ShantanuT01/DACTYL-Pretraining huggingface dataset:
I revisit the infinite-size variant of the Density Matrix Renormalization Group (iDMRG) algorithm for obtaining a fixed-point translationally invariant matrix product wavefunction in the context of one-dimensional quantum systems. A crucial ingredient of this algorithm is an efficient transformation for obtaining the matrix elements of the wavefunction as the lattice size is increased, and I introduce here a versatile transformation that is demonstrated to be much more effective than previous versions. The resulting algorithm has a surprisingly close relationship to Vidal's Time Evolving Block Decimation for infinite systems, but allows much faster convergence. Access to a translationally invariant matrix product state allows the calculation of correlation functions based on the transfer matrix, which directly gives the spectrum of all correlation lengths. I also show some advantages of the Matrix Product Operator (MPO) technique for constructing expectation values of higher moments, such as the exact variance $<(H-E)^2>$.
The magnetization process of the isotropic Heisenberg antiferromagnet on the kagome lattice is studied. Data obtained from the numerical-diagonalization method are reexamined from the viewpoint of the derivative of the magnetization with respect to the magnetic field. We find that the behavior of the derivative at approximately one-third of the height of the magnetization saturation is markedly different from that for the cases of typical magnetization plateaux. The magnetization process of the kagome-lattice antiferromagnet reveals a new phenomenon, which we call the "magnetization ramp".
It is shown that, in addition to the Thomson scattering, the absorption due to the electron-electron, electron-ion and the electron -atom collisions in a partially ionized cosmic plasma would also contribute to the optical depth of the cosmic microwave background (CMB). The absorption depth depends on the plasma temperature and frequency of the CMB radiation. The absorption effects are prominent at the low frequency part of the CMB spectrum. These effects when included in the interpretation of the CMB spectrum may necessitate a revised view of the ioniziation of the universe.
We investigate the clustering of HI-selected galaxies in the ALFALFA survey and compare results with those obtained for HIPASS. Measurements of the angular correlation function and the inferred 3D-clustering are compared with results from direct spatial-correlation measurements. We are able to measure clustering on smaller angular scales and for galaxies with lower HI masses than was previously possible. We calculate the expected clustering of dark matter using the redshift distributions of HIPASS and ALFALFA and show that the ALFALFA sample is somewhat more anti-biased with respect to dark matter than the HIPASS sample.
In this paper, we consider fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature which naturally arise in conformal geometry. Moreover, we prove the a priori estimates for solutions to these equations and establish the existence results. Our results can be viewed as an extension of previous results given by Gursky-Viaclovsky and Li-Sheng.
We prove a recent conjecture of Blanco and Petersen (arXiv:1206.0803v2) about an expansion formula for inversions and excedances in the symmetric group.
Using Fe/GaAs Schottky tunnel barriers as electrical spin detectors, we show that the magnitude and sign of their spin-detection sensitivities can be widely tuned with the voltage bias applied across the Fe/GaAs interface. Experiments and theory establish that this tunability derives not just simply from the bias dependence of the tunneling conductances $G_{\uparrow,\downarrow}$ (a property of the interface), but also from the bias dependence of electric fields in the semiconductor which can dramatically enhance or suppress spin-detection sensitivities. Electrons in GaAs with fixed polarization can therefore be made to induce either positive or negative voltage changes at spin detectors, and some detector sensitivities can be enhanced over ten-fold compared to the usual case of zero-bias spin detection.
We present and discuss near-ultraviolet and optical ground-based spectra of the 20 brightest Seyfert 2 nuclei, and HST ultraviolet images and ultraviolet spectroscopy for a few of them. The goal is to study the starburst-AGN connection and the origin of the featureless continuum. The results indicate that half of the nuclei in the sample harbor a young and/or intermediate age population. These stars are formed in powerful and dusty starbursts of short duration, that have bolometric luminosities similar to the estimated bolometric luminosities of their obscured Seyfert 1 nuclei.
