ShantanuT01/DACTYL-Pretraining huggingface dataset:
Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action are derived. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still present as a part of gauge freedom. 3+1 decomposition introduces tangent Minkowski structures hence Hamilton-Dirac approach to dynamics works with Lorentz connection over the spatial section. The second class constraints are analyzed and Dirac bracket is defined. Reduction of the phase space is performed and canonical coordinates are introduced.
We show that the recent observation that near extremal NS fivebranes decay due to Hawking radiation, can be understood in terms of their coupling to RR states which does not vanish even as the string coupling goes to zero.
Discovering new materials with ultrahigh thermal conductivity has been a critical research frontier and driven by many important technological applications ranging from thermal management to energy science. Here we have rigorously investigated the fundamental lattice vibrational spectra in ternary compounds and determined the thermal conductivity using a predictive ab initio approach. Phonon transport in B-X-C (X = N, P, As) groups is systematically quantified with different crystal structures and high-order anharmonicity involving a four-phonon process. Our calculation found an ultrahigh room-temperature thermal conductivity through strong carbon-carbon bonding up to 2100 W/mK beyond most common materials and the recently discovered boron arsenide. This study provides fundamental insight into the atomistic design of thermal conductivity and opens up opportunities in new materials searching towards complicated compound structures.   DOI: 10.1103/PhysRevB.103.L041203
Methanol ice is embedded in interstellar ice mantles present in dense molecular clouds. We aim to measure the sputtering efficiencies starting from different ice mantles of varying compositions experimentally, in order to evaluate their potential impact on astrochemical models. The sputtering yields of complex organic molecules is of particular interest, since few mechanisms are efficient enough to induce a significant feedback to the gas phase. We irradiated methanol and carbon dioxide ice mixtures of varying ratios with swift heavy ions in the electronic sputtering regime. We monitored the evolution of the infrared spectra and the species released to the gas phase with a mass spectrometer. Methanol and 13C-methanol isotopologue were used to remove any ambiguity on the measured irradiation products. The sputtering of methanol embedded in carbon dioxide ice is an efficient process leading to the ejection of intact methanol in the gas phase. We establish that when methanol is embedded in a carbon-dioxide-rich mantle exposed to cosmic rays, a significant fraction is sputtered as intact molecules. The sputtered fraction follows the time-dependent bulk composition of the ice mantle, the latter evolving with time due to the radiolysis-induced evolution of the bulk. If methanol is embedded in a carbon dioxide ice matrix, as the analyses of the spectral shape of the CO2 bending mode observations in some lines of sight suggest, the overall methanol sputtering yield is higher than if embedded in a water ice mantle. The sputtering is increased by a factor close to the dominant ice matrix sputtering yield, which is about six times higher for pure carbon dioxide ice when compared to water ice. These experiments are further constraining the cosmic-ray-induced ice mantle sputtering mechanisms important role in the gas-phase release of complex organic molecules from the interstellar solid phase.
The nonaxisymmetric Ekman flow excited inside a neutron star following a rotational glitch is calculated analytically including stratification and compressibility. For the largest glitches, the gravitational wave strain produced by the hydrodynamic mass quadrupole moment approaches the sensitivity range of advanced long-baseline interferometers. It is shown that the viscosity, compressibility, and orientation of the star can be inferred in principle from the width and amplitude ratios of the Fourier peaks (at the spin frequency and its first harmonic) observed in the gravitational wave spectrum in the plus and cross polarizations. These transport coefficients constrain the equation of state of bulk nuclear matter, because they depend sensitively on the degree of superfluidity.
The dynamics of optical switching in semiconductor microcavities in the strong coupling regime is studied using time- and spatially-resolved spectroscopy. The switching is triggered by polarised short pulses which create spin bullets of high polariton density. The spin packets travel with speeds of the order of 106 m/s due to the ballistic propagation and drift of exciton-polaritons from high to low density areas. The speed is controlled by the angle of incidence of the excitation beams, which changes the polariton group velocity.
