ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that the higher order derivative $\alpha^{'}$ corrections to the DBI and Chern-Simon action is derived from non-commutativity in the Seiberg-Witten limit, and is shown to agree with Wyllard's (hep-th/0008125) result, as conjectured by Das et al., (hep-th/0106024). In calculating the corrections, we have expressed $\hat F$ in terms F, $\hat A$ in terms of A up to order ${\cal O}(A^3)$, and made use of it.
We concretely define the identity string field as a surface state and deal with it consistently in terms of conformal field theory language, never using its formal properties nor oscillator representation of it. The generalized gluing and resmoothing theorem provides us with a powerful computational tool which fits into our framework. Among others, we can prove that in some situations the identity state defined this way actually behaves itself like an identity element under the *-product. We use these CFT techniques to give an explicit expression of the classical solution in the ordinary cubic string field theory having the property that the conjectured vacuum string field theory action arises when the cubic action is expanded around it.
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.
We calculate the three- and four-particle correlations of identical pions in an evolving pion gas (EPG) model with Bose-Einstein condensation. The multi-pion correlation functions in the EPG model are analyzed in different momentum intervals and compared with the experimental data for Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. It is found that the multi-pion correlation functions and cumulant correlation functions are sensitive to the condensation fraction of the EPG sources in the low average transverse-momentum intervals of the three and four pions. The model results of the multi-pion correlations are consistent with the experimental data in a considerable degree, which gives a source condensation fraction between 16~--~47\%.
Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R^3 in order to extend the set of existing non-rigid shape analysis tools. In fact, we show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.
The temperature and high magnetic field dependence of the longitudinal soundwave mode c_{11} in the two dimensional dimer system SrCu_{2}(BO_{3})_{2} is presented. c_{11}(T) shows anomalies due to strong interdimer spin-strain coupling. We can quantitatively interpret the temperature dependence of c_{11}(T) together with the magnetic susceptibility $\chi_{m}(T)$ with a molecular field approximation of coupled dimer triplets. The sound velocity up to 50T shows very sharp softening between the magnetization plateaus at low temperature. We argue that these pronounced effects arise from a resonant interaction between the phonons and the magnetic excitations which show softening between the plateaus.
We have derived a general rule for the appearance of zero-energy modes in super-chiral defective nanographene. This so-called "super-zero-sum rule" defines the appearance of zero modes in a new class of materials, which we call polymerized phenalenyl-tessellation molecules (poly-PTMs). Through theoretical modeling of the electronic states in these molecular forms, we provide concrete solutions for achieving the quantum-spin systems needed in quantum-information devices. The two-dimensional graph of electronic $\pi$-orbitals in the poly-PTM possesses a number of localized zero modes equivalent to that of vacancies in PTMs. In addition to the modes confined to each PTM, another type of zero mode may appear according to the super-zero-sum rule supported by super-chirality. Since the magnetic interactions among quantum spins in the zero modes are determined by how they appear (which is governed by the super-zero-sum rule), our rule is indispensable for designing quantum-information devices using electron zero modes in poly-aromatic hydrocarbons and defective graphene with vacancies.
We calculate synchrotron radio emission and gamma-ray emission due to bremsstrahlung, inverse-Compton scattering and $pi^0$-decay from the remnant of supernova which exploded in the circumstellar matter (CSM) formed by the progenitor's stellar wind. This sort of situation is a possible origin of mixed-morphology supernova remnants (SNRs) like W49B, which exhibit recombination-radiation spectra in X-ray emission. We assume that the CSM of 1.5 $M_{odot}$ exists at 0.07--3 pc away from the supernova in the interstellar medium (ISM) of density 0.016 cm$^{-3}$. When the blast wave breaks out of the CSM into the ISM, its velocity rapidly increases and hence particle acceleration is enhanced. The maximum energy of protons reaches $sim$ 1300 TeV just after the break-out with $sim$ 0.5% of the explosion energy. We consider the non-thermal emission from the blast-shocked ISM shell after the break-out. Synchrotron radio flux at 1 GHz is tens Jy, comparable to the observed from mixed-morphology SNRs. Because of low density, the gamma-ray luminosity is dominated by inverse-Compton scattering, which is higher than the $pi^0$-decay luminosity by an order of magnitude. The total gamma-ray luminosity including bremsstrahlung is of the order of $10^{33}$ erg s$^{-1}$ lower than the typical value $10^{35}$--$10^{36}$ erg s$^{-1}$ observed from mixed-morphology SNRs. However, if, e.g., $sim$10% of accelerated protons interact with some matter of density $sim$100 cm$^{-3}$, $pi^0$-decay gamma-ray luminosity would be enhanced to be comparable with the observed value.
