ShantanuT01/DACTYL-Pretraining huggingface dataset:
We construct the enveloping fundamental spin model of the t-J hamiltonian using the Quantum Inverse Scattering Method (QISM), and present all three possible Algebraic Bethe Ans\"atze. Two of the solutions have been previously obtained in the framework of Coordinate Space Bethe Ansatz by Sutherland and by Schlottmann and Lai, whereas the third solution is new. The formulation of the model in terms of the QISM enables us to derive explicit expressions for higher conservation laws.
The metal-insulator transition and the problem of d-electron delocalization are investigated in the pyrite system NiS_{2-x}Se_x under pressure using density functional theory (DFT). We test several approximations, including the generalized gradient approximation (GGA), the GGA+U approach, and hybrid functionals. In addition we apply the GW approximation and perform Hartree-Fock calculations. The important role of the chalcogen dimers in the electronic structure is discussed within GGA, which sufficiently describes the role of the lattice in the metal-insulator transition. In addition, the magnetic phase diagram is determined. However, the electronic properties are inadequately described -- the insulating ground state of NiS_2 cannot be obtained -- and the magnetic order is slightly overestimated. If correlations are taken into account within GGA+U, the insulator is found, but the non-magnetic ground state of the doped samples is not accessible. Mixing Fock exchange with local approximations as GGA correctly reproduce the insulating ground state in NiS_2, and metallic ground states with doping and pressure. The insulator is -- in contrast to earlier suggestions -- of Mott type, i. e. the gap opens between Ni 3d {eg} states. Due to the Fock term, the magnetic order is strongly overestimated. The applied GW calculations are not able to correct the metallic character of NiS_2 and underestimate the gap by one order of magnitude.
Cluster mass profiles are tests of models of structure formation. Only two current observational methods of determining the mass profile, gravitational lensing and the caustic technique, are independent of the assumption of dynamical equilibrium. Both techniques enable determination of the extended mass profile at radii beyond the virial radius. For 19 clusters, we compare the mass profile based on the caustic technique with weak lensing measurements taken from the literature. This comparison offers a test of systematic issues in both techniques. Around the virial radius, the two methods of mass estimation agree to within about 30%, consistent with the expected errors in the individual techniques. At small radii, the caustic technique overestimates the mass as expected from numerical simulations. The ratio between the lensing profile and the caustic mass profile at these radii suggests that the weak lensing profiles are a good representation of the true mass profile. At radii larger than the virial radius, the lensing mass profile exceeds the caustic mass profile possibly as a result of contamination of the lensing profile by large-scale structures within the lensing kernel. We highlight the case of the closely neighboring clusters MS0906+11 and A750 to illustrate the potential seriousness of contamination of the the weak lensing signal by unrelated structures.
We present new calculations of the astrophysical $S-$factor and reaction rate for the $^{6}$Li$(p,\gamma )^{7}$Be reaction at energies of 10 keV to 5 MeV in the framework of a modified potential cluster model with forbidden states, including low lying resonances. The astrophysical $S(E)-$factor is compared with the available experimental data and calculations done within different models. The results for the $S-$factor are in good agreement with the data set (for $E<0.3$ MeV) and calculations (for $E<0.6$ MeV) of LUNA collaboration (Phys. Rev. C 102$,$ 052802, 2020). The recommended extrapolated zero value $S(0)$ turned out to be 101 eV $\cdot $ b. Using the theoretical total cross-sections$,$ the $^{6}$Li$(p,\gamma)^{7} $Be capture reaction rate is calculated at temperatures ranging from 0.01 to 10 $T_{9}$ and compared with NACRE and NACRE II. Analytical expressions for the $S-$factor and reaction rate are given, and the effect of low-lying resonances on the reaction rate is estimated. We suggest to update the NACRE and NACRE II databases in light of the new LUNA data and present calculations.
