ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the classical and quantum properties of a system of $SU(N)$ non-Abelian Chern-Simons (NACS) particles. After a brief introduction to the subject of NACS particles, we first discuss about the symplectic structure of various $SU(N)$ coadjoint orbits which are the reduced phase space of $SU(N)$ internal degrees of freedom or isospins. A complete Dirac's constraint analysis is carried out on each orbit and the Dirac bracket relations among the isospin variables are calculated. Then, the spatial degrees of freedom and interaction with external gauge field are introduced by considering the total reduced phase space which is given by an associated bundle whose fiber is one of the coadjoint orbits. Finally, the theory is quantized by using the coherent state method and various quantum mechanical properties are discussed in this approach. In particular, a coherent state representation of the Knizhnik-Zamolodchikov equation is given and possible solutions in this representation are discussed.
We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a certain Markov process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is always singular with respect to the Lebesgue measure which in many applications is ``close'' to reality. We first discuss how to rigorously construct the (necessarily) unique stationary version of the system under some natural stability conditions. We then consider the distribution of performance steady-state characteristics, namely, the buffer content, the idle period and the busy period. These derivations are much based on the fact that the inverse of the local time of a Markov process is a L\'evy process (a subordinator) hence making the theory of L\'evy processes applicable. Another important ingredient in our approach is the Palm calculus coming from the point process point of view.
The numerical solution of partial differential equations by discretization techniques is ubiquitous in computational physics. In this work we benchmark this approach in the quantum realm by solving the heat equation for a square plate subject to fixed temperatures at the edges and random heat sources and sinks within the domain. The hybrid classical-quantum approach consists in the solution on a quantum computer of the coupled linear system of equations that result from the discretization step. Owing to the limitations in the number of qubits and their connectivity, we use the Gauss-Seidel method to divide the full system of linear equations into subsystems, which are solved iteratively in block fashion. Each of the linear subsystems were solved using 2000Q and Advantage quantum computers developed by D-Wave Systems Inc. By comparing classical numerical and quantum solutions, we observe that the errors and chain break fraction are, on average, greater on the 2000Q system. Unlike the classical Gauss-Seidel method, the errors of the quantum solutions level off after a few iterations of our algorithm. This is partly a result of the span of the real number line available from the mapping of the chosen size of the set of qubit states. We verified this by using techniques to progressively shrink the range mapped by the set of qubit states at each iteration (increasing floating-point accuracy). As a result, no leveling off is observed. However, an increase in qubits does not translate to an overall lower error. This is believed to be indicative of the increasing length of chains required for the mapping to real numbers and the ensuing limitations of hardware.
We investigate the space of solutions to certain $A$-hypergeometric $\mathscr{D}$-modules, which were defined and studied by Gelfand, Kapranov, and Zelevinsky. We show that the solution space can be identified with certain relative cohomology group of the toric variety determined by $A$, which generalizes the results of Huang, Lian, Yau, and Zhu. As a corollary, we also prove the existence of rank one points for Calabi--Yau complete intersections in toric varieties.
We perform full two-dimensional (2D) numerical relaxations of isospinning soliton solutions in the baby Skyrme model in which the global $O(3)$ symmetry is broken by the 2D analogue of the pion mass term in the Skyrme model. In our calculations we explicitely allow the isospinning solitons to deform and to break the symmetries of the static configurations. We find that stable isospinning baby Skyrme solutions can be constructed numerically for all angular frequencies $\omega\le \text{min}(\mu,1)$, where $\mu$ is the mass parameter of the model. Stable, rotationally-symmetric baby Skyrmion solutions for higher angular velocities are simply an artefact of the hedgehog approximation. Isospinning multisoliton solutions of topological charge $B$ turn out to be unstable to break up into their $B$ charge-1 constituents at some critical breakup frequency value. Furthermore, we find that for $\mu$ sufficiently large the rotational symmetry of charge-2 baby Skyrmions becomes broken at a critical angular frequency $\omega$.
