ShantanuT01/DACTYL-Pretraining huggingface dataset:
The frustrated ferromagnetic spin-1/2 Heisenberg chain is studied by means of a low-energy field theory as well as the density-matrix renormalization group and exact diagonalization methods. Firstly, we study the ground-state phase diagram in a magnetic field and find an `even-odd' (EO) phase characterized by bound pairs of magnons in the region of two weakly coupled antiferromagnetic chains. A jump in the magnetization curves signals a first-order transition at the boundary of the EO phase, but otherwise the curves are smooth. Secondly, we discuss thermodynamic properties at zero field, where we confirm a double-peak structure in the specific heat for moderate frustrating next-nearest neighbor interactions.
We report a polarized Raman scattering study of the lattice dynamics of $\beta$-Li$_2$IrO$_3$ under hydrostatic pressures up to 7.62 GPa. At ambient pressure, $\beta$-Li$_2$IrO$_3$ exhibits the hyperhoneycomb crystal structure and a magnetically ordered state of spin-orbit entangled Jeff = 1/2 moments that is strongly influenced by bond-directional (Kitaev) exchange interactions. At a critical pressure of ~ 4.1 GPa, the phonon spectrum changes abruptly consistent with the reported structural transition into a monoclinic, dimerized phase. A comparison to the phonon spectra obtained from density functional calculations shows reasonable overall agreement. The calculations also indicate that the high-pressure phase is a nonmagnetic insulator driven by the formation of Ir-Ir dimer bonds. Our results thus indicate a strong sensitivity of the electronic properties of $\beta$-Li$_2$IrO$_3$ to the pressure-induced structural transition.
This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.
In this work, we consider rotating BTZ black hole in three dimensions which is dual of one dimensional holographic superconductors. We applied higher order corrections of the entropy, which interpreted as quantum corrections, to the thermodynamics quantities and study modified thermodynamics. We investigate stability of rotating BTZ black hole under effects of higher order quantum corrections, and find that they affect stability of black hole. So, the small black hole has some instabilities and critical points due to the quantum effects. We also study effect of correction terms on the dual picture of rotating BTZ black hole.
We present studies of ballistic transport in three terminal T-shaped junction in a linear and non-linear regime. The floating electrode acts as a scatterer and modifies the conductance in a direct channel (between source and drain electrode). In the low voltage limit, the conductance shows the Wigner threshold effect and the bend resistance. A specific shape of the Wigner singularities can be changed by applied voltage to the floating electrode as well as by a shift of the Fermi level. The system also exhibits filtering properties with current distribution between different modes propagating in the junction. Back action of current flowing in the direct channel on changes of the voltage in the floating electrode is considered in the non-linear regime.
We investigate the tricritical scaling behavior of the two-dimensional spin-$1$ Blume-Capel model using the Wang-Landau method measuring the joint density of states for lattice sizes up to $48\times 48$ sites. The first-order transition curve is systematically determined employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. Deep in the first-order area of the phase diagram, we also find that the specific heat exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. At the tricritical point, we characterize the tricritical exponents through finite-size scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, $y_t = 1.804(5)$, $y_g = 0.80(1)$, and $y_h = 1.925(3)$, provides the first Wang-Landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.
The thermodynamics of the diffuse, X-ray emitting gas in clusters of galaxies is determined by gravitational processes associated with shock heating, adiabatic compression, and non-gravitational processes such as heating by SNe, stellar winds, activity in the central galactic nucleus, and radiative cooling. The effect of gravitational processes on the thermodynamics of the Intra Cluster Medium (ICM) can be expressed in terms of the ICM entropy S ~ ln(T/\rho^{2/3}). We use a generalized spherical model to compute the X-ray properties of groups and clusters for a range of initial entropy levels in the ICM and for a range of mass scales, cosmic epochs and background cosmologies. We find that the statistical properties of the X-ray clusters strongly depend on the value of the initial excess entropy. Assuming a constant, uniform value for the excess entropy, the present-day X-ray data are well fitted for the following range of values K_* = kT/\mu m_p \rho^{2/3} = (0.4\pm 0.1) \times 10^{34} erg cm^2 g^{-5/3} for clusters with average temperatures kT>2 keV; K_* = (0.2\pm 0.1) \times 10^{34} erg cm^2 g^{-5/3} for groups and clusters with average temperatures kT<2 keV. These values correspond to different excess energy per particle of kT \geq 0.1 (K_*/0.4\times 10^{34}) keV. The dependence of K_* on the mass scale can be well reproduced by an epoch dependent external entropy: the relation K_* = 0.8(1+z)^{-1}\times 10^{34} erg cm^2 g^{-5/3} fits the data over the whole temperature range. Observations of both local and distant clusters can be used to trace the distribution and the evolution of the entropy in the cosmic baryons, and ultimately to unveil the typical epoch and the source of the heating processes.
