ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present elastic and inelastic neutron scattering data on LaSrFeO$_4$. We confirm the known magnetic structure with the magnetic moments lying in the tetragonal basal plane, but contrarily to previous reports our macroscopic and neutron diffraction data do not reveal any additional magnetic phase transition connected to a spin reorientation or to a redistribution of two irreducible presentations. Our inelastic neutron scattering data reveals the magnon dispersion along the main-symmetry directions [0 $\xi$ 0] and [$\xi$ -$\xi$ 0]. The dispersion can be explained within linear spin-wave theory yielding an antiferromagnetic nearest-neighbour interaction parameter $J_{1}=7.4(1)$ meV and a next-nearest neighbour interaction parameter $J_{2}=0.4(1)$ meV. The dispersion is gapped with the out-of-plane anisotropy gap found at $\Delta_{out}=5.26(2)$ meV, while evidence is present that the in-plane anisotropy gap lies at lower energies, where it cannot be determined due to limited instrument resolution.
We study the Glauber dynamics on the set of tilings of a finite domain of the plane with lozenges of side 1/L. Under the invariant measure of the process (the uniform measure over all tilings), it is well known that the random height function associated to the tiling converges in probability, in the scaling limit $L\to\infty$, to a non-trivial macroscopic shape minimizing a certain surface tension functional.   According to the boundary conditions the macroscopic shape can be either analytic or contain "frozen regions" (Arctic Circle phenomenon). It is widely conjectured, on the basis of theoretical considerations, partial mathematical results and numerical simulations for similar models, that the Glauber dynamics approaches the equilibrium macroscopic shape in a time of order $L^{2+o(1)}$. In this work we prove this conjecture, under the assumption that the macroscopic equilibrium shape contains no "frozen region".
A multidimensional version of the results of Koml\'os, Major and Tusn\'ady for sums of independent random vectors with finite exponential moments is obtained in the particular case where the summands have smooth distributions which are close to Gaussian ones. The bounds obtained reflect this closeness. Furthermore, the results provide sufficient conditions for the existence of i.i.d. vectors $X_1, X_2,\dots$ with given distributions and corresponding i.i.d. Gaussian vectors $Y_1, Y_2,\dots$ such that, for given small $\varepsilon$, $$ {\mathbf P}\Big\{{\limsup\limits_{n\to\infty} \frac1{\log n}\Bigl|\,\sum\limits_{j=1}^n X_j- \sum\limits_{j=1}^n Y_j\,\Bigr|}\le \varepsilon\Big\}=1. $$
We present a new proof of Corvaja and Zannier's \cite{C-Z} the upper bound of the number of solutions $(x,y)$ of the algebraic equation $P(x,y)=0$ over a field $\mathbb{F}_p$ ($p$ is a prime), in the case, where $x\in g_1G$, $y\in g_2G$, ($g_1G$, $g_2G$ -- are cosets by some subgroup $G$ of a multiplicative group $\mathbb{F}_p^*$). The estimate of Corvaja and Zannier was improved in average, and some applications of it has been obtained. In particular we present the new bounds of additive and polynomial energy.
The coming generation of galaxy surveys will provide measurements of galaxy clustering with unprecedented accuracy and data size, which will allow us to test cosmological models at much higher precision than achievable previously. This means that we must have more accurate theoretical predictions to compare with future observational data. As a first step towards more accurate modelling of the redshift space distortions (RSD) of small-scale galaxy clustering in modified gravity (MG) cosmologies, we investigate the validity of the so-called Skew-T (ST) probability distribution function (PDF) of halo pairwise peculiar velocities in these models. We show that, combined with the streaming model of RSD, the ST PDF substantially improves the small-scale predictions by incorporating skewness and kurtosis, for both $\Lambda$CDM and two leading MG models: $f(R)$ gravity and the DGP braneworld model. The ST model reproduces the velocity PDF and redshift-space halo clustering measured from MG $N$-body simulations very well down to $\sim 5 \, h^{-1}\mathrm{Mpc}$. In particular, we investigate the enhancements of halo pairwise velocity moments with respect to $\Lambda$CDM for a larger range of MG variants than previous works, and present simple explanations to the behaviours observed. By performing a simple Fisher analysis, we find a significnat increase in constraining power to detect modifications of General Relativity by introducing small-scale information in the RSD analyses.
