ShantanuT01/DACTYL-Pretraining huggingface dataset:
We give a simple proof of a recent inequality by W.M. Schmidt and L. Summerer concerning Diophantine exponents for a linear form in three real variables.
We report detailed investigation of quantum oscillations in Sr3Ru2O7, observed inductively (the de Haas-van Alphen effect) and thermally (the magnetocaloric effect). Working at fields from 3 T to 18 T allowed us to straddle the metamagnetic transition region and probe the low- and high-field Fermi liquids. The observed frequencies are strongly field-dependent in the vicinity of the metamagnetic transition, and there is evidence for magnetic breakdown. We also present the results of a comprehensive rotation study. The most surprising result concerns the field dependence of the measured quasiparticle masses. Contrary to conclusions previously drawn by some of us as a result of a study performed with a much poorer signal to noise ratio, none of the five Fermi surface branches for which we have good field-dependent data gives evidence for a strong field dependence of the mass. The implications of these experimental findings are discussed.
In this paper, we study multi-dimensional reflected backward stochastic differential equations with diagonally quadratic generators. Using the comparison theorem for diagonally quadratic BSDEs which is established recently in [14], we obtain the existence and uniqueness of a solution by a penalization method. Moreover, we provide a comparison theorem.
A method for deriving quantum kinetic equations with initial correlations is developed on the basis of the nonequilibrium Green's function formalism. The method is applicable to a wide range of correlated initial states described by nonequilibrium statistical thermodynamics. Initial correlations and the real-time evolution are treated by a unified technique employing many-component ``mixed'' Green's functions. The Dyson equation for the mixed Green's function leads to a set of equations for real-time Green's functions and new (cross) components linking initial correlations with dynamical processes. These equations are used to formulate a generalized Kadanoff-Baym ansatz for correlated initial states. A non-Markovian short-time kinetic equation is derived within the T-matrix approximation for the self-energies. The properties of the memory kernels in this equation are considered in detail in Born approximation for the T-matrices. The kinetic equation is demonstrated to conserve the total energy of the system. An explicit expression for the time-dependent correlation energy is obtained.
We consider the Klein-Gordon equation on a Riemannian surface which is globally well-posed in the energy space. This equation has an homoclinic orbit to the origin, and in this paper we study the dynamics close to it. Using a strategy from Groves-Schneider, we show that there are many solutions which stay close to this homocline during all times. We point out that the solutions we construct are not small.
The relation between star formation rates and stellar masses, i.e. the galaxy main sequence, is a useful diagnostic of galaxy evolution. We present the distributions relative to the main sequence of 55 optically-selected PG and 12 near-IR-selected 2MASS quasars at z <= 0.5. We estimate the quasar host stellar masses from Hubble Space Telescope or ground-based AO photometry, and the star formation rates through the mid-infrared aromatic features and far-IR photometry. We find that PG quasar hosts more or less follow the main sequence defined by normal star-forming galaxies while 2MASS quasar hosts lie systematically above the main sequence. PG and 2MASS quasars with higher nuclear luminosities seem to have higher specific SFRs (sSFRs), although there is a large scatter. No trends are seen between sSFRs and SMBH masses, Eddington ratios or even morphology types (ellipticals, spirals and mergers). Our results could be placed in an evolutionary scenario with quasars emerging during the transition from ULIRGs/mergers to ellipticals. However, combined with results at higher redshift, they suggest that quasars can be widely triggered in normal galaxies as long as they contain abundant gas and have ongoing star formation.
This paper concerns singular perturbation problems where the dynamics of the fast variable evolve in the whole space according to an operator whose infinitesimal generator is formed by a Grushin type second order part and a Ornstein-Uhlenbeck first order part. We prove that the dynamics of the fast variables admits an invariant measure and that the associated ergodic problem has a viscosity solution which is also regular and with logarithmic growth at infinity. These properties play a crucial role in the main theorem which establishes that the value functions of the starting perturbation problems converge to the solution of an effective problem whose operator and initial datum are given in terms of the associated invariant measure.
We precisely determine the infrared (IR) length scale of the no-core shell model (NCSM). In the NCSM, the $A$-body Hilbert space is truncated by the total energy, and the IR length can be determined by equating the intrinsic kinetic energy of $A$ nucleons in the NCSM space to that of $A$ nucleons in a $3(A-1)$-dimensional hyper-radial well with a Dirichlet boundary condition for the hyper radius. We demonstrate that this procedure indeed yields a very precise IR length by performing large-scale NCSM calculations for $^{6}$Li. We apply our result and perform accurate IR extrapolations for bound states of $^{4}$He, $^{6}$He, $^{6}$Li, $^{7}$Li. We also attempt to extrapolate NCSM results for $^{10}$B and $^{16}$O with bare interactions from chiral effective field theory over tens of MeV.
