ShantanuT01/DACTYL-Pretraining huggingface dataset:
It has been known that the Bekenstein-Hawking entropy of the black hole in AdS_5 * S^5 agrees with the free N=4 super Yang-Mills entropy up to the famous factor 4/3. This factor can be interpreted as the ratio of the entropy of the free Yang-Mills to the entropy of the strongly coupled Yang-Mills. In this paper we compute this factor for infinitely many N=1 SCFTs which are dual to toric Sasaki-Einstein manifolds. We observed that this ratio always takes values within a narrow range around 4/3. We also present explicit values of volumes and central charges for new classes of toric Sasaki-Einstein manifolds.
A comparative study is made on the metal-insulator transition of Dirac fermions in the honeycomb and \pi-flux Hubbard models at half filling by means of the variational cluster approximation and cluster dynamical impurity approximation. Paying particular attention to the choice of the geometry of solver clusters and the inclusion of particle-bath sites, we show that the direct transition from the Dirac semimetallic state to the antiferromagnetic Mott insulator state occurs in these models, and therefore, the spin liquid phase is absent in the intermediate region, in agreement with recent quantum-Monte-Carlo--based calculations.
Within the framework of macroscopic quantum electrodynamics and scattering theory, we derive the general expressions for the variance of radiative heat transfer between two arbitrarily shaped objects placed in an arbitrary environment in terms of their T-operators. The such derived expression is valid in the far- and near-field regime of thermal radiation as well as for reciprocal and non-reciprocal objects of any size within a reciprocal or non-reciprocal environment as long as the distances between the objects and their sizes are covered by the macroscopic approach. As special cases we discuss the variance of the radiative heat flux between two nanoparticles and between a nanoparticle and a substrate in near- and far-field regime.
The discovery in 1991 of high temperature superconductivity (SC) in A3C60 compounds, where A is an alkali ion, has been rapidly ascribed to a BCS mechanism, in which the pairing is mediated by on ball optical phonon modes. While this has lead to consider that electronic correlations were not important in these compounds, further studies of various AnC60 with n=1, 2, 4 allowed to evidence that their electronic properties cannot be explained by a simple progressive band filling of the C60 six-fold degenerate t1u molecular level. This could only be ascribed to the simultaneous influence of electron correlations and Jahn-Teller Distortions (JTD) of the C60 ball, which energetically favour evenly charged C60 molecules. This is underlined by the recent discovery of two expanded fulleride Cs3C60 isomeric phases which are Mott insulators at ambient pressure. Both phases undergo a pressure induced first order Mott transition to SC with a (p, T) phase diagram displaying a dome shaped SC, a common situation encountered nowadays in correlated electron systems. NMR experiments allowed us to study the magnetic properties of the Mott phases and to evidence clear deviations from BCS expectations near the Mott transition. So, although SC involves an electron-phonon mechanism, the incidence of electron correlations has an importance on the electronic properties, as had been anticipated from DMFT calculations.
We consider an $n$ by $n$ matrix of the form $A=UTV$, with $U, V$ some independent Haar-distributed unitary matrices and $T$ a deterministic matrix. We prove that for $k\sim n^{1/6}$ and $b^2:=\frac{1}{n}\operatorname{Tr}(|T|^2)$, as $n$ tends to infinity, we have $$\mathbb{E} \operatorname{Tr} (A^{k}(A^{k})^*) \ \lesssim \ b^{2k}\qquad \textrm{and} \qquad\mathbb{E}[|\operatorname{Tr} (A^{k})|^2] \ \lesssim \ b^{2k}.$$ This gives a simple proof (with slightly weakened hypothesis) of the convergence of the support in the Single Ring Theorem, improves the available error bound for this convergence from $n^{-\alpha}$ to $e^{-cn^{1/6}}$ and proves that the rate of this convergence is at most $n^{-1/6}\log n$.
