ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate statistics of the decay process in the equal-mass three-body problem with randomized initial conditions. Contrary to earlier expectations of similarity with "radioactive decay", the lifetime distributions obtained in our numerical experiments turn out to be heavy-tailed, i.e. the tails are not exponential, but algebraic. The computed power-law index for the differential distribution is within the narrow range, approximately from -1.7 to -1.4, depending on the virial coefficient. Possible applications of our results to studies of the dynamics of triple stars known to be at the edge of disruption are considered.
The Wisconsin H-Alpha Mapper (WHAM) has completed a velocity-resolved map of diffuse H-alpha emission of the entire northern sky, providing the first comprehensive picture of both the distribution and kinematics of diffuse ionized gas in the Galaxy. WHAM continues to advance our understanding of the physical conditions of the warm ionized medium through observations of other optical emission lines throughout the Galactic disk and halo. We discuss some highlights from the survey, including an optical window into the inner Galaxy and the relationship between HI and HII in the diffuse ISM.
Solar X-ray spectra from the RESIK crystal spectrometer on the {\em CORONAS-F} spacecraft (spectral range $3.3-6.1$~\AA) are analyzed for thirty-three flares using a method to derive abundances of Si, S, Ar, and K, emission lines of which feature prominently in the spectra. For each spectrum, the method first optimizes element abundances then derives the differential emission measure as a function of temperature based on a procedure given by Sylwester et al. and Withbroe. This contrasts with our previous analyses of RESIK spectra in which an isothermal assumption was used. The revised abundances (on a logarithmic scale with $A({\rm H}) = 12$) averaged for all the flares in the analysis are $A({\rm Si}) = 7.53 \pm 0.08$ (previously $7.89 \pm 0.13$), $A({\rm S}) = 6.91 \pm 0.07$ ($7.16 \pm 0.17$), $A({\rm Ar}) = 6.47 \pm 0.08$ ($6.45 \pm 0.07$), and $A({\rm K}) = 5.73 \pm 0.19$ ($5.86 \pm 0.20$), with little evidence for time variations of abundances within the evolution of each flare. Our previous estimates of the Ar and K flare abundances are thus confirmed by this analysis but those for Si and S are reduced. This suggests the flare abundances of Si and Ar are very close to the photospheric abundance or solar proxies, while S is significantly less than photospheric and the K abundance is much higher than photospheric. These estimates differ to some extent from those in which a single enhancement factor applies to elements with first ionization potential less than 10~eV.
The microscopic description of collectivity in heavy nuclei in the framework of the configuration-interaction shell model has been a major challenge. The size of the model space required for the description of heavy nuclei prohibits the use of conventional diagonalization methods. We have overcome this difficulty by using the shell model Monte Carlo (SMMC) method, which can treat model spaces that are many orders of magnitude larger than those that can be treated by conventional methods. We identify a thermal observable that can distinguish between vibrational and rotational collectivity and use it to describe the crossover from vibrational to rotational collectivity in families of even-even rare-earth isotopes. We calculate the state densities in these nuclei and find them to be in close agreement with experimental data. We also calculate the collective enhancement factors of the corresponding level densities and find that their decay with excitation energy is correlated with the pairing and shape phase transitions.
The paper uses Iwasawa theory at the prime $p=2$ to prove non-vanishing theorems for the value at $s=1$ of the complex $L$-series of certain quadratic twists of the Gross family of elliptic curves with complex multiplication by the field $K = \BQ(\sqrt{-q})$, where $q$ is any prime $\equiv 7 \mod 8$. Our results establish some broad generalizations of the non-vanishing theorem first proven by D. Rohrlich using complex analytic methods. Such non-vanishing theorems are important because it is known that they imply the finiteness of the Mordell-Weil group and the Tate-Shafarevich group of the corresponding elliptic curves over the Hilbert class field of $K$. It is essential for the proofs to study the Iwasawa theory of the higher dimensional abelian variety with complex multiplication which is obtained by taking the restriction of scalars to $K$ of the particular elliptic curve with complex multiplication introduced by Gross.