The Hankel determinants $\left(\frac{r}{2(i+j)+r}\binom{2(i+j)+r}{i+j}\right)_{0\leq i,j \leq n-1}$ of the convolution powers of Catalan numbers were considered by Cigler and by Cigler and Krattenthaler. We evaluate these determinants for $r\le 31$ by finding shifted periodic continued fractions, which arose in application of Sulanke and Xin's continued fraction method. These include some of the conjectures of Cigler as special cases. We also conjectured a polynomial characterization of these determinants. The same technique is used to evaluate the Hankel determinants $\left(\binom{2(i+j)+r}{i+j}\right)_{0\leq i,j \leq n-1} $. Similar results are obtained.
We define and study odd and even analogues of the major index statistics for the classical Weyl groups. More precisely, we show that the generating functions of these statistics, twisted by the one-dimensional characters of the corresponding groups, always factor in an explicit way. In particular, we obtain odd and even analogues of Carlitz's identity, of the Gessel-Simion Theorem, and a parabolic extension, and refinement, of a result of Wachs.
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general procedure to map these deformed algebras to appropriate Lie algebras. This is used, for the non compact cases, to obtain the annihilation operator coherent states, by finding the canonical conjugates of these operators.   Generalized coherent states, in the Perelomov sense also follow from this construction. This allows us to explicitly construct coherent states associated with various quantum optical systems.
A theoretical investigation of a plausible construct for electronic structure in iridate perovskites demonstrates the existence of magnetic multipoles hitherto not identified. The strange multipoles, which are parity-even, time-odd and even rank tensors, are absent from the so-called jeff = 1/2 model. We prove that the strange multipoles contribute to magnetic neutron diffraction, and we estimate their contribution to intensities of Bragg spots for Sr2IrO4. The construct encompasses the jeff = 1/2 model, and it is consistent with the known magnetic structure, ordered magnetic moment, and published resonant x-ray Bragg diffraction data. Over and above time-odd quadrupoles and hexadecapoles, whose contribution changes neutron Bragg intensities by an order of magnitude, according to our estimates, are relatively small triakontadipoles recently proposed as the primary magnetic order-parameter of Sr2IrO4.
The Heliospheric Imagers (HI) on board the two spacecraft of the Solar Terrestrial Relations Observatory (STEREO) provided white-light images of transients in the solar wind from dual perspectives from 2007 to 2014. In this paper, we develop a new method to identify and locate the transients automatically from simultaneous images from the two inner telescopes, known as HI-1, based on a correlation analysis. Correlation coefficient (cc) maps along the Sun-Earth line are constructed for the period from 1 Jan 2010 to 28 Feb 2011. From the maps, transients propagating along the Sun-Earth line are identified, and a 27-day periodic pattern is revealed, especially for small-scale transients. Such a periodicity in the transient pattern is consistent with the rotation of the Sun's global magnetic structure and the periodic crossing of the streamer structures and slow solar wind across the Sun-Earth line, and this substantiates the reliability of our method and the high degree of association between the small-scale transients of the slow solar wind and the coronal streamers. Besides, it is suggested by the cc map that small-scale transients along the Sun-Earth line are more frequent than large-scale transients by a factor of at least 2, and that they quickly diffused into background solar wind within about 40 Rs in terms of the signal-to-noise ratio of white-light emissions. The method provides a new tool to reconstruct inhomogeneous structures in the heliosphere from multiple perspectives.
Three-dimensional epitaxial heterostructures are based on covalently-bonded interfaces, whereas those from 2-dimensional (2D) materials exhibit van der Waals interactions. Under the right conditions, however, material structures with mixed interfacial van der Waals and covalent bonding may be realized. Atomically thin layers formed at the epitaxial graphene (EG)/silicon carbide (SiC) interface indicate that EG/SiC interfaces provide this unique environment and enable synthesis of a rich palette of 2D materials not accessible with traditional techniques. Here, we demonstrate a method termed confinement heteroepitaxy (CHet), to realize air-stable, structurally unique, crystalline 2D-Ga, In, and Sn at the EG/SiC interface. The first intercalant layer is covalently-bonded to the SiC, and is accompanied by a vertical bonding gradient that ends with van der Waals interactions. Such structures break out of plane centrosymmetry, thereby introducing atomically thin, non-centrosymmetric 2D allotropes of 3D materials as a foundation for tunable superconductivity, topological states, and plasmonic properties.