In this paper we study the Ostrovsky-Hunter equation for the case where the flux function $f(x, u)$ may depend on the spatial variable with certain smoothness. Our main results are that if the flux function is smooth enough (specified later), then there exists a unique entropy solution. To show the existence, after proving some a priori estimates we have used the method of compensated compactness and to prove the uniqueness we have employed the method of doubling of variables.
We introduce an inductively defined sequence of directed graphs and prove that the number of edges added at step $k$ is equal to the $k$th Catalan number. Furthermore, we establish an isomorphism between the set of edges adjoined at step $k$ and the set of planar rooted trees with $k$ edges.
We present a determination of the local (z=0) luminosity function of optically selected type 1 (broad-line) Active Galactic Nuclei. Our primary resource is the Hamburg/ESO Survey (HES), which provides a well-defined sample of more than 300 optically bright AGN with redshifts z<0.3 and blue magnitudes B<17.5. AGN luminosities were estimated in two ways, always taking care to minimise photometric biases due to host galaxy light contamination. Firstly, we measured broad-band B_J (blue) magnitudes of the objects over small apertures of the size of the seeing disk. Secondly, we extracted H alpha and H beta broad emission line luminosities from the spectra which should be entirely free of any starlight contribution. The resulting AGN luminosity function (AGNLF) is consistent with a single power law, also when considering the effects of number density evolution within the narrow redshift range. We compared our AGNLF with the H alpha luminosity function of lower luminosity Seyfert 1 galaxies by Hao et al. (2005) and found a smooth transition between both, with excellent agreement in the overlapping region. From the combination of HES and SDSS samples we constructed a single local AGNLF spanning more than 4 orders of magnitude in luminosity. It shows only mild curvature which can be well described as a double power law with slope indices of -2.0 for the faint end and -2.8 for the bright end. We predicted the local AGNLF in the soft X-ray domain and compared this to recent literature data. We also compared the local AGNLF with results obtained at higher redshifts and find strong evidence for luminosity-dependent evolution, in the sense that AGN with luminosities around M_B~-19 are as common in the local universe as they were at z=1.5, supporting the 'AGN downsizing' picture (abridged).
In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a multi-dimensional Markov process, where the coordinates keep track of the number of customers of each class in the system. Based on matrix-analytic techniques and probabilistic arguments we develop a recursive method for the exact determination of the equilibrium joint queue length distribution. The method is applied to a spare parts logistics problem to illustrate the effect of setting repair priorities on the performance of the system. We conclude by briefly indicating how the method can be extended to an $M/M/1$ queueing system with non-preemptive priorities between customer classes.
The World Space Observatory Project is a new space mission concept, grown out the needs of the Astronomical community to have access to the part of the electromagnetic spectrum where all known physics can be studied on all possible time scales: the Ultraviolet range. The physical diagnostics in this domain supply a richness of new experimental data unmatched by any other wavelength range, for the studies of the Universe. As WSO/UV has been driven by the needs of scientists from many different countries, a new implementation model was needed to bring the World Space Observatory to reality. The WSO/UV consists of a single Ultraviolet Telescope in orbit, incorporating a primary mirror of 1.7 m diameter feeding a UV spectrograph and UV Imagers.
The application of new materials in nanotechnology opens new perspectives and enables ground-breaking innovations. Two-dimensional van der Waals materials and more specific, 2D chalcogenides are a promising class of new materials awaiting their usage in the semiconductor industry. However, the integration of van der Waals materials relying on industry-compatible manufacturing processes is still a major challenge. This is currently restricting the application of these new materials to the research laboratories environment only. The large-area and single-crystalline growth of van der Waals materials is one of the most important requirements to meet the challenging demands implied by the semiconductor industry. This review contributes to a more generalized understanding on the integration of van der Waals materials - and in more specific 2D chalcogenides - through the growth process of epitaxy. This, can pursue further the aspiration of large-area, single-crystalline and defect-free epitaxial integration of (quasi) van der Waals homo- and heterostructures into the great world of the semiconductor industry.