We present results from spectroscopic observations with the Michigan/Magellan Fiber System (M2FS) of 182 stellar targets along the line of sight to the newly-discovered `ultrafaint' object Reticulum 2 (Ret 2). For 38 of these targets, the spectra are sufficient to provide simultaneous estimates of line-of-sight velocity ($v_{\rm los}$, median random error $\delta_{v_{\rm los}}=1.3$ km s$^{-1}$), effective temperature ($T_{\rm eff}$, $\delta_{T_{\rm eff}}=464$ K), surface gravity ($\log g$, $\delta_{\rm logg}=0.54$ dex) and iron abundance ([Fe/H], $\delta_{\mathrm{[Fe/H]}}=0.45$ dex). We use these results to confirm 18 stars as members of Ret 2. From the member sample we estimate a velocity dispersion of $\sigma_{v_{\rm los}}=3.6_{-0.6}^{+0.9}$ km s$^{-1}$ about a mean of $\langle v_{\rm los}\rangle =64.8_{-1.0}^{+1.1}$ km s$^{-1}$ in the solar rest frame ($\sim -90.9$ km s$^{-1}$ in the Galactic rest frame), and a metallicity dispersion of $\sigma_{\rm [Fe/H]}=0.50_{-0.13}^{+0.17}$ dex about a mean of $\langle \mathrm{[Fe/H]} \rangle =-2.67_{-0.34}^{+0.34}$. These estimates marginalize over possible velocity and metallicity gradients, which are consistent with zero. Our results place Ret 2 on chemodynamical scaling relations followed by the Milky Way's dwarf-galactic satellites. Under assumptions of dynamic equilibrium and negligible contamination from binary stars---both of which must be checked with deeper imaging and repeat spectroscopic observations---the estimated velocity dispersion suggests a dynamical mass of $M(R_{\rm h})\approx 5R_{\rm h}\sigma_{v_{\rm los}}^2/(2G)=2.4_{-0.8}^{+1.3}\times 10^5$ $M_{\odot}$ enclosed within projected halflight radius $R_{\rm h}\sim 32$ pc, with mass-to-light ratio $\approx 2M(R_{\rm h})/L_{\rm V}=462_{-157}^{+264}$ in solar units.
High value of magnetic moment 0.08 emu/g at room temperature for SnO_2 nanoparticles (NPs) was observed. Surface functionalization with octadecyltrichlorosilane (OTS) enhanced the saturation magnetic moment of NPs to an anomalously high value of 0.187 emu/g by altering the electronic configuration on NPs surface. Surface functionalization also suppressed photoluminescence (PL) peaks arising from oxygen defects around 2 eV and caused an increase in the intensities of two peaks near violet region (2.6 - 3 eV). PL studies under uniform external magnetic field enriched understanding of the role of OTS. Both OTS and external magnetic field significantly modulated the luminescence spectra, by altering the surface electronic structure of NPs. Extra spins on the surface of SnO2 NPs created by the surface functionalization process and their influence on resultant magnetic moment and luminescence properties are discussed in details.