We present 3D-HST, a near-infrared spectroscopic Treasury program with the Hubble Space Telescope for studying the processes that shape galaxies in the distant Universe. 3D-HST provides rest-frame optical spectra for a sample of ~7000 galaxies at 1<z<3.5, the epoch when 60% of all star formation took place, the number density of quasars peaked, the first galaxies stopped forming stars, and the structural regularity that we see in galaxies today must have emerged. 3D-HST will cover 3/4 (625 sq.arcmin) of the CANDELS survey area with two orbits of primary WFC3/G141 grism coverage and two to four parallel orbits with the ACS/G800L grism. In the IR these exposure times yield a continuum signal-to-noise of ~5 per resolution element at H~23.1 and a 5sigma emission line sensitivity of 5x10-17 erg/s/cm2 for typical objects, improving by a factor of ~2 for compact sources in images with low sky background levels. The WFC3/G141 spectra provide continuous wavelength coverage from 1.1-1.6 um at a spatial resolution of ~0."13, which, combined with their depth, makes them a unique resource for studying galaxy evolution. We present the preliminary reduction and analysis of the grism observations, including emission line and redshift measurements from combined fits to the extracted grism spectra and photometry from ancillary multi-wavelength catalogs. The present analysis yields redshift estimates with a precision of sigma(z)=0.0034(1+z), or sigma(v)~1000 km/s. We illustrate how the generalized nature of the survey yields near-infrared spectra of remarkable quality for many different types of objects, including a quasar at z=4.7, quiescent galaxies at z~2, and the most distant T-type brown dwarf star known. The CANDELS and 3D-HST surveys combined will provide the definitive imaging and spectroscopic dataset for studies of the 1<z<3.5 Universe until the launch of the James Webb Space Telescope.
We have mapped over 50 massive, dense clumps with four dense gas tracers: HCN J=1-0 and 3-2; and CS J=2-1 and 7-6 transitions. Spectral lines of optically thin H^{13}CN 3-2 and C^{34}S 5-4 were also obtained towards the map centers. These maps usually demonstrate single well-peaked distributions at our resolution, even with higher J transitions. The size, virial mass, surface density, and mean volume density within a well-defined angular size (FWHM) were calculated from the contour maps for each transition. We found that transitions with higher effective density usually trace the more compact, inner part of the clumps but have larger linewidths, leading to an inverse linewidth-size relation using different tracers. The mean surface densities are 0.29, 0.33, 0.78, 1.09 g cm^{-2} within FWHM contours of CS 2-1, HCN 1-0, HCN 3-2 and CS 7-6, respectively. We find no correlation of L_{IR} with surface density and a possible inverse correlation with mean volume density, contrary to some theoretical expectations. We see no evidence in the data for the relation between L'_{mol} and mean density posited by modelers.   The correlation between L'_{mol} and the virial mass is roughly linear for each dense gas tracer. A nearly linear correlation was found between the infrared luminosity and the line luminosity of all dense gas tracers for these massive, dense clumps, with a lower cutoff in luminosity at L_{IR}=10^{4.5} Lsun. The L_{IR}-L'_{HCN1-0} correlation agrees well with the one found in galaxies. These correlations indicate a constant star formation rate per unit mass from the scale of dense clumps to that of distant galaxies when the mass is measured for dense gas. These results support the suggestion that starburst galaxies may be understood as having a large fraction of gas in dense clumps.