We briefly discuss energy, normal modes and dynamics of a vortex in a trapped Bose-Einstein condensate. Theoretical results are compared with current experiments.
Fast robust methods for calculating likelihoods from CMB observations on small scales generally rely on approximations based on a set of power spectrum estimators and their covariances. We investigate the optimality of these approximation, how accurate the covariance needs to be, and how to estimate the covariance from simulations. For a simple case with azimuthal symmetry we compare optimality of hybrid pseudo-C_l CMB power spectrum estimators with the exact result, indicating that the loss of information is not negligible, but neither is it enough to have a large effect on standard parameter constraints. We then discuss the number of samples required to estimate the covariance from simulations, with and without a good analytic approximation, and assess the use of shrinkage estimators. Finally we discuss how to combine an approximate high-ell likelihood with a more exact low-ell harmonic-space likelihood as a practical method for accurate likelihood calculation on all scales.
In 1888, Hilbert proved that every non-negative quartic form f=f(x,y,z) with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and used advanced methods from topology and algebraic geometry. Up to now, no elementary proof is known. Here we present a completely new approach. Although our proof is not easy, it uses only elementary techniques. As a by-product, it gives information on the number of representations f=p_1^2+p_2^2+p_3^2 of f up to orthogonal equivalence. We show that this number is 8 for generically chosen f, and that it is 4 when f is chosen generically with a real zero. Although these facts were known, there was no elementary approach to them so far.
We present a new approach for chemical evolution modelling, specifically designed to investigate the chemical properties of dwarf galaxies in a full cosmological framework. In particular, we focus on the Sculptor dwarf spheroidal galaxy as a test bed for our model. We select four candidate Sculptor-like galaxies from the satellite galaxy catalogue generated by implementation of a version of the Munich semi-analytic model for galaxy formation on the level 2 Aquarius dark matter simulations. We follow explicitly the evolution of several chemical elements, both in the cold gas out of which the stars form and in the hot medium residing in the halo. We take into account in detail the lifetimes of stars of different initial masses, the distribution of the delay times for type Ia supernova explosions and the dependency of the stellar yields from the initial metallicity of the stars. We allow large fractions of metals to be deposited into the hot phase, either directly as stars die or through reheated gas flows powered by supernova explosions. In order to reproduce both the observed metallicity distribution function and the observed abundance ratios of long-lived stars of Sculptor, large fractions of the reheated metals must never re-enter regions of active star formation. Our analysis sets further constraints on the semi-analytical models and, at large, on possible metal enrichment scenarios for the Sculptor dwarf spheroidal galaxy.
In this paper we use the effective blackfold description of branes to extend the study of the thermal BIon, a D-brane and parallel anti-D-brane connected by a wormhole with F-string charge in hot flat space, by introducing a radial boost along the brane. The boosted system behaves qualitatively differently from both the extremal and the thermal BIon considered previously. Interestingly, we are able to formulate a first law of thermodynamics for the system as a whole, despite the fact that it is not a stationary blackfold. In particular, the global temperature is given by the rest frame temperature times the gamma factor of special relativity which is the inverse transformation compared to the case of stationary blackfolds. In addition we define two new kinds of thermodynamic conjugate variables, the energy flux $W$ and the integrated velocity on the brane. We find that a phase transition occurs by varying the energy flux $W$. Below a critical value of $W$ the brane separation $\Delta$ changes only slightly with $W$. Instead above the critical value $\Delta$ grows exponentially.
Seeking a better understanding of the electron transport in n-doped zinc blende GaN and wurtzite AlN, it was performed here a theoretical study resorting to Non Equilibrium Statistical Operator Method, which provides a set of coupled nonlinear differential evolution equations that provides a description of the dissipative phenomena developed in the system. The ultrafast time evolution (and the steady-state) of the electron drift velocity is obtained assuming different values for the electron effective mass.
We review the general heat kernel method for the Dirac spinor field as an elementary example in any arbitrary background. We, then compute the first three Seeley-DeWitt coefficients for the massless free spin-3/2 Rarita-Schwinger field without imposing any limitations on the background geometry.
Environmental concerns are the chief drive for more innovative recycling techniques for end-of-life polymeric products. One attractive option is taking advantage of C and H content of polymeric waste in steelmaking industry. In this work, we examined the interaction of two high production polymers, i.e., polyurethane and polysulfide with molten iron using ab initio molecular dynamics simulation. We demonstrate that both polymers can be used as carburizers for molten iron. Additionally, we found that light weight H$_2$ and CH$_x$ molecules were released as by-products of the polymer-molten iron interaction. The outcomes of this study will have applications in the carburization of molten iron during ladle metallurgy and waste plastic injection in electric arc furnace.