A birational map from a projective space onto a not too much singular projective variety with a single irreducible non-singular base locus scheme (special birational transformation) is a rare enough phenomenon to allow meaningful and concise classification results.   We shall concentrate on transformations defined by quadratic equations onto some varieties (especially projective hypersurfaces of small degree), where quite surprisingly the base loci are interesting projective manifolds appearing in other contexts; for example, exceptions for adjunction theory, small degree or small codimensional manifolds, Severi or more generally homogeneous varieties.   In particular, we shall classify: quadro-quadric transformations into a quadric hypersurface; quadro-cubic transformations into a del Pezzo variety; transformations whose base locus (scheme) has dimension at most three.
Exact diagonalizations with a realistic interaction show that configurations with four neutrons in a major shell and four protons in another -or the same- major shell, behave systematically as backbending rotors. The dominance of the $q\cdot q$ component of the interaction is explained by an approximate form of SU3 symmetry. It is suggested that these configurations are associated with the onset of rotational motion in medium and heavy nuclei.
A theoretical approach to photoconversion efficiency modeling in perovskite p-i-n structures is developed. The results of this modeling compare favorably with the experiment and indicate that the surfaces of the perovskite solar cells (SCs) are naturally textured. It is shown that photoconversion efficiency in the limiting case of negligible Shockley-Read-Hall and surface recombination and in the absence of optical losses reaches the value of 29%. In the realistic case, the current-voltage curve ideality factor equals 2. This value is not due to recombination in the space-charge region; rather, it can be explained by taking into account the effect of the rear surface and high excitation level.
We present results for a model that describes a quantum point contact. We show how electron-electron correlations, within the unrestricted Hartree-Fock approximation, generate a magnetic moment in the point contact. Having characterized the magnetic structure of the contact, we map the problem onto a simple one-channel model and calculate the temperature dependence of the conductance for different gate voltages. Our results are in good agreement with experimental results obtained in GaAs devices and support the idea of Kondo effect in these systems.
The moduli space of Higgs bundles has two stratifications. The Bialynicki-Birula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises from the Harder-Narasimhan type of the vector bundle underlying a Higgs bundle. While these two stratification coincide in the case of rank two Higgs bundles, this is not the case in higher rank. In this paper we analyze the relation between the two stratifications for the moduli space of rank three Higgs bundles.
We show that Bernshteyn's proof of the breakthrough result of Molloy that triangle-free graphs are choosable from lists of size $(1+o(1))\Delta/\log\Delta$ can be adapted to yield a stronger result. In particular one may prove that such list sizes are sufficient to colour any graph of maximum degree $\Delta$ provided that vertices sharing a common colour in their lists do not induce a triangle in $G$, which encompasses all cases covered by Molloy's theorem. This was thus far known to be true for lists of size $(1000+o(1))\Delta/\log\Delta$, as implies a more general result due to Amini and Reed. We also prove that lists of length $2(r-2)\Delta \log_2\log_2\Delta/\log_2\Delta$ are sufficient if one replaces the triangle by any $K_r$ with $r\geq 4$, pushing also slightly the multiplicative factor of $200r$ from Bernshteyn's result down to $2(r-2)$. All bounds presented are also valid within the more general setting of correspondence colourings.
In this letter we report numerical results giving, as a function of time, the energy fluctuation of a Fermi-Pasta-Ulam system in dynamical contact with a heat bath, the initial data of the FPU system being extracted from a Gibbs distribution at the same temperature of the bath. The aim is to get information on the specific heat of the FPU system in the spirit of the fluctuation--dissipation theorem. While the standard equilibrium result is recovered at high temperatures, there exists a critical temperature below which the energy fluctuation as a function of time tends to an asymptotic value sensibly lower than the one expected at equilibrium. This fact appears to exhibit the existence of a metastable state for generic initial conditions. An analogous phenomenon of metastability was up to now observed in FPU systems only for exceptional initial data having vanishing Gibbs measure, namely excitations of a few low--frequency modes (as in the original FPU work).