We present the first high-resolution X-ray study of emission line variability with superorbital phase in the neutron star binary LMC X-4. Our analysis provides new evidence from X-ray spectroscopy confirming accretion disk precession as the origin of the superorbital period. The spectra, obtained with the Chandra High-Energy Transmission Grating Spectrometer (HETGS) and the XMM-Newton Reflection Grating Spectrometer (RGS), contain a number of emission features, including lines from hydrogen-like and helium-like species of N, O, Ne, and Fe, a narrow O VII RRC, and fluorescent emission from cold Fe. We use the narrow RRC and the He-alpha triplets to constrain the temperature and density of the (photoionized) gas. By comparing spectra from different superorbital phases, we attempt to isolate the contributions to line emission from the accretion disk and the stellar wind. There is also evidence for highly ionized iron redshifted and blueshifted by ~25,000 km/s. We argue that this emission originates in the inner accretion disk, and show that the emission line properties in LMC X-4 are natural consequences of accretion disk precession.
The optical and infrared spectra of a wide variety of `cool' astronomical objects including the Sun, sunspots, K-, M- and S-type stars, carbon stars, brown dwarfs and extrasolar planets are reviewed. The review provides the necessary astronomical background for chemical physicists to understand and appreciate the unique molecular environments found in astronomy. The calculation of molecular opacities needed to simulate the observed spectral energy distributions is discussed.
The proton analyzing power Ay0 and the deuteron tensor analyzing power T20 are evaluated for the pd <-> pi+ t process, in the energy region around and above the Delta resonance. These calculations extend a previous analysis of the excitation function and differential cross-section, based on a model embodying one-- and two-body p-wave absorption mechanisms and isobar excitation. The three-nucleon bound state and the pd scattering state are evaluated through Faddeev techniques for both the Bonn and Paris potentials. The spin variables exhibit a greater sensitivity to the number of included three-nucleon partial waves than the cross-sections, while the role played by the initial-- or final-state interactions appears to be small. The results for the tensor analyzing power at backward angles show a non-negligible dependence on the potentials employed, consistently with what has been previously found for the cross-sections. The calculation of spin observables gives a clear indication that other reaction mechanisms (presumably s-wave two-body absorption) have to be included in the model, in order to reproduce the experimental data below the Delta-resonance, in analogy with the simpler pp <-> pi+ d process.
In contrast to common belief, the chirally symmetric Nambu--Jona-Lasinio model does not contain massless pions, due to strong chiral fluctuations. Although quarks acquire spontaneously a nonzero constituent mass $M$, pions have a nonzero mass equal to the mass of $ \s $-mesons, both being of the order of $M$. This result is found in several cutoff schemes. Our derivation is nonperturbative, but involves a simple approximation (London limit) which should, however, receive only quantitative, no qualitative corrections.
We present a study of the impact of a bright quasar on the redshifted 21cm signal during the Epoch of Reionization (EoR). Using three different cosmological radiative transfer simulations, we investigate if quasars are capable of substantially changing the size and morphology of the H II regions they are born in. We choose stellar and quasar luminosities in a way that is favourable to seeing such an effect. We find that even the most luminous of our quasar models is not able to increase the size of its native H II region substantially beyond those of large H II regions produced by clustered stellar sources alone. However, the quasar H II region is found to be more spherical. We next investigate the prospects of detecting such H II regions in the redshifted 21cm data from the Low Frequency Array (LOFAR) by means of a matched filter technique. We find that H II regions with radii ~ 25 comoving Mpc or larger should have a sufficiently high detection probability for 1200 hours of integration time. Although the matched filter can in principle distinguish between more and less spherical regions, we find that when including realistic system noise this distinction can no longer be made. The strong foregrounds are found not to pose a problem for the matched filter technique. We also demonstrate that when the quasar position is known, the redshifted 21cm data can still be used to set upper limits on the ionizing photon rate of the quasar. If both the quasar position and its luminosity are known, the redshifted 21 cm data can set new constrains on quasar lifetimes.
In this expository note, we offer an overview of the relationship between Hodge-theoretic and geometric compactifications of moduli spaces of algebraic varieties.
The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counter-propagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. In this paper, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to experimentally demonstrate simultaneous SLP trapping of two optical pulses for the duration from 0.8 $\mu$s to 2.0 $\mu$s. The characteristic dissipation time, obtained by the release efficiency measurement from the SLP trapping state, is 1.22 $\mu$s, which corresponds to an effective Q-factor of $2.9\times 10^9$. Our work is expected to bring forth interesting SLP-based applications, such as, efficient photon-photon interaction, spatially multi-mode coherent quantum memory, creation of exotic photonic gas states, etc.
A classification of twin primes implies special twin primes. When applied to triplets, it yields exceptional prime number triplets. These generalize yielding exceptional prime number multiplets.