We have proven that there exists a quantum state approximating any multi-copy state universally when we measure the error by means of the normalized relative entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been open for more than ten years. For a deeper analysis, we have solved the mini-max problem concerning `approximation error' up to the second order. Furthermore, we have applied this result to quantum lossless data compression, and have constructed a universal quantum lossless data compression.
We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence of (i) composite scaling laws, (ii) small critical exponents \tau associated with the power-law fragment-size distribution, and (iii) the typical pattern of cracks. The proposed computer simulations do not require numerical solutions of the Newton's equations of motion, nor several additional assumptions normally used in discrete element models. The model is also able to predict some physical aspects which could be tested in new experiments of fragmentation of brittle systems.
A long-term project, aiming at systematic search for variable stars in Galactic Open Clusters, was started at the Geneva Observatory in 2002. We have been observing regularly a sample of twenty-seven Galactic Open Clusters in the U, B, V Geneva filters. The goal is to identify and to study their variable stars, as well as the connection between the variable stars in a cluster and the cluster properties. We present the status of this work in progress, and show preliminary results for one of these clusters, IC 4651.
Density functional theory calculations of electronic transport based on local exchange and correlation functionals contain self-interaction errors. These originate from the interaction of an electron with the potential generated by itself and may be significant in metal-molecule-metal junctions due to the localized nature of the molecular orbitals. As a consequence, insulating molecules in weak contact with metallic electrodes erroneously form highly conducting junctions, a failure similar to the inability of local functionals of describing Mott-Hubbard insulators. Here we present a fully self-consistent and still computationally undemanding self-interaction correction scheme that overcomes these limitations. The method is implemented in the Green's function non-equilibrium transport code Smeagol and applied to the prototypical cases of benzene molecules sandwiched between gold electrodes. The self-interaction corrected Kohn-Sham highest occupied molecular orbital now reproduces closely the negative of the molecular ionization potential and is moved away from the gold Fermi energy. This leads to a drastic reduction of the low bias current in much better agreement with experiments.
Hybrid mesons with exotic quantum numbers $J^{PC}=1^{-+}$ are examined in soft-wall AdS/QCD. The predicted mass spectrum is compared to the measured values of the candidates $\pi_1(1400)$, $\pi_1(1600)$ and $\pi_1(2015)$. Thermal effects are analysed through the spectral function in the AdS-Black Hole model, and the differences with the Hawking-Page description are discussed.
The technique of dispersion integration over the mass of composite particle is used to describe the reaction of the deuteron photodisintegration. The influence of the final state interaction (FSI) on the total cross section, calculated with and without inelasticity is investigated. Numerical results depend on the choice of the vertex function for the isobar photoproduction.
We report on the simple fabrication of hysteresis-free and electrically stable organic field-effect transistors (OFETs) and inverters operating at voltages <1-2 V, enabled by the almost trap-free interface between the organic semiconductor and an ultra-thin (<20 nm) and highly insulating single-layer fluoropolymer gate dielectric (Cytop). OFETs with PTCDI-C13 (N,N'-ditridecylperylene-3,4,9,10-tetracarboxylicdiimide) as semiconductor exhibit outstanding transistor characteristics: very low threshold voltage (0.2V), onset at 0V, steep subthreshold swing (0.1-0.2 V/decade), no hysteresis and excellent stability against gate bias stress. It is gratifying to notice that such small OFET operating voltages can be achieved with the relatively simple processing techniques employed in this study.