We investigate the possibility that gauginos are massless at tree level and that the U(1) R-invariance is broken spontaneously by Higgs vevs, like the chiral symmetry of quarks in the standard model, or else explicitly by dimension 2 or 3 SUSY-breaking terms in the low energy effective Lagrangian. Gluino and lightest neutralino masses then depend on only a few parameters. For a SUSY-breaking scale <~ 400 GeV, the gluino and lightest neutralino have masses typically in the range 1/10 ~ 2 1/2 GeV. On the other hand, for a SUSY-breaking scale several TeV or larger, radiative contributions can yield gluino and lightest neutralino masses of O(50-300) GeV and O(10-30) GeV, respectively. As long as the Higgs vev is the only source of R-invariance breaking, or if SUSY breaking only appears in dimension 2 terms in the effective Lagrangian, the gluino is generically the lightest SUSY particle, modifying the usual phenomenology in interesting ways.
We analyze homodyne detection of macroscopically bright multimode nonclassical states of light and propose their application in quantum communication. We observe that the homodyne detection is sensitive to a mode-matching of the bright light to the highly intense local oscillator. Unmatched bright modes of light result in additional noise which technically limits detection of Gaussian entanglement at macroscopic level. When the mode-matching is sufficient, we show that multimode quantum key distribution with bright beams is feasible. It finally merges the quantum communication with classical optical technology of visible beams of light.
Contents: APS April Meeting, by Aaron Zimmerman; Cosmic Explorer, the Next Exploration Step, by Varun Srivastava, Kathryne J. Daniel, and Stefan Ballmer
A generalized form of the Hastings and Levitov (HL) algorithm for simulation of diffusion-limited aggregation (DLA) restricted in a sector geometry is studied. It is found that this generalization with uniform measure produces "wedge-like" fractal patterns in the physical space, whose fractal dimension and anisotropy exponent depend significantly on the opening angle $\beta$ of the sector. The morphological properties and the overall shape of the patterns are analyzed by computing the angular two-point density correlation function of the patterns. We also find that the fractal dimension of the patterns with sinusoidal distributed measure depend weakly on $\beta$ with almost the same dimension as the radial DLA cluster. The anisotropy exponent and the visual appearance of the patterns in this case are shown to be compatible with those of the advection-diffusion-limited aggregation (ADLA) clusters.
Consider a planar random point process made of the union of a point (the origin) and of a Poisson point process with a uniform intensity outside a deterministic set surrounding the origin. When the intensity goes to infinity, we show that the Voronoi cell associated with the origin converges from above to a deterministic convex set. We describe this set and give the asymptotics of the expectation of its defect area, defect perimeter and number of vertices. On the way, two intermediary questions are treated. First, we describe the mean characteristics of the Poisson-Voronoi cell conditioned on containing a fixed convex body around the origin and secondly, we show that the nucleus of such cell converges to the Steiner point of the convex body. As in R\'enyi and Sulanke's seminal papers on random convex hulls, the regularity of the convex body has crucial importance. We deal with both the smooth and polygonal cases. Techniques are based notably on accurate estimates of the area of the Voronoi flower and of the support function of the cell containing the origin as well as on an Efron-type relation.
We have fabricated single electron tunneling structures by forming nanogap metallic electrodes directly upon single self-assembled InAs quantum dots (QDs). The fabricated samples exhibited clear Coulomb blockade effects. Furthermore, a clear Kondo effect was observed when strong coupling between the electrodes and the QDs was realized using a large QD with a diameter of ~ 100 nm. From the temperature dependence of the linear conductance at the Kondo valley, the Kondo temperature TK was determined to be ~ 81 K. This is the highest TK ever reported for artificial quantum nanostructures.