Rotation is expected to have an important influence on the structure and the evolution of stars. However, the mechanisms of angular momentum transport in stars remain theoretically uncertain and very complex to take into account in stellar models. To achieve a better understanding of these processes, we desperately need observational constraints on the internal rotation of stars, which until very recently were restricted to the Sun. In this paper, we report the detection of mixed modes - i.e. modes that behave both as g modes in the core and as p modes in the envelope - in the spectrum of the early red giant KIC7341231, which was observed during one year with the Kepler spacecraft. By performing an analysis of the oscillation spectrum of the star, we show that its non-radial modes are clearly split by stellar rotation and we are able to determine precisely the rotational splittings of 18 modes. We then find a stellar model that reproduces very well the observed atmospheric and seismic properties of the star. We use this model to perform inversions of the internal rotation profile of the star, which enables us to show that the core of the star is rotating at least five times faster than the envelope. This will shed new light on the processes of transport of angular momentum in stars. In particular, this result can be used to place constraints on the angular momentum coupling between the core and the envelope of early red giants, which could help us discriminate between the theories that have been proposed over the last decades.
Recently we obtained an evolution equation of gluon TMDs, which addresses a problem of unification of different kinematic regimes. It describes evolution in the whole range of Bjorken $x_B$ and the whole range of transverse momentum $k_\perp$. In this notes I study different limits of this evolution equation and show how it yields several well-known and some previously unknown results.
On the basis of a dynamical Relativistic Mean Field (RMF) model we study the response of a nucleus on the antiproton implanted in its interior. We solve the Vlasov equation for the antiproton-nuclear system and show assuming a moderately attractive antiproton optical potential that the compressed state is formed on a rather short time scale of about 4-10 fm/c. The evolution of the system after antiproton annihilation is simulated using the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) transport model. Finally, several sensitive observables to the antiproton annihilation in a compressed nuclear configuration are proposed, e.g. the nucleon kinetic energy spectra and the total invariant mass distributions of produced mesons.
The existence of a very special ratcheting regime has recently been reported in a granular packing subjected to cyclic loading \cite{alonso04}. In this state, the system accumulates a small permanent deformation after each cycle. After a short transient regime, the value of this permanent strain accumulation becomes independent on the number of cycles. We show that a characterization of the material response in this peculiar state is possible in terms of three simple macroscopic variables. They are defined that, they can be easily measured both in the experiments and in the simulations. We have carried out a thorough investigation of the micro- and macro-mechanical factors affecting these variables, by means of Molecular Dynamics simulations of a polydisperse disk packing, as a simple model system for granular material. Biaxial test boundary conditions with a periodically cycling load were implemented. The effect on the plastic response of the confining pressure, the deviatoric stress and the number of cycles has been investigated. The stiffness of the contacts and friction has been shown to play an important role in the overall response of the system. Specially elucidating is the influence of the particular hysteretical behavior in the stress-strain space on the accumulation of permanent strain and the energy dissipation.
This paper presents a middle-level video representation named Video Primal Sketch (VPS), which integrates two regimes of models: i) sparse coding model using static or moving primitives to explicitly represent moving corners, lines, feature points, etc., ii) FRAME /MRF model reproducing feature statistics extracted from input video to implicitly represent textured motion, such as water and fire. The feature statistics include histograms of spatio-temporal filters and velocity distributions. This paper makes three contributions to the literature: i) Learning a dictionary of video primitives using parametric generative models; ii) Proposing the Spatio-Temporal FRAME (ST-FRAME) and Motion-Appearance FRAME (MA-FRAME) models for modeling and synthesizing textured motion; and iii) Developing a parsimonious hybrid model for generic video representation. Given an input video, VPS selects the proper models automatically for different motion patterns and is compatible with high-level action representations. In the experiments, we synthesize a number of textured motion; reconstruct real videos using the VPS; report a series of human perception experiments to verify the quality of reconstructed videos; demonstrate how the VPS changes over the scale transition in videos; and present the close connection between VPS and high-level action models.
In this paper, we point out that a measurement of the charge radius of Boron-8 provides indirect access to the S-factor for radiative proton capture on Beryllium-7 at low energies. We use leading-order halo effective field theory to explore this correlation and we give a relation between the charge radius and the S-factor. Furthermore, we present important technical aspects relevant to the renormalization of pointlike P-wave interactions in the presence of a repulsive Coulomb interaction.