We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between their corresponding strings. This allows a straightforward application of classical coding theory to find arrangements of operators or states with a given distance distribution. Using the simplex or extended Reed-Solomon code in our construction recovers the discrete Wigner function, which has important applications in quantum information theory.
We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture, thus strengthening the counterexamples built by Reguera--Thiele. We show a certain logarithmic blow-up for the end-point estimates of important weighted singular operators.
For certain sequences $A$ of positive integers with missing $g$-adic digits, the Dirichlet series $F_A(s) = \sum_{a\in A} a^{-s}$ has abscissa of convergence $\sigma_c < 1$. The number $\sigma_c$ is computed. This generalizes and strengthens a classical theorem of Kempner on the convergence of the sum of the reciprocals of a sequence of integers with missing decimal digits.
We compute the Boundary Superstring Field Theory partition function on the annulus in the presence of independent linear tachyon profiles on the two boundaries. The R-R sector is found to contribute non-trivially to the derivative terms of the space-time effective action. In the process we construct a boundary state description of D-branes in the presence of a linear tachyon. We quantize the open string in a tachyonic background and address the question of open/closed string duality.
Identification of gamma-ray-emitting Galactic sources is a long-standing problem in astrophysics. One such source, 1AGL J2022+4032, coincident with the interior of the radio shell of the supernova remnant Gamma Cygni (SNR G78.2+2.1) in the Cygnus Region, has recently been identified by Fermi as a gamma-ray pulsar, LAT PSR J2021+4026. We present long-term observations of 1AGL J2022+4032 with the AGILE gamma-ray telescope, measuring its flux and light curve. We compare the light curve of 1AGL J2022+4032 with that of 1AGL J2021+3652 (PSR J2021+3651), showing that the flux variability of 1AGL J2022+4032 appears to be greater than the level predicted from statistical and systematic effects and producing detailed simulations to estimate the probability of the apparent observed variability. We evaluate the possibility that the gamma-ray emission may be due to the superposition of two or more point sources, some of which may be variable, considering a number of possible counterparts. We consider the possibility of a nearby X-ray quiet microquasar contributing to the flux of 1AGL J2022+4032 to be more likely than the hypotheses of a background blazar or intrinsic gamma-ray variabilty of LAT PSR J2021+4026.
We discuss the geometrical optics of coincidence imaging for two kinds of spatial correlations which are related to a classical thermal light source and a two-photon quantum entangled state.
The existence of reference levels of signals which determine directly the temperature dependence of emission factor in deep level transient phenomena is discussed. The basic algebraic structure of reference levels in the classical DLTS is studied and various signal forms with derived reference levels are given. We then demonstrate the use of these signal forms and compare them with the classical DLTS double boxcar signal.
Cation displacements, oxygen octahedral tilts, and magnetism of epitaxial, ferrimagnetic, insulating GdTiO3 films sandwiched between cubic SrTiO3 layers are studied using scanning transmission electron microscopy and magnetization measurements. With decreasing GdTiO3 film thickness, structural (GdFeO3-type) distortions are reduced, concomitant with a reduction in the Curie temperature. Ferromagnetism persists to smaller deviations from the cubic perovskite structure than is the case for the bulk rare earth titanates. The results indicate that the FM ground state is controlled by the narrow bandwidth, exchange and orbital ordering, and only to second order depends on amount of the GdFeO3-type distortion.
In this paper we investigate the inclusive associated production of {\Upsilon} + {\gamma} at the hadron collider. We calculate the color-singlet sub-processes and all three color-octet sub-processes at the next-to-leading order. Seven sets of long distance matrix elements(LDMEs), which are extracted from the studies on the prompt production of {\Upsilon} at hadron colliders, are used to give the numerical results and we find that there are three sets of LDMEs give the unphysical results on the yield and the polarization for this process. The yield is enhanced by several or two orders times comparing to that of color-singlet process and the polarization changes from longitudinal to slightly transverse or even mainly transverse in the large pt region. The estimation results indicate that to study the process at the large hadron collider (LHC) is difficult and it may be well investigated at the future Super Proton-Proton Collider(SPPC).