We study the non-Euclidean (incompatible) elastic energy functionals in the description of prestressed thin films, at their singular limits ($\Gamma$-limits) as $h\to 0$ in the film's thickness $h$. Firstly, we extend the prior results [Lewicka-Pakzad, Bhattacharya-Lewicka-Schaffner, Lewicka-Raoult-Ricciotti] to arbitrary incompatibility metrics that depend on both the midplate and the transversal variables (the "non-oscillatory" case). Secondly, we analyze a more general class of incompatibilities, where the transversal dependence of the lower order terms is not necessarily linear (the "oscillatory" case), extending the results of [Agostiniani-Lucic-Lucantonio, Schmidt] to arbitrary metrics and higher order scalings. We exhibit connections between the two cases via projections of appropriate curvature forms on the polynomial tensor spaces. We also show the effective energy quantisation in terms of scalings as a power of $h$ and discuss the scaling regimes $h^2$ (Kirchhoff), $h^4$ (von K\'arm\'an) in the general case, as well as all possible (even powers) regimes for conformal metrics, thus paving the way to the subsequent complete analysis of the non-oscillatory setting in [Lewicka]. Thirdly, we prove the coercivity inequalities for the singular limits at $h^2$- and $h^4$- scaling orders, while disproving the full coercivity of the classical von K\'arm\'an energy functional at scaling $h^4$.
We study photon pair generation through scalar spontaneous four-wave mixing in single-mode fibre and for frequency-degenerate pumps; we concentrate on source geometries which fulfil full group velocity matching (GVM), i.e. where the pump, signal and idler propagate at identical group velocities. We discuss two experimental techniques which permit the attainment of full GVM, and discuss the resulting two-photon state properties. In particular, we show that full GVM can lead to sources which approach phasematching unconstrained by dispersion and therefore with a remarkably large bandwidth. We also discuss the generation of nearly-factorablestates as an application of full GVM.
The two pulsating pre-main sequence (PMS) stars V 588 Mon and V 589 Mon were observed by CoRoT for 23.4 days in March 2008 during the Short Run SRa01 and in 2004 and 2006 by MOST for a total of ~70 days. We present their photometric variability up to 1000 $\mu$ Hz and down to residual amplitude noise levels of 23 and 10 ppm of the CoRoT data for V 588 Mon and V 589 Mon, respectively. The CoRoT imagette data as well as the two MOST data sets allowed for detailed frequency analyses using Period04 and SigSpec. We confirm all previously identified frequencies, improve the known pulsation spectra to a total of 21 frequencies for V 588 Mon and 37 for V 589 Mon and compare them to our PMS model predictions. No model oscillation spectrum with l = 0, 1, 2, and 3 p-modes matches all the observed frequencies. When rotation is included we find that the rotationally split modes of the slower rotating star, V 589 Mon, are addressable via perturbative methods while for the more rapidly rotating star, V 588 Mon, they are not and, consequently, will require more sophisticated modeling. The high precision of the CoRoT data allowed us to investigate the large density of frequencies found in the region from 0 to 300 $\mu$Hz. The presence of granulation appears to be a more attractive explanation than the excitation of high-degree modes. Granulation was modeled with a superposition of white noise, a sum of Lorentzian-like functions and a Gaussian. Our analysis clearly illustrates the need for a more sophisticated granulation model.
In cold molecular clouds submillimetre emission lines are excited by the ambient radiation field. The pumping is dominated by the cosmic microwave background (CMB). It is usual in molecular line radiative transfer modelling to simply assume that this is the only incident radiation field. In this paper, a molecular line transport code and a dust radiative transfer code are used to explore the effects of the inclusion of a full interstellar radiation field (ISRF) on a simple test molecular cloud. It is found that in many galactic situations, the shape and strength of the line profiles that result are robust to variations in the ISRF and thus that in most cases, it is safe to adopt the CMB radiation field for the molecular line transport calculations. However, we show that in two examples, the inclusion of a plausible radiation field can have a significant effect on the the line profiles. Firstly, in the vicinity of an embedded massive star, there will be an enhanced far infared component to the radiation field. Secondly, for molecular clouds at large redshift, the CMB temperature increases and this of course also alters the radiation field. In both of these cases, the line profiles are weakened significantly compared to a cloud exposed to a standard radiation field. Therefore this effect should be accounted for when investigating prestellar cores in massive star forming regions and when searching for molecular clouds at high redshift.