Extremely metal-poor low-mass stars experience an ingestion of protons into the helium-rich layer during the core He-flash, resulting in the production of neutrons through the reactions ^{12}C(p,\gamma)^{13}N(\beta)^{13}C(\alpha,n)^{16}O. This is a potential site for the production of s-process elements in extremely metal-poor stars not occurring in more metal-rich counterparts. Observationally, the signatures of s-process elements in the two most iron deficient stars observed to date, HE1327-2326 & HE0107-5240, still await for an explanation. We investigate the possibility that low-mass EMP stars could be the source of s-process elements observed in extremely iron deficient stars, either as a result of self-enrichment or in a binary scenario as the consequence of a mass transfer episode. We present evolutionary and post-processing s-process calculations of a 1Msun stellar model with metallicities Z=0, 10^{-8} and 10^{-7}. We assess the sensitivity of nucleosynthesis results to uncertainties in the input physics of the stellar models, particularly regarding the details of convective mixing during the core He-flash. Our models provide the possibility of explaining the C, O, Sr, and Ba abundance for the star HE0107-5240 as the result of mass-transfer from a low-mass EMP star. The drawback of our model is that if mass would be transferred before the primary star enters the AGB phase, nitrogen would be overproduced and the ^{12}C/^{13}C abundance ratio would be underproduced in comparison to the observed values. Our results show that low-mass EMP stars cannot be ruled out as the companion stars that might have polluted HE1327-2326 & HE0107-5240 and produced the observed s-process pattern. However, more detailed studies of the core He-flash and the proton ingestion episode are needed to determine the robustness of our predictions.
A theorem of Kurzweil ('55) on inhomogeneous Diophantine approximation states that if $\theta$ is an irrational number, then the following are equivalent: (A) for every decreasing positive function $\psi$ such that $\sum_{q = 1}^\infty \psi(q) = \infty$, and for almost every $s\in\mathbb R$, there exist infinitely many $q\in\mathbb N$ such that $\|q\theta - s\| < \psi(q)$, and (B) $\theta$ is badly approximable. This theorem is not true if one adds to condition (A) the hypothesis that the function $q\mapsto q\psi(q)$ is decreasing. In this paper we find a condition on the continued fraction expansion of $\theta$ which is equivalent to the modified version of condition (A). This expands on a recent paper of D. H. Kim ('14).
Using Floquet-Bloch theory we study the effect of circularly and linearly polarized light on the electronic structure of (LaNiO$_3$)$_2$/(LaAlO$_3$)$_N$ heterostructure grown along the (111) direction. In equilibrium, a tight-binding fit to the first principles band structure shows that nearest-neighbor hopping plays a dominant role while second-neighbor hopping breaks the particle-hole symmetry and determines the finer band features. The four bands of the LaNiO$_3$ bilayer exhibit both quadratic band touching points and Dirac points. By varying the amplitude of the incident light, one can independently tune the first and second-neighbor hopping for fixed frequency, which leads to considerable control over the Floquet band structure. We investigate this control in detail, and study how the quadratic and Dirac band touchings are influenced by the polarization and intensity of the light. We derive effective 2-band Hamiltonians (for both quadratic and Dirac band touching points) that accurately captures these results. We further study an extended model which explicitly includes oxygen $p$-orbitals and compare the results to the effective model that contains only the nickel $d$-orbitals. We conclude with a computation of the frequency dependent optical Hall conductivity using the full four band model and analyze the various inter-band contributions of the Floquet modes.
We measure the high-frequency emission of a single Cooper pair transistor(SCPT) in the regime where transport is only due to tunneling of Cooper pairs. This is achieved by coupling on-chip the SCPT to a superconductor-insulator-superconductor junction and by measuring the photon assisted tunneling current of quasiparticles across the junction. This technique allows a direct detection of the AC Josephson effect of the SCPT and provides evidence of Landau-Zener transitions for proper gate voltage. The emission in the regime of resonant Cooper pair tunneling is also investigated. It is interpreted in terms of transitions between charge states coupled by the Josephson effect.