We report an experimental Raman study of few-layer graphene after chemical doping achieved by a plasma process in CHF$_3$ gas. A systematic reduction of both the splitting and the area of the 2D band is observed with increasing the doping level. Both effects can be ascribed to the electron-electron correlation, which on the one hand reduces the electron-phonon coupling strength, and on the other hand affects the probability of the double resonant Raman process.
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes, which correspond respectively to deterministic and stochastic Master Equation dynamics. For the quantum feedback control scheme with continuous non-demolition observations we exploit the separation theorem of filtering and control aspects for quantum stochastic dynamics to derive a generalized Hamilton-Jacobi-Bellman equation. If the control is restricted to only Hamiltonian terms this is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term. In this work, we consider, in particular, the case when control is restricted to only observation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure state from a mixed state of a quantum two-level system.
We present a spectral study of the black hole candidate MAXI J1348-630 during its 2019 outburst, based on monitoring observations with Insight-HXMT and Swift. Throughout the outburst, the spectra are well fitted with power-law plus disk-blackbody components. In the soft-intermediate and soft states, we observed the canonical relation L ~ T_in^4 between disk luminosity L and peak colour temperature T_in, with a constant inner radius R_in (traditionally identified with the innermost stable circular orbit). At other stages of the outburst cycle, the behaviour is more unusual, inconsistent with the canonical outburst evolution of black hole transients. In particular, during the hard rise, the apparent inner radius is smaller than in the soft state (and increasing), and the peak colour temperature is higher (and decreasing). This anomalous behaviour is found even when we model the spectra with self-consistent Comptonization models, which take into account the up-scattering of photons from the disk component into the power-law component. To explain both those anomalous trends at the same time, we suggest that the hardening factor for the inner disk emission was larger than the canonical value of ~1.7 at the beginning of the outburst. A more physical trend of radii and temperature evolution requires a hardening factor evolving from ~3.5 at the beginning of the hard state to ~1.7 in the hard intermediate state. This could be evidence that the inner disk was in the process of condensing from the hot, optically thin medium and had not yet reached a sufficiently high optical depth for its emission spectrum to be described by the standard optically-thick disk solution.
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such multiparameter estimation can be achieved depends on understanding the many subtleties that come into play: establishing solid foundations is key to delivering future technology for this task. In this article we discuss the state of the art of quantum multiparameter estimation, with a particular emphasis on its theoretical tools, on application to imaging problems, and on the possible avenues towards the next developments.
The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear and (ii) forecasting errors and observational noises are taken Gaussian. Here, we offer an important generalization to the case where errors and noises have heavy tail distributions such as power laws and L\'evy laws. The main tool needed to solve this ``Kalman-L\'evy'' filter is the ``tail-covariance'' matrix which generalizes the covariance matrix in the case where it is mathematically ill-defined (i.e. for power law tail exponents $\mu \leq 2$). We present the general solution and discuss its properties on pedagogical examples. The standard Kalman-Gaussian filter is recovered for the case $\mu = 2$. The optimal Kalman-L\'evy filter is found to deviate substantially fro the standard Kalman-Gaussian filter as $\mu$ deviates from 2. As $\mu$ decreases, novel observations are assimilated with less and less weight as a small exponent $\mu$ implies large errors with significant probabilities. In terms of implementation, the price-to-pay associated with the presence of heavy tail noise distributions is that the standard linear formalism valid for the Gaussian case is transformed into a nonlinear matrice equation for the Kalman-L\'evy filter. Direct numerical experiments in the univariate case confirms our theoretical predictions.
We show that the introduction of thermal noise in Invasion Percolation (IP) brings the system outside the critical point. This result suggests a possible definition of SOC systems as ordinary critical systems where the critical point correspond to set to 0 one of the parameters. We recover both IP and EDEN model, for $T \to 0$, and $T \to \infty$ respectively. For small $T$ we find a dynamical second order transition with correlation length diverging when $T \to 0$.
Chen [Ann. Appl. Probab. {\bf 11} (2001), 1242--1262] derived exact convergence rates in a central limit theorem and a local limit theorem for a supercritical branching Wiener process.We extend Chen's results to a branching random walk under weaker moment conditions. For the branching Wiener process, our results sharpen Chen's by relaxing the second moment condition used by Chen to a moment condition of the form $ \E X (\ln^+X )^{1+\lambda}< \infty$. In the rate functions that we find for a branching random walk, we figure out some new terms which didn't appear in Chen's work.The results are established in the more general framework, i.e. for a branching random walk with a random environment in time.The lack of the second moment condition for the offspring distribution and the fact that the exponential moment does not exist necessarily for the displacements make the proof delicate; the difficulty is overcome by a careful analysis of martingale convergence using a truncating argument. The analysis is significantly more awkward due to the appearance of the random environment.