We present first results from the analysis of a sample of 14 planetary nebulae with [WC] nucleus with detected faint carbon and oxygen recombination lines (RLs). The results are based on deep echelle spectra obtained with MIKE on the 6.5 m Magellan-Clay telescope in Chile.
An interesting class of automatic sequences emerges from iterated paperfolding. The sequences generate curves in the plane with an almost periodic structure. We generalize the results obtained by Davis and Knuth on the self-avoiding and planefilling properties of these curves, giving simple geometric criteria for a complete classification. Finally, we show how the automatic structure of the sequences leads to self-similarity of the curves, which turns the planefilling curves in a scaling limit into fractal tiles. For some of these tiles we give a particularly simple formula for the Hausdorff dimension of their boundary.
A new microscopic nucleon-nucleon (NN) interaction has been derived for the first time from the popular relativistic mean field theory (RMFT) Lagrangian. The NN interaction so obtained remarkably relate to the inbuilt fundamental parameters of RMFT. Furthermore, by folding it with the RMFT-densities of cluster and daughter nuclei to obtain the optical potential, it's application is also examined to study the exotic cluster radioactive decays, and results obtained found comparable with the successfully used M3Y phenomenological effective NN interactions. The presently derived NN-interaction can also be used to calculate a number of other nuclear observables.
A well-known folklore result in the MCMC community is that the Metropolis-Hastings algorithm mixes quickly for any unimodal target, as long as the tails are not too heavy. Although we've heard this fact stated many times in conversation, we are not aware of any quantitative statement of this result in the literature, and we are not aware of any quick derivation from well-known results. The present paper patches this small gap in the literature, providing a generic bound based on the popular "drift-and-minorization" framework of Rosenthal (1995). Our main contribution is to study two sublevel sets of the Lyapunov function and use path arguments in order to obtain a sharper general bound than what can typically be obtained from multistep minorization arguments.
Recent PHOBOS measurements of the excitation function for the pseudo-rapidity dependence of elliptic flow in Au+Au collisions at RHIC, have posed a significant theoretical challenge. We show here that these data are described by the Buda-Lund model. A universal scaling curve, predicted by the Buda-Lund hydro model, describes not only PHOBOS data, but also recent, detailed PHENIX and STAR elliptic flow data. This is a consequence of perfect fluid hydrodynamics as implemented in the Buda-Lund hydro model.
In the ring of holomorphic functions at the origin of C^2, we consider the equation uf'_x+vf'_y=wf where f and w are given. We introduce intersection multiplicities relative to w and f'_y along the branches of f, and we study the solutions (u,v) using these valuations. As an application, we construct an explicit functional equation satisfied by f.
The corrections to the gravitational potential due to a Sol extra dimensional compact manifold, denoted as $M_A^3$, are studied. The total spacetime is $M^4\times M_A^3$. We compare the range of the corrections to the range of the $T^3$ corrections. It is found that for small values of the radius of the extra dimensions ($R<10^{-6}$) the the Sol manifold corrections are large compared to the 3-torus corrections. Also, Sol manifolds corrections can be larger, comparable or smaller compared to the 3-torus case, for larger $R$.
We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable. We look at Hamiltonians like $H(x,\sigma(x)p,\omega)$ where $\sigma(x)$ is a matrix associated to a Carnot group. The rescaling considered is consistent with the underlying Carnot group structure, thus anisotropic. We will prove that under suitable assumptions for the Hamiltonian, the solutions of the $\varepsilon$-problem converge to a deterministic function which can be characterized as the unique (viscosity) solution of a suitable deterministic Hamilton-Jacobi problem.