and polarized CP-violation asymmetries are considerable in both $\Lambda_{b}\to\Lambda\mu^{+}\mu^{-}$ and $\Lambda_{b}\to\Lambda\tau^{+}\tau^{-}$ channels and hence they give clear indication of new physics arising from the neutral $Z^{\prime}$ gauge boson. It is hoped that the measurements of these CP-violating asymmetries will not only help us to relate new physics, but also help us to determine the precise values of the parameters of new gauge boson $Z^{\prime}$.
The ground state properties and neutron structure factor for the two-dimensional antiferromagnet on the triangular lattice, with uni-directional anisotropy in the nearest-neighbor exchange couplings and a weak Dzyaloshinskii-Moriya (DM) interaction, are studied. This Hamiltonian has been used to interpret neutron scattering measurements on the spin 1/2 spiral spin-density-wave system, Cs_2CuCl_4, [R. Coldea, et al., Phys. Rev. B 68, 134424 (2003)]. Calculations are performed using a 1/S expansion, taking into account interactions between spin-waves. The ground state energy, the shift of the ordering wave-vector, Q, and the local magnetization are all calculated to order 1/S^2. The neutron structure factor, obtained using anharmonic spin-wave Green's functions to order 1/S, is shown to be in reasonable agreement with published neutron data, provided that slightly different parameters are used for the exchange and DM interactions than those inferred from measurements in high magnetic field.
Deep neural networks (DNNs), especially deep convolutional neural networks (CNNs), have emerged as the powerful technique in various machine learning applications. However, the large model sizes of DNNs yield high demands on computation resource and weight storage, thereby limiting the practical deployment of DNNs. To overcome these limitations, this paper proposes to impose the circulant structure to the construction of convolutional layers, and hence leads to circulant convolutional layers (CircConvs) and circulant CNNs. The circulant structure and models can be either trained from scratch or re-trained from a pre-trained non-circulant model, thereby making it very flexible for different training environments. Through extensive experiments, such strong structure-imposing approach is proved to be able to substantially reduce the number of parameters of convolutional layers and enable significant saving of computational cost by using fast multiplication of the circulant tensor.
A new generalization of the t-J model with a nearest-neigbour hopping is formulated and solved exactly by the Bethe-ansatz method in the thermodymanic limit. The model describes the dymanics of fermions with different spins and with isotropic and anisotropic interactions.
We investigated the temperature dependence of the superlattice intensity and thermal diffuse scattering intensity of BaAl2O4, which has a network structure with corner-sharing AlO4 tetrahedra, via synchrotron X-ray diffraction experiments. The temperature variation of the superlattice intensity revealed that the structural phase transition occurs at TC = 451.4 K from the P6322 parent crystal structure to the low-temperature superstructure with a cell volume of 2a x 2b x c. BaAl2O4 exhibits an unconventional structural phase transition driven by two competing soft modes, q1/2 ~ (1/2, 1/2, 0) and q1/3 ~ (1/3, 1/3, 0). When approaching the TC from above, the soft mode with q1/3 appeared first and was followed by the q1/2 soft mode. The thermal diffuse scattering intensities from both soft modes increased sharply at TC; therefore, both modes condensed simultaneously. The first principles calculation revealed that structural instabilities exist at the M- and K-points, at which the calculated imaginary frequencies are similar. The small energy difference of these structural instabilities generates the two competing soft modes and determines the eventual low-temperature crystal structure.
We show that the order complex of intervals of a poset, ordered by inclusion, is a Tchebyshev triangulation of the order complex of the original poset. Besides studying the properties of this transformation, we show that the dual of the type $B$ permutohedron is combinatorially equivalent to the suspension of the order complex of the poset of intervals of a Boolean algebra (with the minimum and maximum elements removed).
We study the nonminimally coupled complex scalar field within the framework of teleparallel gravity. Coupling of the field nonminimally to the torsion scalar destroys the Lorentz invariance of the theory in the sense that the resulting equations of motion depend on the choice of a tetrad. For the assumed static spherically symmetric spacetime, we find a tetrad which leads to a self-consistent set of equations, and we construct the self-gravitating configurations of the scalar field---boson stars. The resulting configurations develop anisotropic principal pressures and satisfy the dominant energy condition. An interesting property of the configurations obtained with sufficiently large field-to-torsion coupling constant is the outwardly increasing energy density, followed by an abrupt drop towards the usual asymptotic tail. This feature is not present in the boson stars with the field minimally or nonminimally coupled to the curvature scalar, and therefore appears to be a torsion--only effect.
An eigenstate decoherence hypothesis states that each individual eigenstate of a large closed system is locally classical-like. We extend this hypothesis to account for a typically extremely short time scale of decoherence. The extension implies that nondiagonal matrix elements of certain operators - quantumness witnesses - are suppressed as long as the energy difference between corresponding eigenstates is smaller than the inverse decoherence time.
We present master formulas for the divergent part of the one-loop effective action for a minimal operator of any order in the 4-dimensional curved space and for an arbitrary nonminimal operator in the flat space.
We bring the two color maps for the plane component magnetic field of our Galaxy in coordinates of (R;l) and (DM;l). It was shown that magnetic field has reversals of the direction in neighbor spiral arms, in agreement with known models for the Galactic magnetic field. For the Sagittarius spiral arm region there is, however, some disagreement with standard magnetic field models. The major discrepancy is the fact that in the Sagittarius arm region the magnetic field in Southern hemisphere of the Galaxy, have opposite direction to the field of the Northern hemisphere. We think that the Sagittarius spiral arm, at last the magnetic spiral arm in this region is not symmetric to the Galactic plane, and is located mainly in Northern hemisphere.
The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar fields and can be performed in an explicit way for both metric and general metric-dilaton cases. In view of this we can evaluate the structure of possible counterterms and show that they contains second derivative structures only. The calculations in the theory with an auxiliary fields require some special procedure to be applied. We perform the explicit calculations in a different gauges and explore the features of the auxiliary fields.
Observations performed in the last few years indicate that most massive early-type galaxies (ETGs) observed at redshift z>1 exhibit sizes smaller by a factor of a few than local ETGs of analogous stellar mass. We present numerical simulations of the effect of baryonic mass loss on the structure of a spheroidal stellar system, embedded in a dark matter halo. This process, invoked as a possible explanation of the observed size increase of ETGs since z \sim 2, could be caused either by QSO/starburst driven galactic winds, promptly ejecting from Early Type Galaxies (ETGs) the residual gas and halting star formation (galactic winds), or by stellar mass returned to the ISM in the final stages of stellar evolution. Indeed, we find that a conceivable loss of about 50% of the baryonic mass can produce a significant size increase. However, the puffing up due to galactic winds occurs when the stellar populations are much younger than the estimated ages >0.5 Gyr of compact high-z ETGs. Therefore, while it may have had a role in deciding the final structure of ETGs, it cannot explain the evolution observed so far of their size-mass relation; its signature should be searched for in much younger systems. Conversely, the mass loss due to stellar evolution could cause a relatively modest expansion of passively evolving stellar systems later on, contributing to, without dominating, the observed evolution of their mass-size relationship.