Isophotal analysis of M87, using data from the Advanced Camera for Surveys, reveals a projected displacement of 6.8 +/- 0.8 pc (~ 0.1 arcsec) between the nuclear point source (presumed to be the location of the supermassive black hole, SMBH) and the photo-center of the galaxy. The displacement is along a position angle of 307 +/- 17 degrees and is consistent with the jet axis. This suggests the active SMBH in M87 does not currently reside at the galaxy center of mass, but is displaced in the counter-jet direction. Possible explanations for the displacement include orbital motion of an SMBH binary, gravitational perturbations due to massive objects (e.g., globular clusters), acceleration by an asymmetric or intrinsically one-sided jet, and gravitational recoil resulting from the coalescence of an SMBH binary. The displacement direction favors the latter two mechanisms. However, jet asymmetry is only viable, at the observed accretion rate, for a jet age of >0.1 Gyr and if the galaxy restoring force is negligible. This could be the case in the low density core of M87. A moderate recoil ~1 Myr ago might explain the disturbed nature of the nuclear gas disk, could be aligned with the jet axis, and can produce the observed offset. Alternatively, the displacement could be due to residual oscillations resulting from a large recoil that occurred in the aftermath of a major merger any time in the last 1 Gyr.
The Hermitian Yang-Mills equations on certain vector bundles over Calabi-Yau cones can be reduced to a set of matrix equations; in fact, these are Nahm-type equations. The latter can be analysed further by generalising arguments of Donaldson and Kronheimer used in the study of the original Nahm equations. Starting from certain equivariant connections, we show that the full set of instanton equations reduce, with a unique gauge transformation, to the holomorphicity condition alone.
In this study optical/near-infrared(NIR) broad band photometry and optical spectroscopic observations of the GRB 030329 host galaxy are presented. The Spectral Energy Distribution (SED) of the host is consistent with a starburst galaxy template with a dominant stellar population age of ~150 Myr and an extinction Av ~0.6. Analysis of the spectral emission lines shows that the host is likely a low metallicity galaxy. Two independent diagnostics, based on the restframe UV continuum and the [OII] line flux, provide a consistent unextincted star formation rate of SFR ~0.6 Mo yr^-1. The low absolute magnitude of the host (M_B ~ -16.5) implies a high specific star formation rate value, SSFR = ~34 Mo yr^-1 (L/L*)^-1.
High and low resolution $IUE$ spectra of V838 Her in the early outburst stages exhibit a strong absorption feature shortward of $\lambda$3130. We discuss the nature of this spectral feature and provide convincing evidence that it corresponds to the blue-shifted resonance doublet of singly-ionized $^7$Be, recently discovered in other novae. During the evolution of the outburst the appearance of an emission feature close to $\lambda$3130 is also identified as $^7$Be II $\lambda$3132 because the usual identification as the O III $\lambda$3133.7 Bowen fluorescence line is hardly compatible with both the known oxygen under-abundance in the nova ejecta and the low optical depths in the nebula due to the high outflow velocity. The average $^7$Be abundance relative to hydrogen, estimated by four different methods, i.e. the $^7$Be II / Mg II absorption ratio, and the $^7$Be II / Mg II, $^7$Be II / He II$_{1640}$, and $^7$Be II / H$\beta$ emission ratios is N(Be)/N(H) $\approx$ 2.5 $\times 10^{-5}$ (by number), i.e. $\approx$ 1.7 $\times 10^{-4}$ by mass. This corresponds to an overproduction of $^7$Be by about 1 dex in comparison with the theoretical models of massive CO and ONe novae. Since $^7$Be all converts into $^7$Li, the $^7$Be/H abundance implies a $^7$Li/H overabundance of about 4 dex over the $^7$/H meteoritic value and indicates a total ejected mass of $^7$Li of $\approx$ 9.5$\times$10$^{-10}$ $M_{\odot}$. These data are in line with previous observations and indicate that large amounts of $^7$Li can be synthesized in a variety of novae, including very fast ONe novae.