This is a review of current theory of black-hole dynamics, concentrating on the framework in terms of trapping horizons. Summaries are given of the history, the classical theory of black holes, the defining ideas of dynamical black holes, the basic laws, conservation laws for energy and angular momentum, other physical quantities and the limit of local equilibrium. Some new material concerns how processes such as black-hole evaporation and coalescence might be described by a single trapping horizon which manifests temporally as separate horizons.
Random Phase Approximation (RPA) is the basic method for calculation of excited states of nuclei over the Hartree-Fock ground state, suitable also for energy density functionals (EDF or DFT). We developed a convenient formalism for expressing densities and currents in a form of reduced matrix elements, which allows fast calculation of spectra for spherical nuclei. All terms of Skyrme functional were taken into account, so it is possible to calculate electric, magnetic and vortical/toroidal/compression transitions and strength functions of any multipolarity. Time-odd (spin) terms in Skyrme functional become important for magnetic M1 and isovector toroidal E1 transitions. It was also found that transition currents in pygmy region (low-lying part of E1 resonance) exhibit isoscalar toroidal flow, so the previously assumed picture of neutron-skin vibration is not the only mechanism present in pygmy transitions.   RPA calculations with heavy axially-symmetric nuclei now become feasible on ordinary PC. Detailed formulae for axial Skyrme RPA are given. Some numerical results are shown in comparison with the approximate approach of separable RPA, previously developed in our group for fast calculation of strength functions.
We extracted, from strongly-correlated ab-initio calculations, a complete model for the chain subsystem of the $Sr_{0.4}Ca_{13.6}Cu_{24}O_{41}$ incommensurate compound. A second neighbor $t-J+V$ model has been determined as a function of the fourth crystallographic parameter $\tau$, for both low and room temperature crystallographic structures. The analysis of the obtained model shows the crucial importance of the structural modulations on the electronic structure through the on-site energies and the magnetic interactions. The structural distortions are characterized by their long range effect on the cited parameters that hinder the reliability of analyses such as BVS. One of the most striking results is the existence of antiferromagnetic nearest-neighbor interactions for metal-ligand-metal angles of $90^\circ$. A detailed analysis of the electron localization and spin arrangement is presented as a function of the chain to ladder hole transfer and of the temperature. The obtained spin arrangement is in agreement with antiferromagnetic correlations in the chain direction at low temperature.
After observing that some constructions and results in the $p$-adic Langlands programme are somehow independent from $p$, we formulate the hypothesis that this astonishing uniformity could be explained by a 1-adic Langlands correspondence.
In this paper we study the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space $ H^{1/2} (\R) $ or $ H^{1/2}(\T) $. We prove the strong convergence in the energy space of the solution to this equation toward the solution of the Benjamin-Ono equation as the dissipation coefficient converges to $ 0 $.
Recent measurements of the pi^+pi^- invariant mass distribution at RHIC show a shifted peak for the rho meson in 100A GeV in peripheral Au + Au and even in p + p collisions. A recent theoretical study based on a picture of in-medium production rates of pions, showed that a large shift could result from a combination of the Boltzmann factor and the collisional broadening of the rho. Here we argue that the two-pion density of states is the appropriate quantity if one assumes a sudden break-up of the system. Methods for calculating the density of states which include Bose effects are derived. The resulting invariant mass distributions are significantly enhanced at lower masses and the rho peak is shifted downward by ~ 35 MeV.
Fundamental parameters and time-evolution of mass loss are investigated for post-main-sequence stars in the Galactic globular cluster 47 Tucanae (NGC 104). This is accomplished by fitting spectral energy distributions (SEDs) to existing optical and infrared photometry and spectroscopy, to produce a true Hertzsprung--Russell diagram. We confirm the cluster's distance as 4611 (+213, -200) pc and age as 12 +/- 1 Gyr. Horizontal branch models appear to confirm that no more RGB mass loss occurs in 47 Tuc than in the more-metal-poor omega Centauri, though difficulties arise due to inconsistencies between the models. Using our SEDs, we identify those stars which exhibit infrared excess, finding excess only among the brightest giants: dusty mass loss begins at a luminosity of ~ 1000 Lsun, becoming ubiquitous above 2000 Lsun. Recent claims of dust production around lower-luminosity giants cannot be reproduced, despite using the same archival Spitzer imagery.