We are monitoring 27 galaxies within 10 Mpc using the Large Binocular Telescope to search for failed supernovae (SNe), massive stars that collapse to form a black hole without a SN explosion. We present the results from the first 4 years of survey data, during which these galaxies were observed to produce 3 successful core-collapse SNe. We search for stars that have "vanished" over the course of our survey, by examining all stars showing a decrease in luminosity of $\Delta \nu L_{\nu} \ge 10^4L_{\odot}$ from the first to the last observation. We also search for the low luminosity, long duration transients predicted by \citet{lovegrove2013} for failed explosions of red supergiants. After analyzing the first 4 years of data in this first direct search for failed SNe, we are left with one candidate requiring further study. This candidate has an estimated mass of 18-25$M_{\odot}$, a mass range likely associated with failed SNe and, if real, implies that failed SN represent a median fraction of $f \simeq 0.30$ of core-collapses, with symmetric 90% confidence limits of $0.07 \le f \le 0.62$. If follow up data eliminate this candidate, we find an upper limit on the fraction of core collapses leading to a failed SN of $f<0.40$ at 90% confidence. As the duration of the survey continues to increase, it will begin to constrain the $f \simeq$ 10-30% failure rates needed to explain the deficit of massive SN progenitors and the observed black hole mass function.
Inspired by recent experimental findings that will be presented elsewhere, we formulate and investigate a model of a superconducting junction that combines the electron propagation in a quantum channel with an arbitrary transmission, and that through a localized state. Interesting situation occurs if the energy of the localized state is close to Fermi level, that is, the state is in resonant tunnelling regime. Since this energy is affected by the gate voltage, we expect a drastic modification of transport properties of the junction in a narrow interval of the gate voltages where the energy distance to Fermi level is of the order of $\Gamma, \Delta$, $\Gamma$ being the energy broadening of the localized state, $\Delta$ being the superconducting energy gap.   We consider the model neglecting the interaction in the localized state, as well as accounting for the interaction in a simplistic mean-field approach where it manifests itself as a spin-splitting. This spin splitting is also contributed by external magnetic field. We also take into account the spin-orbit interaction that can be significant in realistic experimental circumstances.   In normal state, we find that the model may describe both peak and dip in the transmission at resonant gate voltage. Spin splitting splits the positions of these peculiarities. Fano interference of the transmission amplitudes results in an asymmetric shape of the peaks/dips. In superconducting state, the spin splitting results in a complex dependence of the superconducting current on the superconducting phase. In several cases, this is manifested as a pair of $0 - \pi$ transitions in the narrow interval of gate voltages.   The article in the present form is not intended for a journal submission.
We study the dynamical polarization function and plasmon modes for spin-orbit coupled noncentrosymmetric metals (NCMs). These systems have different Fermi surface topology for Fermi energies above and below the spin degenerate point which is also known as the band touching point (BTP). We calculate the exact dynamical polarization function numerically and also provide its analytical expression in the long wavelength limit. We obtain the plasmon dispersion within the framework of random phase approximation. In NCMs, there is a finite energy gap in between intra and interband particle hole continuum (PHC) for vanishing excitation wavevector. In the long wavelength limit, the width of interband PHC behaves differently for Fermi energies below and above the BTP as a clear signature of the Fermi surface topology change. We find a single undamped optical plasmon mode lying in between the intra and interband PHC for Fermi energies above and below the BTP. The plasmon mode below the BTP has smaller velocity than that of above the BTP. It is interesting to find that as we tune the Fermi energy around the BTP, the plasmon mode becomes damped within a range of e-e interaction strength. For Fermi energies above and below the BTP, we also obtain an approximate analytical result of plasma frequency and plasmon dispersion which match well with their numerical counterparts in the long wavelength limit. The plasmon dispersion is $\propto q^2$ with $q$ being the wave vector for plasmon excitation in the long wavelength limit. We find that varying the carrier density with fixed e-e interaction strength or vice versa does not change the number of undamped plasmon mode, although damped plasmon modes can be more in number for some values of these parameters. We demonstrate our results by calculating the loss function and optical conductivity which can be measured in experiments.