Levitated nanoparticles are being intensively investigated from two different perspectives: as a potential realisation of macroscopic quantum coherence; and as ultra-sensitive sensors of force, down to the zeptoNewton level, with a range of various applications, including the search for Dark Matter. A future aim is to merge these two strands, enabling the development of quantum-limited sensors. Here we propose that mechanical cross-correlation spectra $S_{xy}(\omega)$ offer new possibilities: once detector misalignment errors are minimised, the spectral shape of $S_{xy}(\omega)$ directly points out the orientation of an external stochastic force, offering something akin to a compass in the $x-y$ plane. We analyse this for detection of microscopic gas currents, but any broad spectrum directed force will suffice, enabling straightforward investigation with laboratory test forces with or without cavities. For a cavity set-up, we analyse misalignment imprecisions between detectors and motional modes due to for example optical back-actions that mask the signature of the directed forces, and show how to suppress them. Near quantum regimes, we quantify the imprecision due to the $x-y$ correlating effect of quantum shot noise imprecision.
We discuss three practical methods for performing Eulerian rotations of Slater determinants in a three-dimensional Cartesian geometry. In addition to the straightforward application of the active form of the quantum mechanical rotation operator, we introduce two methods using a passive position-space rotation followed by an active spin-space rotation, one after variation and the other before variation. These methods can be used to initialize reactions involving deformed nuclei where a particular alignment of the deformed nuclei with respect to the collision axis is desired. We show that doing the rotation before the variation is the most efficient way of generating such initial states.
We consider the Kolmogorov operator $K$ associated to a stochastic Navier-Stokes equation driven by space-time white noise on the two-dimensional torus with periodic boundary conditions and a rotating reference frame, introducing fictitious forces such as the Coriolis force. This equation then serves as a simple model for geophysical flows. We prove that the Gaussian measure induced by the enstrophy is infinitesimally invariant for $K$ on finitely based cylindrical test functions and moreover $K$ is $L^1$-unique w. r. t. the enstrophy measure for sufficiently large viscosity.
We consider a class of ultra-parabolic Kolmogorov-type operators satisfying the Hormander's condition. We prove an intrinsic Taylor formula with global and local bounds for the remainder given in terms of the norm in the homogeneous Lie group naturally associated to the differential operator.
We use the octahedron recurrence to give a simplified statement and proof of a formula for iterated birational rowmotion on a product of two chains, first described by Musiker and Roby. Using this, we show that weights of certain chains in rectangles shift in a predictable way under the action of rowmotion. We then define generalized Stanley-Thomas words whose cyclic rotation uniquely determines birational rowmotion on the product of two chains. We also discuss the relationship between rowmotion and birational RSK and give a birational analogue of Greene's theorem in this setting.
The spectral evolution of transient X-ray binaries can be reproduced by an interplay between two flows separated at a radius $R_J$: a standard accretion disk (SAD) in the outer parts and a jet-emitting disk (JED) in the inner parts. In the previous papers of this series, we recover the spectral evolution in both X-rays and radio for four outbursts of GX339-4 by playing independently with the two parameters: $R_J$ and the accretion rate $\dot{M}_{in}$. In this paper, we compare the time evolution of $R_J$ and $\dot{M}_{in}$ for the four outbursts. We show that despite the undeniable differences between the time evolution of each outburst, a unique pattern in the $\dot{M}_{in}-R_J$ plane seems to be followed by all cycles within the JED-SAD model. We call this pattern a fingerprint, and show that even the 'failed' outburst considered follows it. We also compute the radiative efficiency in X-rays during the cycles and consider its impact on the radio--X-ray correlation. Within the JED-SAD paradigm, we find that the accretion flow is always radiatively efficient in the hard states, with between $15\%$ and $40\%$ of the accretion power being radiated away at any given time. Moreover, we show that the radiative efficiency evolves with the accretion rate because of key changes in the JED thermal structure. These changes give birth to two different regimes with different radiative efficiencies: the thick disk and the slim disk. While the existence of these two regimes is intrinsically linked to the JED-SAD model, we show direct observational evidence of the presence of two different regimes using the evolution of the X-ray power-law spectral index, a model-independent estimate. We then argue that these two regimes could be the origin of the gap in X-ray luminosity in the hard state, the wiggles and different slopes seen in the radio--X-ray correlation, and even the existence of outliers.