We present the WFC3 Infrared Spectroscopic Parallel (WISP) Survey. WISP is obtaining slitless, near-infrared grism spectroscopy of ~ 90 independent, high-latitude fields by observing in the pure parallel mode with Wide Field Camera-3 on the Hubble Space Telescope for a total of ~ 250 orbits. Spectra are obtained with the G102 (lambda=0.8-1.17 microns, R ~ 210) and G141 grisms (lambda=1.11-1.67 microns, R ~ 130), together with direct imaging in the J- and H-bands (F110W and F140W, respectively). In the present paper, we present the first results from 19 WISP fields, covering approximately 63 square arc minutes. For typical exposure times (~ 6400 sec in G102 and ~ 2700 sec in G141), we reach 5-sigma detection limits for emission lines of 5 x 10^(-17) ergs s^(-1) cm^(-2) for compact objects. Typical direct imaging 5sigma-limits are 26.8 and 25.0 magnitudes (AB) in F110W and F140W, respectively. Restricting ourselves to the lines measured with highest confidence, we present a list of 328 emission lines, in 229 objects, in a redshift range 0.3 < z < 3. The single-line emitters are likely to be a mix of Halpha and [OIII]5007,4959 A, with Halpha predominating. The overall surface density of high-confidence emission-line objects in our sample is approximately 4 per arcmin^(2).These first fields show high equivalent width sources, AGN, and post starburst galaxies. The median observed star formation rate of our Halpha selected sample is 4 Msol/year. At intermediate redshifts, we detect emission lines in galaxies as faint as H_140 ~ 25, or M_R < -19, and are sensitive to star formation rates down to less than 1 Msol/year. The slitless grisms on WFC3 provide a unique opportunity to study the spectral properties of galaxies much fainter than L* at the peak of the galaxy assembly epoch.
In this work we apply the stacking technique to estimate the average fractional polarisation from 30 to 353 GHz of a primary sample of 1560 compact sources - essentially all radio sources - detected in the 30 GHz Planck all-sky map and listed in the second version of the Planck Catalogue of Compact Sources (PCCS2). We divide our primary sample in two subsamples according to whether the sources lay (679 sources) or not (881 sources) inside the sky region defined by the Planck Galactic mask (fsky ~ 60 per cent) and the area around the Magellanic Clouds. We find that the average fractional polarisation of compact sources is approximately constant (with frequency) in both samples (with a weighted mean over all the channels of 3.08 per cent outside and 3.54 per cent inside the Planck mask). In the sky region outside the adopted mask, we also estimate the {\mu} and {\sigma} parameters for the log-normal distribution of the fractional polarisation, finding a weighted mean value over all the Planck frequency range of 1.0 for {\sigma} and 0.7 for {\mu} (that would imply a weighted mean value for the median fractional polarisation of 1.9 per cent).
The population dynamics of single- and bi-exciton states in semiconductor nanocrystals is modeled numerically in the presence of Coulomb coupling between single- and two-exciton states and a dissipation channel in order to study the transient bi-exciton population that occurs in an optically excited semiconductor nanocrystal. The results show that the system evolution strongly changes if the dissipation is included. In a certain range of parameters, the growth of the exciton number (MEG process) is fast (on picosecond time scale) and the following decay (Auger process) is much slower (hundreds of picoseconds). In some cases, the maximum occupation of the bi-exciton state increases when dissipation is included. The dynamics of an ensemble of nanocrystals with a certain size dispersion is studied by averaging over the energy of the bi-exciton state which can be different for each single nanocrystal. The validity of Markov and secular approximation is also verified.