A "practical number" is a positive integer $n$ such that every positive integer less than $n$ can be written as a sum of distinct divisors of $n$. We prove that most of the binomial coefficients are practical numbers. Precisely, letting $f(n)$ denote the number of binomial coefficients $\binom{n}{k}$, with $0 \leq k \leq n$, that are not practical numbers, we show that \begin{equation*} f(n) < n^{1 - (\log 2 - \delta)/\log \log n} \end{equation*} for all integers $n \in [3, x]$, but at most $O_\gamma(x^{1 - (\delta - \gamma) / \log \log x})$ exceptions, for all $x \geq 3$ and $0 < \gamma < \delta < \log 2$. Furthermore, we prove that the central binomial coefficient $\binom{2n}{n}$ is a practical number for all positive integers $n \leq x$ but at most $O(x^{0.88097})$ exceptions. We also pose some questions on this topic.
Polarized dust emission is a key tracer in the study of interstellar medium and of star formation. The observed polarization, however, is a product of magnetic field structure, dust grain properties and grain alignment efficiency, as well as their variations in the line of sight, making it difficult to interpret polarization unambiguously. The comparison of polarimetry at multiple wavelengths is a possible way of mitigating this problem. We use data from HAWC+/SOFIA and from SCUBA-2/POL-2 (from the BISTRO survey) to analyse the NGC 2071 molecular cloud at 154, 214 and 850 $\mu$m. The polarization angle changes significantly with wavelength over part of NGC 2071, suggesting a change in magnetic field morphology on the line of sight as each wavelength best traces different dust populations. Other possible explanations are the existence of more than one polarization mechanism in the cloud or scattering from very large grains. The observed change of polarization fraction with wavelength, and the 214-to-154 $\mu$m polarization ratio in particular, are difficult to reproduce with current dust models under the assumption of uniform alignment efficiency. We also show that the standard procedure of using monochromatic intensity as a proxy for column density may produce spurious results at HAWC+ wavelengths. Using both long-wavelength (POL-2, 850 $\mu$m) and short-wavelength (HAWC+, $\lesssim 200\, \mu$m) polarimetry is key in obtaining these results. This study clearly shows the importance of multi-wavelength polarimetry at submillimeter bands to understand the dust properties of molecular clouds and the relationship between magnetic field and star formation.
In this work we establish a correspondence between the tachyon, K-essence and dilaton scalar field models with the interacting entropy-corrected holographic dark (ECHD) model in non-flat FRW universe. The reconstruction of potentials and dynamics of these scalar fields according to the evolutionary behavior of the interacting ECHDE model are be done. It has been shown that the phantom divide can not be crossed in ECHDE tachyon model while it is achieved for ECHDE K-essence and ECHDE dilaton scenarios. At last we calculate the limiting case of interacting ECHDE model, without entropy-correction.
An arc-weighted digraph is a pair $(D,\omega)$ where $D$ is a digraph and $\omega$ is an \emph{arc-weight function} that assigns\ to each arc $uv$ of $D$ a nonzero real number $\omega(uv)$. Given an arc-weighted digraph $(D,\omega)$ with vertices $v_{1},\ldots,v_{n}$, the weighted adjacency matrix of $(D,\omega)$ is defined as the matrix $A(D,\omega)=[a_{ij}]$ where $a_{ij}=\omega(v_{i}v_{j})$, if $v_{i}v_{j}\ $an arc of $D$ and $0$ otherwise. Let $(D,\omega)$ be a positive arc-weighted digraphs and assume that $D$ is loopless and symmetric. A skew-signing of $(D,\omega)$ is an arc-weight function $\omega^{\prime}$ such that $\omega^{\prime}(uv)=\pm \omega(uv)$ and $\omega^{\prime}(uv)\omega^{\prime}(vu)<0$ for every arc $uv$ of $D$. In this paper, we give necessary and sufficient conditions under which the characteristic polynomial of $A(D,\omega^{\prime})$ is the same for every skew-signing $\omega^{\prime}$ of $(D,\omega)$. Our Main Theorem generalizes a result of Cavers et al (2012) about skew-adjacency matrices of graphs.