Functional equations like exact renormalisation group and Dyson-Schwinger equations have contributed to a better understanding of non-perturbative phenomena in quantum field theories in terms of the underlying Green functions. In Yang-Mills theory especially the Landau gauge has been used, as it is the most accessible gauge for these methods. In the maximally Abelian gauge first results have been obtained which are very encouraging because Abelian infrared dominance has been found: The Abelian part of the gauge field propagator is enhanced at low momenta and thereby dominates the dynamics in the infrared. Also the ambiguity of two different types of solutions (decoupling and scaling) exists in both gauges. It is demonstrated how the two solutions are related in the maximally Abelian gauge. As in all two-point Dyson-Schwinger equations of the MAG the infrared dominant diagrams are sunset diagrams, in addition, a BPHZ regularisation and renormalisation of a test system with a sunset-like diagram is presented.
Here, we are concerned with comparing estimation schemes for the quantum state under continuous measurement (quantum trajectories), namely quantum state filtering and, as introduced by us [Phys. Rev. Lett. 115, 180407 (2015)], quantum state smoothing. Unfortunately, the cumulative errors in the most typical simulations of quantum trajectories with a total time of simulation $T$ can reach orders of $T \Delta t$. Moreover, these errors may correspond to deviations from valid quantum evolution as described by a completely positive map. Here we introduce a higher-order method that reduces the cumulative errors in the complete positivity of the evolution to of order $T\Delta t^2$, whether for linear (unnormalised) or nonlinear (normalised) quantum trajectories. Our method also guarantees that the discrepancy in the average evolution between different detection methods (different `unravellings', such as quantum jumps or quantum diffusion) is similarly small. This equivalence is essential for comparing quantum state filtering to quantum state smoothing, as the latter assumes that all irreversible evolution is unravelled, although the estimator only has direct knowledge of some records. In particular, here we compare, for the first time, the average difference between filtering and smoothing conditioned on an event of which the estimator lacks direct knowledge: a photon detection within a certain time window. We find that the smoothed state is actually {\em less pure}, both before and after the time of the jump. Similarly, the fidelity of the smoothed state with the `true' (maximal knowledge) state is also lower than that of the filtered state before the jump. However, after the jump, the fidelity of the smoothed state is higher.
Using the data schemes developed by Arrondo-Sols-Speiser, we give a rigorous definition of algebraic differential equations on the complex projective space $P^n$. For an algebraic subvariety $S \subseteq P^n$, we present an explicit formula for the degree of the divisor of solutions of a differential equation on $S$ and give some examples of applications. We extend the technique and result to the real case.
Let G be a finite group acting on a smooth projective curve X. This induces an action of G on the Jacobian JX of X and thus a decomposition of JX up to isogeny. The most prominent example of such a situation is the group G of two elements. Let X --> Y denote the corresponding quotient map. Then JX is isogenous to the product of JY with the Prym variety of X/Y. In this paper some general results on group actions on abelian varieties are given and applied to deduce a decomposition of the jacobian JX for arbitrary group actions. Several examples are given.
A principal candidate for quiescent non-thermal gamma-ray emission from magnetars is resonant inverse Compton scattering in the strong fields of their magnetospheres. This paper outlines expectations for such emission, formed from non-thermal electrons accelerated in a pulsar-like polar cap potential upscattering thermal X-rays from the hot stellar surface. The resultant spectra are found to be strikingly flat, with fluxes and strong pulsation that could be detectable by GLAST.
The MAGIC telescope is the largest single-dish Imaging Atmospheric Cherenkov Telescope (IACT) with the lowest energy threshold among the current generation of IACTs as low as 25 GeV. Therefore, the MAGIC telescope is a perfect instrument to study the galactic sources especially in the context of observations with the satellite observatories Fermi and AGILE. This paper will give an overview of the MAGIC results on the galactic sources including detailed observations of binary systems, supernova remnants and the first detection of the Crab pulsar above 25 GeV .