From the tau-lepton analysis of the charged Higgs decay of the top quark at the Tevatron, t -> H+ b -> tau+ nu_{tau} b, it is possible to set rather stringent bounds on the (tan(beta),M_{H+})-plane, if one assumes that H+ is a charged member of a generic two-Higgs-doublet model. However, if we consider the possibility that H+ is supersymmetric, then we find that the allowed region in the (tan(beta),M_{H+})-plane can be significantly modified by the MSSM quantum corrections. Throughout our analysis we correlate the top quark results with the limits imposed by radiative and semileptonic B-meson decays. Remarkably, one can envision situations in the MSSM parameter space where H+ completely eludes those bounds, i.e. a charged Higgs with a mass below the top quark mass could coexist with essentially any value of tan(beta).
Let C be a curve of genus g, and let SU(r) be the moduli space of vector bundles of rank r on C, with trivial determinant. A general E in SU(r) defines a theta divisor in the linear system |r Theta|, where Theta is the canonical theta divisor in Pic^{g-1}(C). This defines a rational map SU(r) - - > |r Theta|, which is the map associated to the determinant bundle on SU(r) (the positive generator of Pic(SU(r)). In this paper we prove that in genus 2 this map is generically finite and dominant. The same method, together with some classical work of Morin, shows that in rank 3 and genus 3 the theta map is a finite morphism -- in other words, every E in SU(3) admits a theta divisor.
We use a three-body model to investigate breakup reactions of 11Li (n+n+9Li) on a light target. The interaction parameters are constrained by known properties of the two-body subsystems, the 11Li binding energy and fragmentation data. The remaining degrees of freedom are discussed. The projectile-target interactions are described by phenomenological optical potentials. The model predicts dependence on beam energy and target, differences between longitudinal and transverse momentum distributions and provides absolute values for all computed differential cross sections. We give an almost complete series of observables and compare with corresponding measurements. Remarkably good agreement is obtained. The relative neutron-9Li p-wave content is about 40%. A p-resonance, consistent with measurements at about 0.5 MeV of width about 0.4 MeV, seems to be necessary. The widths of the momentum distributions are insensitive to target and beam energy with a tendency to increase towards lower energies. The transverse momentum distributions are broader than the longitudinal due to the diffraction process. The absolute values of the cross sections follow the neutron-target cross sections and increase strongly for beam energies decreasing below 100 MeV/u.
We prove maximal inequalities for $L_q$-valued martingales obtained by stochastic integration with respect to compensated random measures. A version of these estimates for integrals with respect to compensated Poisson random measures were first obtained by Dirksen (arXiv:1208:3885) using arguments based on inequalities for sums of independent Banach-space-valued random variables, geometric properties of Banach spaces, and decoupling inequalities. Our proofs are completely different and rely almost exclusively on classical stochastic analysis for real semimartingales.
The possibility that some Markarian objects (e.g. Mkn 501, Mkn 421 and Mkn 766) host massive binary black hole systems with eccentric orbits at their centers has been considered. These systems could be sources of gravitational radiation for space-based gravitational wave interferometers like LISA and ASTROD. In the framework of the Lincoln -- Will approximation we simulate coalescence of such systems, calculate gravitational wave templates and discuss parameters of these binary black hole systems corresponding to the facilities of LISA and ASTROD. We discuss also the possibility to extract information about parameters of the binary black hole systems (masses, of components, distances between them, eccentricity and orbit inclination angle with respect to line of sight) from future gravitational wave measurements.