We study the different phases of a system of monodispersed hard rods of length $k$ on a cubic lattice using an efficient cluster algorithm which can simulate densities close to the fully-packed limit. For $k\leq 4$, the system is disordered at all densities. For $k=5,6$, we find a single density-driven transition from a disordered phase to high density layered-disordered phase in which the density of rods of one orientation is strongly suppressed, breaking the system into weakly coupled layers. Within a layer, the system is disordered. For $k \geq 7$, three density driven transitions are observed numerically: isotropic to nematic to layered-nematic to layered-disordered. In the layered-nematic phase, the system breaks up into layers, with nematic order in each in each layer, but very weak correlation between the ordering direction between different layers. We argue that the layered-nematic phase is a finite-size effect, and in the thermodynamic limit, the nematic phase will have higher entropy per site.
We establish estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model with i.i.d. exponential weights. There are four estimates: upper and lower bounds on the probabilities of both fast and slow coalescence on the correct spatial scale with exponent $3/2$. Our proofs utilize a geodesic duality introduced by Pimentel and properties of the increment-stationary last-passage percolation process. For fast coalescence our bounds are new and they have matching optimal exponential order of magnitude. For slow coalescence we reproduce bounds proved earlier with integrable probability inputs, except that our upper bound misses the optimal order by a logarithmic factor.
Dwarf galaxies (M*<10^9 Msun) are key drivers of mass assembly in high mass galaxies, but relatively little is understood about the assembly of dwarf galaxies themselves. Using the \textsc{NewHorizon} cosmological simulation (40 pc spatial resolution), we investigate how mergers and fly-bys drive the mass assembly and structural evolution of around 1000 field and group dwarfs up to z=0.5. We find that, while dwarf galaxies often exhibit disturbed morphologies (5 and 20 per cent are disturbed at z=1 and z=3 respectively), only a small proportion of the morphological disturbances seen in dwarf galaxies are driven by mergers at any redshift (for 10^9 Msun, mergers drive only 20 per cent morphological disturbances). They are instead primarily the result of interactions that do not end in a merger (e.g. fly-bys). Given the large fraction of apparently morphologically disturbed dwarf galaxies which are not, in fact, merging, this finding is particularly important to future studies identifying dwarf mergers and post-mergers morphologically at intermediate and high redshifts. Dwarfs typically undergo one major and one minor merger between z=5 and z=0.5, accounting for 10 per cent of their total stellar mass. Mergers can also drive moderate star formation enhancements at lower redshifts (3 or 4 times at z=1), but this accounts for only a few per cent of stellar mass in the dwarf regime given their infrequency. Non-merger interactions drive significantly smaller star formation enhancements (around two times), but their preponderance relative to mergers means they account for around 10 per cent of stellar mass formed in the dwarf regime.
The Bel-Robinson tensor $T_{\alpha\beta\mu\nu}$ was proposed in 1958. The main application of this tensor is for describing gravitational energy. It is known that $T_{\alpha\beta\mu\nu}$ has many nice properties such as being completely symmetric. It is easy to prove this property using spinors as shown in Penrose's book. The present paper provides an alternative way, using the tensorial method to prove that $T_{\alpha\beta\mu\nu}$ is indeed totally symmetric. Moreover, we also found that the well known identity in vacuum, $R_{\alpha\lambda\sigma\tau}R_{\beta}{}^{\lambda\sigma\tau} \equiv 1/4g_{\alpha\beta}R_{\rho\lambda\sigma\tau} R^{\rho\lambda\sigma\tau}$, which can be proven by the same tensorial method.
We present a formula for an infinite number of universal quantum logic gates, which are $4$ by $4$ unitary solutions to the Yang-Baxter (Y-B) equation. We obtain this family from a certain representation of the cyclic group of order $n$. We then show that this {\it discrete} family, parametrized by integers $n$, is in fact, a small sub-class of a larger {\it continuous} family, parametrized by real numbers $\theta$, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian.
Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-eternal domination model. Inequality chains consisting of the domination, eternal domination, m-eternal domination, independence, and clique covering numbers of graph are explored in this paper. Among other results, we characterize bipartite and triangle-free graphs with domination and eternal domination numbers equal to two, trees with equal m-eternal domination and clique covering numbers, and two classes of graphs with equal domination, eternal domination and clique covering numbers.