Development of new greenhouse gas scavengers is actively pursued nowadays. Volatility caused solvent consumption and significant regeneration costs associated with the aqueous amine solutions motivate search for more technologically and economically advanced solutions. We hereby used hybrid density functional theory to characterize thermodynamics, structure, electronic and solvation properties of amino and carboxamido functionalized C60 fullerene. C60 is non-volatile and supports a large density of amino groups on its surface. Attachment of polar groups to fullerene C60 adjusts its dipole moment and band gap quite substantially, ultimately resulting in systematically better hydration thermodynamics. Reaction of polyaminofullerenes with CO2 is favored enthalpically, but prohibited entropically at standard conditions. Free energy of the CO2 capture by polyaminofullerenes is non-sensitive to the number of amino groups per fullerene. This result fosters consideration of polyaminofullerenes for CO2 fixation.
We analysed new simultaneous \emph{Suzaku} and \emph{Swift} data of the Broad Line Seyfert 1 (BLS1) galaxy CBS 126. A clear Fe emission line and a strong soft excess are present in the source spectra. We fit the spectra with a relativistic reflection model and find the model tends to fit the data with a high iron abundance possibly due to the large soft excess present. By checking the difference and the RMS spectra, we find there is likely an absorption edge at $\sim$ 0.89 keV, which might be caused by oxygen or neon. We also produced an analysis of the time-resolved spectra in order to examine the existence of the edge. Although high iron abundance is required more in the time-resolved spectra, a model of solar iron abundance together with an absorption edge gives a more physical explanation. Variation of the ionisation parameter is an alternative, plausible explanation for the excess seen in the difference spectra. It is difficult to know if there are warm absorbers in this source from the current data. To further investigate the presence of possible warm absorbers, higher signal-to-noise low-energy data are needed. The work presented here tentatively suggests that the spectra of a BLS1 can be explained by a relativistic reflection model similar to that often seen in their narrow-line cousins.
With the legacy of Spitzer and current advances in (sub)mm astronomy, a large number of 'transitional' disks has been identified which are believed to contain gaps or have developped large inner holes, some filled with dust. This may indicate that complex geometries may be a key feature in disk evolution that has to be understood and modeled correctly. The disk around LkCa 15 is such a disk, with a gap ranging from ~5 - 50 AU, as identified by Espaillat et al. (2007) using 1+1D radiative transfer modelling. To fit the SED, they propose 2 possible scenarios for the inner (<5 AU) disk - optically thick or optically thin - and one scenario for the outer disk. We use the gapped disk of LkCa 15 as a showcase to illustrate the importance of 2D radiative transfer in transitional disks, by showing how the vertical dust distribution in dust-filled inner holes determines not only the radial optical depth but also the outer disk geometry. We use MCMax, a 2D radiative transfer code with a self-consistent vertical structure, to model the SED. We identify two possible geometries for the inner and outer disk, that are both different from those in Espaillat et al. (2007). An inner disk in hydrostatic equilibrium reprocesses enough starlight to fit the near infrared flux, but also casts a shadow on the inner rim of the outer disk. This requires the outer disk scale height to be large enough to rise out of the shadow. An optically thin inner disk does not cast such a shadow, and the SED can be fitted with a smaller outer disk scale height. For the dust in the inner regions to become optically thin however, the scale height would have to be so much larger than its hydrostatic equilibrium value that it effectively becomes a dust shell. It is currently unclear if a physical mechanism exists which could provide for such a configuration.
A one-dimensional driven two-species model with parallel sublattice update and open boundaries is considered. Although the microscopic many-body dynamics is symmetric with respect to the two species and interactions are short-ranged, there is a region in parameter space with broken symmetry in the steady state. The sublattice update is deterministic in the bulk and allows for a detailed analysis of the relaxation dynamics, so that symmetry breaking can be shown to be the result of an amplification mechanism of fluctuations. In contrast to previously considered models, this leads to a proof for spontaneous symmetry breaking which is valid throughout the whole region in parameter space with a symmetry broken steady state.