In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of semi-Markov processes is established. The variable order $\alpha(x)$-fractional diffusion equation is a particular case of our analysis and it turns out that it is associated with a suitable (non-independent) time-change of the Brownian motion. The resulting process is semi-Markovian and its paths have intervals of constancy, as it happens for the delayed Brownian motion, suitable to model trapping effects induced by the medium. However in our scenario the interval of constancy may be position dependent and this means traps of space-varying depth as it happens in a disordered medium. The strength of the trapping is investigated by means of the asymptotic behaviour of the process: it is proved that, under some technical assumptions on $\alpha(x)$, traps make the process non-diffusive in the sense that it spends a negligible amount of time out of a neighborhood of the region $\text{argmin}(\alpha(x))$ to which it converges in probability under some more restrictive hypotheses on $\alpha(x)$.
Aims. Atomic diffusion, including the effect of radiative accelerations on individual elements, leads to important variations of the chemical composition inside the stars. The accumulation in specific layers of the elements, which are the main contributors of the local opacity, leads to hydrodynamical instabilities that modify the internal stellar structure and surface abundances. Our aim is to study these effects and compare the resulting surface abundances with spectroscopic observations Methods. We computed the detailed structure of A-type stars including these effects. We used the Toulouse-Geneva Evolution Code (TGEC), where radiative accelerations are computed using the Single Valued Parameter (SVP) method, and we added double-diffusive convection with mixing coefficients deduced from three-dimensional (3D) simulations. Results. We show that the modification of the initial chemical composition has important effects on the internal stellar mixing and leads to different surface abundances of the elements. The results fit the observed surface chemical composition well if the layers, which are individually mixed by double-diffusive convection, are connected.
Let $\ell>2$ be a positive integer, $\zeta_\ell$ a primitive $\ell$-th root of unity, and $K$ a number field containing $\zeta_\ell+\zeta_\ell^{-1}$ but not $\zeta_\ell$. In a recent paper, Chonoles et. al. study iterated towers of number fields over $K$ generated by the generalized Rikuna polynomial, $r_n(x,t;\ell) \in K(t)[x]$. They note that when $K = \mathbb{Q}$, $t \in \{0,1\}$, and $\ell=3$, the only ramified prime in the resulting tower is 3, and they ask under what conditions is the number of ramified primes small. In this paper, we apply a theorem of Gu\`ardia, Montes, and Nart to derive a formula for the discriminant of $\mathbb{Q}(\theta)$ where $\theta$ is a root of $r_n(x,t;3)$, answering the question of Chonoles et. al. in the case $K = \mathbb{Q}$, $\ell=3$, and $t \in \mathbb{Z}$. In the latter half of the paper, we identify some cases where the dynamics of $r_n(x,t;\ell)$ over finite fields yields an explicit description of the decomposition of primes in these iterated extensions.
The evolutionary mechanism underlying Type Ia supernova explosions remains unknown. Recent efforts to constrain progenitor models based on the influence that their high energy emission would have on the interstellar medium (ISM) of galaxies have proven successful. For individual remnants, Balmer-dominated shocks reveal the ionization state of hydrogen in the immediately surrounding gas. Here we report deep upper limits on the temperature and luminosity of the progenitors of four Type Ia remnants with associated Balmer filaments: SN 1006, 0509-67.5, 0519-69.0, and DEM L71. For SN 1006, existing observations of helium line emission in the diffuse emission ahead of the shock provide an additional constraint on the helium ionization state in the vicinity of the remnant. Using the photoionization code Cloudy, we show that these constraints exclude any hot, luminous progenitor for SN 1006, including stably hydrogen or helium nuclear-burning white dwarfs, as well as any Chandrasekhar-mass white dwarf accreting matter at $\gtrsim 9.5\times10^{-8}M_{\odot}/$yr via a disk. For 0509-67.5, the Balmer emission alone rules out any such white dwarf accreting $\gtrsim 1.4\times10^{-8}M_{\odot}/$yr. For 0519-69.0 and DEM L71, the inferred ambient ionization state of hydrogen is only weakly in tension with a recently hot, luminous progenitor, and cannot be distinguished from e.g., a relatively higher local Lyman continuum background, without additional line measurements. Future deep spectroscopic observations will resolve this ambiguity, and can either detect the influence of any luminous progenitor or rule out the same for all resolved SN Ia remnants.