Spectrum generating algebras are used in various fields of physics as models to determine quantum structure, including energy levels and transition strengths. The advantage of such models is that their group structure allows an extensive understanding of the system being studied. In addition they possess a simple classical limit, at least for bosonic systems. In this paper we discuss an algebraic model of nuclear structure, the Interacting Boson Model (IBM), and show that in one limit its group structure is particularly simple. For zero angular momentum there is an effective lower dimensional group structure which describes the system both classically and quantum mechanically.
We present the internal kinematics of UCD3, the brightest known ultra-compact dwarf galaxy (UCD) in the Fornax cluster, making this the first UCD with spatially resolved spectroscopy. Our study is based on seeing-limited observations obtained with the ARGUS Integral Field Unit of the VLT/FLAMES spectrograph under excellent seeing conditions (0.5 - 0.67 arcsec FWHM). The velocity field of UCD3 shows the signature of weak rotation, comparable to that found in massive globular clusters. Its velocity dispersion profile is fully consistent with an isotropic velocity distribution and the assumption that mass follows the light distribution obtained from Hubble Space Telescope imaging. In particular, there is no evidence for the presence of an extended dark matter halo contributing a significant (>~33 per cent within R < 200 pc) mass fraction, nor for a central black hole more massive than ~5 per cent of the UCD's mass. While this result does not exclude a galaxian origin for UCD3, we conclude that its internal kinematics are fully consistent with it being a massive star cluster.
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works~\cite{AG1,AG2,ACGM1,ACGM2} we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: 1) a random-walk-based notion of well-distributed points in a graph 2) how to describe metastable dynamics in finite settings by means of Markov intertwining dualities 3) coarse graining schemes for networks and associated processes 4) wavelets-like pyramidal algorithms for graph signals.
Reflectance and transmittance of graphene in the optical region are analyzed as a function of frequency, temperature, and carrier density. We show that the optical graphene properties are determined by the direct interband electron transitions. The real part of the dynamic conductivity in doped graphene at low temperatures takes the universal constant value, whereas the imaginary part is logarithmically divergent at the threshold of interband transitions.
In reply to the criticism made by Mielke in the pereceding Comment [Phys. Rev. D69 (2004) 128501] on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for {\it all} sources with spin and is by no means restricted to the Dirac field. In this sense the $SL(4,R)$-covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem.
When a signal is injected in a parametric oscillator close enough to its resonance, the oscillator frequency and phase get locked to those of the injected signal. Here, we demonstrate two frequency locking schemes using a Josephson mixer in the parametric down-conversion regime, pumped beyond the parametric oscillation threshold. The circuit then emits radiation out of two spectraly and spatially separated resonators at frequencies determined by the locking schemes that we choose. When we inject the signal close to a resonance, it locks the oscillator emission to the signal frequency by injection locking. When we inject the signal close to the difference of resonances, it locks the oscillator emission by parametric locking. We compare both schemes and investigate the dependence of the parametric locking range on the pump and the injection signal power. Our results can be interpreted using Adler's theory for lasers, which makes a new link between laser physics and superconducting circuits that could enable better understanding of pumped circuits for quantum information applications such as error correction, circulators and photon number detectors.
We present seven new abundance measurements of the elements O, C and Si at z > 4.5, doubling the existing sample of weakly depleted elements in gas-rich galaxies, in order to constrain the first ~1 billion years of cosmic metal evolution. These measurements are based on quasar spectra of damped Lyman-alpha absorbers (DLAs) and sub-DLAs obtained with the Magellan Inamori Kyocera Echelle (MIKE) and Magellan Echellette (MagE) spectrographs on Magellan-South, and the X-Shooter spectrograph on the Very Large Telescope. We combine these new measurements with those drawn from the literature to estimate the NHI-weighted binned mean metallicity of -1.51 +\- 0.18 at z = 4.8. This metallicity value is in excellent agreement with the prediction from lower redshift DLAs, supporting the interpretation that the metallicity evolution is smooth at z ~ 5, rather than showing a sudden decline at z > 4.7. Furthermore, the metallicity evolution trends for the DLAs and sub-DLAs are similar within our uncertainties. We also find that the [C/O] ratios for z ~ 5 DLAs are consistent with those of the very metal-poor DLAs. Additionally, using [C/O] and [Si/O] to constrain the nucleosynthesis models, we estimate that the probability distributions of the progenitor star masses for three relatively metal-poor DLAs are centered around 12 M_{\odot} to 17 M_{\odot}. Finally, the z ~ 5 absorbers show a different metallicity-velocity dispersion relation than lower redshift DLAs, suggesting that they may be tracing a different population of galaxies.