Group action is a standard approach to obtain $t$-designs. In this approach, selecting a specific permutation group with a certain degree of transitivity or homogeneity and a proper set of base blocks is important for obtaining $t$-$(v, k, \lambda)$ designs with computable parameters $t, v, k$, and $\lambda$. The general affine group $\GA_1(q)$ is $2$-transitive on $\gf(q)$, and has relatively a small size. In this paper, we determine the parameters of a number of infinite families of $2$-designs obtained from the action of the group $\GA_1(q)$ on certain base blocks, and demonstrate that some of the $2$-designs give rise to linear codes with optimal or best parameters known. Open problems are also presented.
As natural consequences of the accretion process, outflows are one of the few (indirect) tracers of accretion. We used CO(2-1) PdBI observations towards 6 MDCs in Cygnus-X, containing 9 high-mass cores, to investigate what the accretion process and origin of the material feeding the precursors of high-mass stars are. We compared our sample to low-mass objects from the literature and developed simple evolutionary models to reproduce the observables. We find that 8/9 high-mass cores drive clear individual outflows as true equivalents of Class 0 protostars in the high-mass regime. The remaining core has only a tentative outflow detection. It could be amongst the first examples of a true individual high-mass prestellar core. We find that the momentum flux of high-mass objects has a linear relation to the envelope mass, as a scale-up of the relations found for low-mass protostars. This suggests a fundamental proportionality between accretion rates and mass reservoir, suggesting identical collapse timescales for all masses. We conclude that if the pre-collapse evolution is quasi-static, the fragmentation scale (which is similar for all masses) would limit the size of the initial mass reservoirs, leading to shorter free-fall times for higher mass stars. However, as we find identical collapse timescales for all masses, a significant turbulent/magnetic support is needed to slow down the collapse of the more massive envelopes in a quasi-static view. With this support still to be discovered, and with indications of large dynamics in pre-collapse gas for high-mass star formation, we propose that such an identical collapse timescale implies that the initial densities, which should set the duration of the collapse, should be similar for all masses. This suggests that the mass that incorporates massive stars has to have been accreted in a dynamical way from larger scales than those of low-mass stars.
We present a lattice calculation of neutron-deuteron scattering at very low energies and investigate in detail the impact of the topological finite-volume corrections. Our calculations are carried out in the framework of pionless effective field theory at leading order in the low-energy expansion. Using lattice sizes and a lattice spacing comparable to those employed in nuclear lattice simulations, we find that the topological volume corrections must be taken into account in order to obtain correct results for the neutron-proton S-wave scattering lengths.
We use a modified pulsar current analysis to study magnetic field decay in radio pulsars. In our approach we analyse the flow, not along the spin period axis as has been performed in previous studies, but study the flow along the direction of growing characteristic age, $\tau=P/(2\dot P)$. We perform extensive tests of the method and find that in most of the cases it is able to uncover non-negligible magnetic field decay (more than a few tens of per cent during the studied range of ages) in normal radio pulsars for realistic initial properties of neutron stars. However, precise determination of the magnetic field decay timescale is not possible at present. The estimated timescale may differ by a factor of few for different sets of initial distributions of neutron star parameters. In addition, some combinations of initial distributions and/or selection effects can also mimic enhanced field decay. We apply our method to the observed sample of radio pulsars at distances $<10$ kpc in the range of characteristic ages $8 \times 10^4 < \tau < 10^6$ years where, according to our study, selection effects are minimized. By analysing pulsars in the Parkes Multibeam and Swinburne surveys we find that, in this range, the field decays roughly by a factor of two. With an exponential fit this corresponds to the decay time scale $\sim 4 \times 10^5$ yrs. With larger statistics and better knowledge of the initial distribution of spin periods and magnetic field strength, this method can be a powerful tool to probe magnetic field decay in neutron stars.