The effects of confining molecular hydrogen within carbon nanohorns are studied via high-resolution quasielastic and inelastic neutron spectroscopies. Both sets of data are remarkably different from those obtained in bulk samples in the liquid and crystalline states. At temperatures where bulk hydrogen is liquid, the spectra of the confined sample show an elastic component indicating a significant proportion of immobile molecules as well as distinctly narrower quasielastic line widths and a strong distortion of the line shape of the para - ortho rotational transition. The results show that hydrogen interacts far more strongly with such carbonous structures than it does to carbon nanotubes, suggesting that nanohorns and related nanostructures may offer significantly better prospects as lightweight media for hydrogen storage applications.
Here we report the measurement of the interfacial spin accumulation induced by the spin Hall effect in Pt and W thin films using magneto-optical Kerr microscopy. We show that the Kerr rotation has opposite sign in Pt and W and scales linearly with current density. By comparing the experimental results with ab-initio calculations of the spin Hall and magneto-optical Kerr effects, we quantitatively determine the current-induced spin accumulation at the Pt interface as $5*10^{-12} \mu_B$A$^{-1}$cm$^2$ per atom. From thickness-dependent measurements, we determine the spin diffusion length in a single Pt film to be $11 \pm 3$ nm, which is significantly larger compared to that of Pt adjacent to a magnetic layer.
We prove an optimal stability estimate for Electrical Impedance Tomography with local data, in the case when the conductivity is precisely known on a neighborhood of the boundary. The main novelty here is that we provide a rather general method which enables to obtain the H\"older dependence of a global Dirichlet to Neumann map from a local one on a larger domain when, in the layer between the two boundaries, the coefficient is known.
The intrinsic linewidth $\Gamma_{TA}$ of the transverse acoustic (TA) phonon observed in the relaxor ferroelectric compound Pb(Mg$_{1/3}$Nb$_{2/3})_{0.8}$Ti$_{0.2}$O$_3$ (PMN-20%PT) begins to broaden with decreasing temperature around 650 K, nearly 300 K above the ferroelectric transition temperature $T_c$ ($\sim 360$ K). We speculate that this anomalous behavior is directly related to the condensation of polarized, nanometer-sized, regions at the Burns temperature $T_d$. We also observe the ``waterfall'' anomaly previously seen in pure PMN, in which the transverse optic (TO) branch appears to drop precipitously into the TA branch at a finite momentum transfer $q_{wf} \sim 0.15$ \AA$^{-1}$. The waterfall feature is seen even at temperatures above $T_d$. This latter result suggests that the PNR exist as dynamic entities above $T_d$.
We discuss convergence issues as well as short distance constraints on the deuteron wave functions based on chiral perturbation theory relevant to pion deuteron scattering. Non-analytical terms arise in the multiple scattering series for the pion-deuteron scattering length limiting the accuracy of the calculations. This result resembles similar findings in the structure of the NN interaction. The effects are found not to be numerically large. The iso-scalar $\pi N $ scattering length from the iso-vector one and the $\pi d$ scattering length yields values compatible with the experimental number and with much smaller errors.
We study numerically the nonequilibrium dynamical behavior of an Ising model with mixed two-spin and four-spin interactions after a sudden quench from the high-temperature phase to the first-order phase transition point. The autocorrelation function is shown to approach its limiting value, given by the magnetization in the ordered phase at the transition point, m_c, through a stretched exponential decay. On the other hand relaxation of the magnetization starting with an uncorrelated initial state with magnetization, m_i, approaches either m_c, for m_i>0.5, or zero, for m_i<0.5. For small m_i and for m_i slightly larger than 0.5 the relaxation of the magnetization shows an asymptotic power-law time dependence, thus from a nonequilibrium point of view the transition is continuous.
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a striking behaviour in the steady state. As the parameters are varied, the system undergoes a dynamical phase transition in all dimensions. In one phase the mass distribution decays exponentially for large mass whereas in the other phase there is a power law distribution of masses which coexists with an infinite mass aggregate. The model is investigated analytically within mean field theory, and numerically in one dimension.