Time-delay measurements of 0957+561 based on radio monitoring now agree with optical monitoring. Recent models incorporate many recent observations, but the systematic uncertainties in the models still dominate the uncertainty in the cosmological results. VLBI observations of the milli-arcsec jet structure have provided the most important set of modeling constraints. We present new observations of this structure, made at 18 cm with the Very Long Baseline Array, the Very Large Array, and the Green Bank 140 ft. telescope. Compared to the data set of Garrett et al. (1994), ours has a similar theoretical noise level (20 microJy), but nearly twice as many baselines (66 compared to 36) and more uniform coverage of the UV plane. Our initial maps confirm the basic jet structures seen by Garrett et al., with comparable RMS noise (60-80 microJy), and are in reasonable agreement with the jet structure model of Barkana et al. (1999). The maps also hint at a new compact component leaving the core, and a previously undetected diffuse component at the end of the jet. Further refinements in fringe-fitting, mapping, and self-calibration should yield significantly lower RMS noise (closer to the theoretical level). We will use a modified form of the CalTech VLBI Modelfit program (written by Barkana et al. 1999) to determine the magnification matrix between the images. The refined magnification matrix should provide stronger constraints on the lens model, and thus reduce the uncertainty in the cosmological results.
We release the spectra for the more than 57000 objects presented in the First VIPERS Data Release. For each object we distribute the observed, wavelength and flux calibrated spectrum, as well as cleaned spectra, where artifacts due to fringing are removed. We also provide the sky and noise spectrum and the 2D spectrum. Data can be downloaded from http://vipers.inaf.it.
One approximation is made to describe a M+1 electron many-body wavefunction by a M electron many-body wavefunction and a single electron wavefunction. Under this approximation, we have derived the Coulomb energy which relates the exciton energy $E_{exc}$ in a quantum dot with the quasiparticle band gap (defined as the difference between the ionization energy and the electron affinity), and the Coulomb energy which relates $E_{exc}$ with the single particle eigen values. We found that these two Coulomb energies are different. We have compared our results with the formulae used in different groups, which are proposed either {\it ad hov}, or from the classical electrostatic point of view. We found important difference between our results and the classical formula. Finally, under the above approximation, we provided an effective single particle Hamiltonian, which gives the quasiparticle band structure in a bulk system.
A wealth of recent studies have shown that the LMC is likely massive, with a halo mass $>10^{11} M_\odot$. One consequence of having such a nearby and massive neighbour is that the inner Milky Way is expected to be accelerated with respect to our Galaxy's outskirts (beyond $\sim 30$ kpc). In this work we compile a sample of $\sim 500$ stars with radial velocities in the distant stellar halo, $r_{\rm GC}> 50$ kpc, to test this hypothesis. These stars span a large fraction of the sky and thus give a global view of the stellar halo. We find that stars in the Southern hemisphere are on average blueshifted, while stars in the North are redshifted, consistent with the expected, mostly downwards acceleration of the inner halo due to the LMC. We compare these results with simulations and find the signal is consistent with the infall of a $1.5\times10^{11} M_\odot$ LMC. We cross-match our stellar sample with \textit{Gaia} DR2 and find that the mean proper motions are not yet precise enough to discern the LMC's effect. Our results show that the outer Milky Way is significantly out of equilibrium and that the LMC has a substantial effect on our Galaxy.
The indefinite integral of the homogenized Ornstein-Uhlenbeck process is a well-known model for physical Brownian motion, modelling the behaviour of an object subject to random impulses [L. S. Ornstein, G. E. Uhlenbeck: On the theory of Brownian Motion. In: Physical Review. 36, 1930, 823-841]. One can scale these models by changing the mass of the particle and in the small mass limit one has almost sure uniform convergence in distribution to the standard idealized model of mathematical Brownian motion. This provides one well known way of realising the Wiener process. However, this result is less robust than it would appear and important generic functionals of the trajectories of the physical Brownian motion do not necessarily converge to the same functionals of Brownian motion when one takes the small mass limit. In presence of a magnetic field the area process associated to the physical process converges - but not to L\'evy's stochastic area. As this area is felt generically in settings where the particle interacts through force fields in a nonlinear way, the remark is physically significant and indicates that classical Brownian motion, with its usual stochastic calculus, is not an appropriate model for the limiting behaviour.   We compute explicitly the area correction term and establish convergence, in the small mass limit, of the physical Brownian motion in the rough path sense. The small mass limit for the motion of a charged particle in the presence of a magnetic field is, in distribution, an easily calculable, but "non-canonical" rough path lift of Brownian motion. Viewing the trajectory of a charged Brownian particle with small mass as a rough path is informative and allows one to retain information that would be lost if one only considered it as a classical trajectory. We comment on the importance of this point of view.