In this paper, we study moments of Hurwitz class numbers associated to imaginary quadratic orders restricted into fixed arithmetic progressions. In particular, we fix $t$ in an arithmetic progression $t\equiv m\pmod{M}$ and consider the ratio of the $2k$-th moment to the zeroeth moment for $H(4n-t^2)$ as one varies $n$. The special case $n=p^r$ yields as a consequence asymptotic formulas for moments of the trace $t\equiv m\pmod{M}$ of Frobenius on elliptic curves over finite fields with $p^r$ elements.
We discuss ferroelectric phase transitions into single- and multidomain states in very thin films using continuous theory. It is shown that in nearly cubic ferroelectrics the domain state may survive down to atomic film thicknesses, unlike the single domain state, which is almost always unstable or metastable. This conclusion is valid almost irrespective of the nature of electrodes (metallic or semiconducting) and whether or not the screening carriers may be present in the ferroelectric itself.
A study of various SUSY scenarios is presented in which the lightest supersymmetric particle is the gravitino $\sG$ and the next-to-lightest supersymmetric particle is a scalar tau $\stau$ with lifetimes ranging from seconds to years. Gravitinos are interesting dark matter candidates which can be produced in decays of heavier sparticles at the International Linear Collider (ILC), but remain undetected in direct searches of astrophysical experiments. We investigate the detection and measurement of metastable staus, which may be copiously produced at the ILC either directly or via cascade decays. A proper choice of the experimental conditions will allow one to stop large samples of staus in the calorimeters of the ILC detector and to study the subsequent decays $\stau\to\tau\sG$. Detailed simulations show that the properties of the stau and the gravitino, such as stau mass and lifetime and gravitino mass, can be accurately determined at a future ILC and may provide direct access to the gravitational coupling, respectively Planck scale.
A modular grid is a pair of sequences $(f_m)_m$ and $(g_n)_n$ of weakly holomorphic modular forms such that for almost all $m$ and $n$, the coefficient of $q^n$ in $f_m$ is the negative of the coefficient of $q^m$ in $g_n$. Zagier proved this coefficient duality in weights $1/2$ and $3/2$ in the Kohnen plus space, and such grids have appeared for Poincar\'{e} series, for modular forms of integral weight, and in many other situations. We give a general proof of coefficient duality for canonical row-reduced bases of spaces of weakly holomorphic modular forms of integral or half-integral weight for every group $\Gamma \subseteq {\text{SL}}_2(\mathbb{R})$ commensurable with ${\text{SL}}_2(\mathbb{Z})$. We construct bivariate generate functions that encode these modular forms, and study linear operations on the resulting modular grids.
We study GL(2)-bundles with connections with a small parameter on a smooth projective curve. We describe an open subset in the moduli space of such bundles. The description degenerates into the Hitchin fibration as the parameter tends to zero.
We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geq 3$. We also provide results for forces with singularity up to $\alpha < d-1$ but with large enough cut-off. This last result thus almost includes the most interesting case of Coulombian or gravitational interaction, but it is also interesting when the strength of the singularity $\alpha$ is larger but close to one, in which case it allows for very small cut-off.
We present the analysis of KIC 7760680, the rotating Slowly Pulsating B-type star identified in the Kepler photometry. The oscillation spectrum of the star exhibits a series of 36 frequencies which are quasi-equally spaced in period. We confirm that this series can be associated with prograde dipole modes of consecutive radial orders. In our studies, the effects of rotation were included in the MESA equilibrium models as well as in the puslational calculations in the framework of the traditional approximation. We find that pulsational models computed with the OPLIB opacities best reproduce the observed frequency range. The modified opacity data with an enhancement of the opacity at $\log T=5.3$, 5.46 and 5.06 were tested as well. Increasing the OPLIB opacities by about 50% at $\log T=5.3$ is sufficient to excite modes in the whole range of 36 frequency peaks of KIC 7760680.