Mixed states of a quantum system, represented by density operators, can be decomposed as a statistical mixture of pure states in a number of ways where each decomposition can be viewed as a different preparation recipe. However the fact that the density matrix contains full information about the ensemble makes it impossible to estimate the preparation basis for the quantum system. Here we present a measurement scheme to (seemingly) improve the performance of unsharp measurements. We argue that in some situations this scheme is capable of providing statistics from a single copy of the quantum system, thus making it possible to perform state tomography from a single copy. One of the byproduct of the scheme is a way to distinguish between different preparation methods used to prepare the state of the quantum system. However, our numerical simulations disagree with our intuitive predictions. We show that a counter-intuitive property of a biased classical random walk is responsible for the proposed mechanism not working.
In this book chapter, we will briefly review the current empirical understanding of the relation between accretion state and and outflows in accreting stellar mass black holes. The focus will be on the empirical connections between X-ray states and relativistic (`radio') jets, although we are now also able to draw accretion disc winds into the picture in a systematic way. We will furthermore consider the latest attempts to measure/order jet power, and to compare it to other (potentially) measurable quantities, most importantly black hole spin.
We present the first detection of a correlation between the Lyman-$\alpha$ forest and cosmic microwave background (CMB) lensing. For each Lyman-$\alpha$ forest in SDSS-III/BOSS DR12, we correlate the one-dimensional power spectrum with the CMB lensing convergence on the same line of sight from Planck. This measurement constitutes a position-dependent power spectrum, or a squeezed bispectrum, and quantifies the non-linear response of the Lyman-$\alpha$ forest power spectrum to a large-scale overdensity. The signal is measured at 5~$\sigma$ and is consistent with the $\Lambda$CDM expectation. We measure the linear bias of the Lyman-$\alpha$ forest with respect to the dark matter distribution, and constrain a combination of non-linear terms including the non-linear bias. This new observable provides a consistency check for the Lyman-$\alpha$ forest as a large-scale structure probe and tests our understanding of the relation between intergalactic gas and dark matter. In the future, it could be used to test hydrodynamical simulations and calibrate the relation between the Lyman-$\alpha$ forest and dark matter.
We investigate the effect of disorder on the heat transport properties of the $S=\tfrac{1}{2}$ Heisenberg chain compound Sr$_2$CuO$_3$ upon chemically substituting Sr by increasing concentrations of Ca. As Ca occupies sites outside but near the Cu-O-Cu spin chains, bond disorder, i.e. a spatial variation of the exchange interaction $J$, is expected to be realized in these chains. We observe that the magnetic heat conductivity ($\kappa_{\mathrm{mag}}$) due to spinons propagating in the chains is gradually but strongly suppressed with increasing amount of Ca, where the doping dependence can be understood in terms of increased scattering of spinons due to Ca-induced disorder. This is also reflected in the spinon mean free path which can be separated in a doping independent but temperature dependent scattering length due to spinon-phonon scattering, and a temperature independent but doping dependent spinon-defect scattering length. The latter spans from very large ($>$ 1300 lattice spacings) to very short ($\sim$ 12 lattice spacings) and scales with the average distance between two neighboring Ca atoms. Thus, the Ca-induced disorder acts as an effective defect within the spin chain, and the doping scheme allows to cover the whole doping regime between the clean and the dirty limits. Interestingly, at maximum impurity level we observe, in Ca-doped Sr$_2$CuO$_3$, an almost linear increase of $\kappa_{\mathrm{mag}}$ at temperatures above 100 K which reflects the intrinsic low temperature behavior of heat transport in a Heisenberg spin chain. These findings are quite different from that observed for the Ca-doped double spin chain compound, SrCuO$_2$, where the effect of Ca seems to saturate already at intermediate doping levels.
We investigate the high resolution coding problem for solutions of stochastic differential equations in the L^p[0,1]- and the C[0,1]-space. Tight asymptotic estimates are found under weak regularity assumptions. The main technical tool is a decoupling method which allows us to relate the complexity of the diffusion process to that of the Wiener process under certain random distortions.