The origins of indirect spin exchange in crystalline thin films of Copper Octabutoxy Phthalocyanine (Cu-OBPc) are investigated using Magnetic Circular Dichroism (MCD) spectroscopy. These studies are made possible by a solution deposition technique which produces highly ordered films with macroscopic grain sizes suitable for optical studies. For temperatures lower than 2 K, the contribution of a specific state in the valence band manifold originating from the hybridized lone pair in nitrogen orbitals of the Phthalocyanine ring, bears the Brillouin-like signature of an exchange interaction with the localized $\textit{d}$-shell Cu spins. A comprehensive MCD spectral analysis coupled with a molecular field model of a $\sigma\pi-d$ exchange analogous to $\textit{sp-d}$ interactions in Diluted Magnetic Semiconductors (DMS) renders an enhanced Zeeman splitting and a modified $\textit{g}$-factor of -4 for the electrons that mediate the interaction. These studies define an experimental tool for identifying electronic states involved in spin-dependent exchange interactions in organic materials.
We review two recently developed efficient methods for calculating rate constants of processes dominated by rare events in high-dimensional complex systems. The first is transition interface sampling (TIS), based on the measurement of effective fluxes through hypersurfaces in phase space. TIS improves efficiency with respect to standard transition path sampling (TPS) rate constant techniques, because it allows a variable path length and is less sensitive to recrossings. The second method is the partial path version of TIS. Developed for diffusive processes, it exploits the loss of long time correlation. We discuss the relation between the new techniques and the standard reactive flux methods in detail. Path sampling algorithms can suffer from ergodicity problems, and we introduce several new techniques to alleviate these problems, notably path swapping, stochastic configurational bias Monte Carlo shooting moves and order-parameter free path sampling. In addition, we give algorithms to calculate other interesting properties from path ensembles besides rate constants, such as activation energies and reaction mechanisms.
We present the large statistics of the galaxy effective radius in the rest-frame far-infrared (FIR) wavelength Re(FIR) obtained from 1627 deep ALMA 1-mm band maps that become public by 2017 July. Our ALMA sample consists of 1034 sources at z=0-6 that typically have the star-formation rate of ~100-1000 M$_{\odot}$/yr and the stellar mass of ~10$^{10}$-10$^{11.5}$ M$_{\odot}$. We homogeneously derive Re(FIR) and FIR luminosity L_FIR of our ALMA sources via the same uv-visibility method with the exponential disk fitting, carefully evaluating the selection and measurement incompletenesses by realistic Monte-Carlo simulations. We find that there is a positive correlation between Re(FIR) and L_FIR at the >99% significance level. The best-fit power-law function, Re(FIR) $\propto$ L_FIR$^{\alpha}$, provides $\alpha=0.28+/-0.07$, and shows that the average Re(FIR) at a fixed L_FIR decreases toward high redshifts. The best-fit $\alpha$ and the redshift evolution of Re(FIR) are similar to those of the galaxy effective radius in the rest-frame UV (optical) wavelength Re(UV) (Re(Opt.)) revealed by Hubble Space Telescope (HST) studies. We identify that our ALMA sources have significant trends of Re(FIR) <~ Re(UV) and Re(Opt.), suggesting that dusty starbursts take place in a compact region. Moreover, Re(FIR) of our ALMA sources is comparable to Re(Opt.) of quiescent galaxies at z~1-3 as a function of stellar mass, supporting the evolutionary connection between these two galaxy populations. We also investigate rest-frame UV and optical morphologies of our ALMA sources with deep HST images, and find that ~30-40% of our ALMA sources are classified as major mergers. This indicates that dusty starbursts are triggered not only by the major mergers but also the other mechanism(s).
This paper assesses the importance of three-body triple dipole interactions for quasi-one dimensional phases of He, Ne, H_2, Ar, Kr and Xe confined within interstitial channels or on the external surfaces of nanotube bundles. We find the substrate-mediated contribution to be substantial: for interstitial H_2 the well depth of the effective pair potential is reduced to approximately one half of its value in free space.   We carry out ab initio calculations on linear and equilateral configurations of H_2 trimer and find that overlap interactions do not greatly change the DDD interaction in the linear configuration when the spacing is greater than about 3 A. However, the DDD interaction alone is clearly insufficient for the triangular configurations studied.