The cotangent bundle of a non-uniruled projective manifold is generically nef, due to a theorem of Miyaoka. We show that the cotangent bundle is actually generically ample, if the manifold is of general type and study in detail the case of intermediate Kodaira dimension. Moreover, manifolds with generically nef and ample tangent bundles are investigated as well as connections to classical theorems on vector fields on projective manifolds.
It is known that the concept of limiting polarization introduced seventy years ago by K G Budden has the capacity to explain the magnitude of circular polarization seen in normal pulsars with rotation periods of the order of one second under the assumption of a high-multiplicity electron-positron plasma. However, a review of limiting polarization under the same assumption in millisecond pulsars indicates that it is inapplicable there because the region of limiting polarization lies far outside the light cylinder. The present paper, using the ion-proton model, evaluates circular polarization both generally and specifically for J2144-3933, and gives a fairly detailed understanding of the observations in normal pulsars including the change of sign as a function of frequency seen in J0908-4913. But it also fails to explain circular polarization in millisecond pulsars owing to the smaller particle number densities and birefringence of the magnetosphere in these objects. However, the review of limiting polarization finds that, within the ion-proton model, this distinct process can describe their circular polarization. It is argued that certain features of millisecond pulsar Stokes profiles are clearly consistent with limiting polarization.
The diffractive $\phi$-meson photoproduction amplitude is dominated by the Pomeron exchange process and contains the terms that govern the spin-spin and spin-orbital interactions.   We show that these terms are responsible for the spin-flip transitions at forward photoproduction angles and appear in the angular distributions of $\phi\to K^+K^-$ -decay in reactions with unpolarized and polarized photon beams.   At large momentum transfers, the main contribution to the $\phi$-meson photoproduction is found to be due to the excitation of nucleon resonances.   Combined analysis of $\omega$ and $\phi$ photoproduction indicates strong OZI-rule violation in $\phi NN^*$ - couplings.   We also show that the spin observables are sensitive to the dynamics of $\phi$-meson photoproduction at large angles and could help distinguish different theoretical models of nucleon resonances.   Predictions for spin effects in $\phi$-meson photoproduction are presented for future experimental tests.
We report multi-wavelength and multi-viewpoint observations of a solar eruptive event which involves loop-loop interactions. During a C2.0 flare, motions associated with inflowing and outflowing plasma provide evidence for ongoing magnetic reconnection. The flare loop top and a rising "concave-up" feature are connected by a current-sheet-like structure (CSLS). The physical properties (thickness, length, temperature, and density) of the CSLS are evaluated. In regions adjacent to the CSLS, the EUV emission (characteristic temperature at 1.6 MK) begins to increase more than ten minutes prior to the onset of the flare, and steeply decreases during the decay phase. The reduction of the emission resembles that expected from coronal dimming. The dynamics of this event imply a magnetic reconnection rate in the range 0.01 -- 0.05.