The ability in experiments to control the relative twist angle between successive layers in two-dimensional (2D) materials offers a new approach to manipulating their electronic properties; we refer to this approach as "twistronics". A major challenge to theory is that, for arbitrary twist angles, the resulting structure involves incommensurate (aperiodic) 2D lattices. Here, we present a general method for the calculation of the electronic density of states of aperiodic 2D layered materials, using parameter-free hamiltonians derived from ab initio density-functional theory. We use graphene, a semimetal, and MoS$_2$, a representative of the transition metal dichalcogenide (TMDC) family of 2D semiconductors, to illustrate the application of our method, which enables fast and efficient simulation of multi-layered stacks in the presence of local disorder and external fields. We comment on the interesting features of their Density of States (DoS) as a function of twist-angle and local configuration and on how these features can be experimentally observed.
The critical relaxation from the low-temperature ordered state of the three-dimensional fully frustrated Ising model on a simple cubic lattice has been studied using the short time dynamics method. Particles with the periodic boundary conditions containing N = 262144 spins have been studied. Calculations have been performed by the standard Metropolis Monte Carlo algorithm. The static critical exponents of the magnetization and correlation radius have been obtained. The dynamic critical exponent of the model under study has been calculated.
We describe string-theory and $d=11$ supergravity solutions involving symmetric spaces of constant negative curvature. Many examples of non-supersymmetric string compactifications on hyperbolic spaces $H_r$ of finite volume are given in terms of suitable cosets of the form $H_r/\Gamma $, where $\Gamma $ is a discrete group. We describe in some detail the cases of the non-compact hyperbolic spaces $F_2$ and $F_3$, representing the fundamental regions of $H_2$ and $H_3$ under $SL(2,Z)$ and the Picard group, respectively. By writing $AdS$ as a U(1) fibration, we obtain new solutions where $AdS_{2p+1}$ gets untwisted by T-duality to ${\bf R}\times SU(p,1)/(SU(p)\times U(1))$. Solutions with time-dependent dilaton field are also constructed by starting with a solution with NS5-brane flux over $H_3$. A new class of non-supersymmetric conformal field theories can be defined via holography.
The problem of weak ferromagnetism in antiferromagnets due to canting of magnetic moments was treated using Green's function technique. At first the eigenvalues and eigenfunctions of the electronic Hamiltonian corresponding to collinear magnetic configuration are calculated which are then used to determine first and second variations of the total energy as a function of the magnetic moments canting angle. Spin-orbit coupling is taken into account via perturbation theory. The results of calculations are used to determine an effective spin Hamiltonian. This Hamiltonian can be mapped on conventional spin Hamiltonian that allows to determine parameters of isotropic and anisotropic (Dzyaloshinskii-Moriya) exchange interactions. The method was applied to the typical antiferromagnets with weak ferromagnetism Fe$_{2}$O$_{3}$ and La$_{2}$CuO$_{4}$. The obtained directions and values of the magnetic moments canting angles are in a reasonable agreement with experimental data.
Using the Dissipation Theorem and a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we give a first-principles derivation of Boltzmann's postulate of equal a priori probability in phase space for the microcanonical ensemble. We show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble.
A linear oscillator very weakly coupled with the object quantum system is proposed as a detector measuring the lifetime of irreversibility exhibited by the system, and classically chaotic coupled kicked rotors are examined as ideal examples. The lifetime increases drastically in close correlation with the enhancement of entanglement entropy(EE) between the kicked rotors. In the transition regime to the full entanglement, the EE of individual eigenstates fluctuates anomalously, and the lifetime also fluctuates in correlation with the EE. In the fully entangled regime the fluctuation disappear, but the lifetime is not yet unique but increases in proportion to the number of superposed eigenstates and is proportional to the square of Hilbert space dimension in the full superposition.