We perform an experimental study of DC current induced microwave emission in a magnetic tunnel junction (MTJ) consisting of three active magnetic layers. For this tri-layer structure, in addition to a conventional bilayer orthogonal MTJ containing a perpendicular free layer and an in-plane fixed layer, a second perpendicular layer has been introduced. We found that the microwave emission frequency induced by spin-transfer torque (STT) can reach as high as 6 GHz in the absence of any applied magnetic field. Moreover, microwave emission is observed for both current polarizations where a redshift is seen with increase in magnitude of current. We discuss spin-dynamics of the observed bi-directional high-frequency emission and the physical origin of the red-shift. The distinct microwave emission properties exhibited in this tri-layer MTJ structure could potentially be useful for future applications in nanoscale spintronics devices such as microwave communication and neuromorphic computing.
A hydrostatic and stationary white dwarf envelope model has been developed for the study of the post-outburst phases of classical novae and their soft X-ray emission. Several white dwarf masses and chemical compositions typical for classical novae have been considered. The results show that the luminosity, maximum effective temperature and envelope masses depend on the white dwarf mass and on the chemical composition. Envelope masses for which equilibrium solutions exist are pretty small ~10^{-7}-10^{-6} Msun, thus leading to a short duration of the soft X-ray emitting phase of classical novae, in agreement with most of the observations. The models presented provide a useful tool for the determination of the white dwarf properties from observable parameters in the X-ray range.
For the ZND model, we show also singularity formation on the downstream side for arbitrary exponentially-growing weighted norms. For the Majda model on the other hand, we establish for appropriate such weighted norms a set of energy estimates implying not only non-formation of singularities near waves of arbitrary amplitude but also full asymptotic orbital stability for small-amplitude ones.
We show the structures of magnetic excitations in spin-1/2 kagome-lattice antiferromagnets Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$ investigated by inelastic neutron scattering in wide energy and momentum ranges. For Cs$_2$Cu$_3$SnF$_{12}$, four single-magnon excitation modes were observed. Low-energy three modes are assigned to be transverse modes and the high-energy fourth mode is suggested to be an amplitude mode. It was found that the broad excitation continuum without a marked structure spreads in a wide energy range from $0.15J$ to approximately $2.5J$ in contrast to the clearly structured excitation continuum observed in the spin-1/2 triangular-lattice Heisenberg antiferromagnet. These findings strongly suggest spinon excitations as elementary excitations in Cs$_2$Cu$_3$SnF$_{12}$. In Rb$_2$Cu$_3$SnF$_{12}$, singlet-triplet excitations from the pinwheel VBS state and their ghost modes caused by the enlargement of the chemical unit cell were clearly confirmed. It was found that the excitation continuum is structured in the low-energy region approximately below $J_{\mathrm{avg}}$ and the almost structureless high-energy excitation continuum extends to approximately $2.6J_{\mathrm{avg}}$. The characteristics of the high-energy excitation continuum are common to both Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$, irrespective of their ground states. The experimental results strongly suggest that the spin liquid component remains in the ground state as quantum fluctuations in Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$.
This paper is concerned with the two-dimensional stationary Navier-Stokes system in the domain exterior to the unit disk. The existence of solutions with critical decay $O(|x|^{-1})$ is established around some explicit flows with large flux. The solutions are obtained for non-symmetric external forces, and moreover, are unique in a certain class.
Noise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which requires large qubit overhead, we turn to quantum error mitigation, in which we make use of extra measurements. Error extrapolation is an error mitigation technique that has been successfully implemented experimentally. Numerical simulation and heuristic arguments have indicated that exponential curves are effective for extrapolation in the large circuit limit with an expected circuit error count around unity. In this article, we extend this to multi-exponential error extrapolation and provide more rigorous proof for its effectiveness under Pauli noise. This is further validated via our numerical simulations, showing orders of magnitude improvements in the estimation accuracy over single-exponential extrapolation. Moreover, we develop methods to combine error extrapolation with two other error mitigation techniques: quasi-probability and symmetry verification, through exploiting features of these individual techniques. As shown in our simulation, our combined method can achieve low estimation bias with a sampling cost multiple times smaller than quasi-probability while without needing to be able to adjust the hardware error rate as required in canonical error extrapolation.