We study the morphology of a set of superclusters drawn from the SDSS DR7. We calculate the luminosity density field to determine superclusters from a flux- limited sample of galaxies from SDSS DR7, and select superclusters with 300 and more galaxies for our study. The morphology of superclusters is described with the fourth Minkowski functional V3, the morphological signature (the curve in the shapefinder's K1-K2 plane) and the shape parameter (the ratio of the shapefinders K1/K2). We investigate the supercluster sample using multidimensional normal mixture modelling, and use Abell clusters to identify our superclusters with known superclusters and to study the large-scale distribution of superclusters. The superclusters in our sample form three chains of superclusters; one of them is the Sloan Great Wall. Most superclusters have filament-like overall shapes. Superclusters can be divided into two sets; more elongated superclusters are more luminous, richer, have larger diameters, and a more complex fine structure than less elongated superclusters. The fine structure of superclusters can be divided into four main morphological types: spiders, multispiders, filaments, and multibranching filaments. We present the 2D and 3D distribution of galaxies and rich groups, the fourth Minkowski functional, and the morphological signature for all superclusters. Widely different morphologies of superclusters show that their evolution has been dissimilar. A study of a larger sample of superclusters from observations and simulations is needed to understand the morphological variety of superclusters and the possible connection between the morphology of superclusters and their large-scale environment.
Sidon sets are those sets such that the sums of two of its elements never coincide. They go back to the 30s when Sidon asked for the maximal size of a subset of consecutive integers with that property. This question is now answered in a satisfactory way. Their natural generalization, called B 2 [g] sets and defined by the fact that there are at most g ways (up to reordering the summands) to represent a given integer as a sum of two elements of the set, are much more difficult to handle and not as well understood. In this article, using a numerical approach, we improve the best upper estimates on the size of a B 2 [g] set in an interval of integers in the cases g = 2, 3, 4 and 5.
We have studied the conductivity peak in the transition region between the two lowest integer Quantum Hall states using transmission measurements of edge magnetoplasmons. The width of the transition region is found to increase linearly with frequency but remains finite when extrapolated to zero frequency and temperature. Contrary to prevalent theoretical pictures, our data does not show the scaling characteristics of critical phenomena.These results suggest that a different mechanism governs the transition in our experiment.
We find some extensions of the Kraft-Russell Generic Equivalence Theorem and using it we obtain a simple proof of a result of Dubouloz and Kishimoto.
In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can think of this function as a generic functional order parameter of the model. In a class of diluted models, and in the Sherrington-Kirkpatrick model, we introduce novel perturbations of the Hamiltonian that yield certain invariance and self-consistency equations for this generic functional order parameter and we use these invariance properties to obtain representations for the free energy in terms of $\sigma$. In the setting of the Sherrington-Kirkpatrick model, the self-consistency equations imply that the joint distribution of spins is determined by the joint distributions of the overlaps, and we give an explicit formula for $\sigma$ under the Parisi ultrametricity hypothesis. In addition, we discuss some connections with the Ghirlanda-Guerra identities and stochastic stability and describe the expected Parisi ansatz in the diluted models in terms of $\sigma$.
We obtain comparison theorems for non-negative solutions of quasilinear elliptic inequalities
Using the Chandra HETG spectrum of EX Hya as an example, we discuss some of the plasma diagnostics available in high-resolution X-ray spectra of magnetic cataclysmic variables. Specifically, for conditions appropriate to collisional ionization equilibrium plasmas, we discuss the temperature dependence of the H- to He-like line intensity ratios and the density and photoexcitation dependence of the He-like R line ratios and the Fe XVII I(17.10 A)/I(17.05 A) line ratio. We show that the plasma temperature in EX Hya spans the range from ~ 0.5 to ~ 10 keV and that the plasma density n > 2E14 cm^{-3}, orders of magnitude greater than that observed in the Sun or other late-type stars.
The antiferromagnetic spin-one chain is considerably one of the most fundamental quantum many-body systems, with symmetry protected topological order in the ground state. Here, we present results for its dynamical spin structure factor at finite temperatures, based on a combination of exact numerical diagonalization, matrix-product-state calculations and quantum Monte Carlo simulations. Open finite chains exhibit a sub-gap band in the thermal spectral functions, indicative of localized edge-states. Moreover, we observe the thermal activation of a distinct low-energy continuum contribution to the spin spectral function with an enhanced spectral weight at low momenta and its upper threshold. This emerging thermal spectral feature of the Haldane spin-one chain is shown to result from intra-band magnon scattering due to the thermal population of the single-magnon branch, which features a large bandwidth-to-gap ratio. These findings are discussed with respect to possible future studies on spin-one chain compounds based on inelastic neutron scattering.
Constantin and Saut showed in 1988 that solutions of the Cauchy problem for general dispersive equations $$   w_t +iP(D)w=0,\quad w(x,0)=q (x), \quad x\in \mathbb{R}^n, \ t\in \mathbb{R} , $$ enjoy the local smoothing property $$ q\in H^s (\R ^n) \implies w\in L^2 \Big (-T,T; H^{s+\frac{m-1}{2}}_{loc} \left (\R^n\right )\Big ) , $$ where $m$ is the order of the pseudo-differential operator $P(D)$. This property, now called local Kato smoothing, was first discovered by Kato for the KdV equation and implicitly shown later by Sj\"olin for the linear Schr\"odinger equation. In this paper, we show that the local Kato smoothing property possessed by solutions general dispersive equations in the 1D case is sharp, meaning that there exist initial data $q\in H^s \left (\R \right )$ such that the corresponding solution $w$ does not belong to the space $ L^2 \Big (-T,T; H^{s+\frac{m-1}{2} +\epsilon}_{loc} \left (\R\right )\Big )$ for any $\epsilon >0$.
The dynamics of a mobile hole in two-dimensional frustrated quantum magnets is investigated by exact diagonalization techniques. Our results provide evidence for spin-charge separation upon doping the kagome lattice, a prototype of a spin liquid. In contrast, in the checkerboard lattice, a symmetry broken Valence Bond Crystal, a small quasi-particle peak is seen for some crystal momenta, a finding interpreted as a restoration of weak holon-spinon confinement.
We examine string field algebra which is generated by star product in Witten's string field theory including ghost part. We perform calculations using oscillator representation consistently. We construct wedge like states in ghost part and investigate algebras among them. As a by-product we have obtained some solutions of vacuum string field theory. We also discuss some problems about identity state. We hope these calculations will be useful for further investigation of Witten type string field theory.
Inclusive electron scattering off 4He is calculated exactly with a complete treatment of the final state interaction within a simple semirealistic potential model. We discuss results for both the longitudinal and the transverse response functions, at various momentum transfers. A consistent meson exchange current is implemented. Good agreement with available experimental data is found for the longitudinal response function, while some strength is still missing in the transverse response function.
Relativistic mean field (RMF) theory is applied to investigate the properties of the radioactive neutron-rich doubly magic nucleus $^{132}$Sn and the corresponding isotopes and isotones. The two-neutron and two-proton separation energies are well reproduced by the RMF theory. In particular, the RMF results agree with the experimental single-particle spectrum in $^{132}$Sn as well as the Nilsson spin-orbit parameter $C$ and orbit-orbit parameter $D$ thus extracted, but remarkably differ from the traditional Nilsson parameters. Furthermore, the present results provide a guideline for the isospin dependence of the Nilsson parameters.
2D image representations are in regular grids and can be processed efficiently, whereas 3D point clouds are unordered and scattered in 3D space. The information inside these two visual domains is well complementary, e.g., 2D images have fine-grained texture while 3D point clouds contain plentiful geometry information. However, most current visual recognition systems process them individually. In this paper, we present a \emph{bidirectional projection network (BPNet)} for joint 2D and 3D reasoning in an end-to-end manner. It contains 2D and 3D sub-networks with symmetric architectures, that are connected by our proposed \emph{bidirectional projection module (BPM)}. Via the \emph{BPM}, complementary 2D and 3D information can interact with each other in multiple architectural levels, such that advantages in these two visual domains can be combined for better scene recognition. Extensive quantitative and qualitative experimental evaluations show that joint reasoning over 2D and 3D visual domains can benefit both 2D and 3D scene understanding simultaneously. Our \emph{BPNet} achieves top performance on the ScanNetV2 benchmark for both 2D and 3D semantic segmentation. Code is available at \url{https://github.com/wbhu/BPNet}.