ShantanuT01/DACTYL-Pretraining huggingface dataset:
A particular family of Discrete Time Quantum Walks (DTQWs) simulating fermion propagation in $2$D curved space-time is revisited. Usual continuous covariant derivatives and spin-connections are generalized into discrete covariant derivatives along the lattice coordinates and discrete connections. The concepts of metrics and $2$-beins are also extended to the discrete realm. Two slightly different Riemann curvatures are then defined on the space-time lattice as the curvatures of the discrete spin connection. These two curvatures are closely related and one of them tends at the continuous limit towards the usual, continuous Riemann curvature. A simple example is also worked out in full.
Recent progress in the formulation of relativistic hydrodynamics for particles with spin one-half is reviewed. We start with general arguments advising introduction of a tensor spin chemical potential that plays a role of the Lagrange multiplier coupled to the spin angular momentum. Then, we turn to a discussion of spin-dependent distribution functions that have been recently proposed to construct a hydrodynamic framework including spin and serve as a tool in phenomenological studies of hadron polarization. Distribution functions of this type are subsequently used to construct the equilibrium Wigner functions that are employed in the semi-classical kinetic equation. The semi-classical expansion elucidates several aspects of the hydrodynamic approach, in particular, shows the ways in which different possible versions of hydrodynamics with spin can be connected by pseudo-gauge transformations. These results point out at using the de~Groot - van~Leeuwen - van~Weert versions of the energy-momentum and spin tensors as the most natural and complete physical variables. Finally, a totally new method is proposed to design hydrodynamics with spin, which is based on the classical treatment of spin degrees of freedom. Interestingly, for small values of the spin chemical potential the new scheme brings the results that coincide with those obtained before. The classical approach also helps us to resolve problems connected with the normalization of the spin polarization three-vector. In addition, it clarifies the role of the Pauli-Lubanski vector and the entropy current conservation. We close our review with several general comments presenting possible future developments of the discussed frameworks.
The parallel code NMAGIC is an implementation of a particle-based method to create made-to-measure models in agreement with observations of galaxies. It works by slowly correcting the particle weights of an evolving N-body system, until a satisfactory compromise is achieved between the goodness of the fit to a given set of observational data, and some degree of smoothness (regularization) of the underlying particle model. We briefly describe the method together with a new regularization scheme in phase-space, which improves recovering the correct orbit structure in the models. We also mention some practical applications showing the power of the technique in investigating the dynamics of galaxies.
This paper is devoted to study the effects of electromagnetic field on the energy density inhomogeneity in the relativistic self-gravitating fluids for spherically symmetric spacetime. Two important equations of the Weyl tensor are formulated which help to analyze the energy density inhomogeneity in this scenario. We investigate two types of fluids, i.e., non-dissipative and dissipative. The non-dissipative fluid further includes dust, locally isotropic, and locally anisotropic charged fluids. We explore the effects of different factors on energy density inhomogeneity in all these cases, in particular, the effect of charge.
(Et4N)3Fe2F9 exhibits a butterfly--shaped hysteresis below 5 K when the magnetic field is parallel to the threefold axis, in accordance with a very slow magnetization relaxation in the timescale of minutes. This is attributed to an energy barrier Delta=2.40 K resulting from the S=5 dimer ground state of [Fe2F9]^{3-} and a negative axial anisotropy. The relaxation partly occurs via thermally assisted quantum tunneling. These features of a single-molecule magnet are observable at temperatures comparable to the barrier height, due to an extremely inefficient energy exchange between the spin system and the phonons. The butterfly shape of the hysteresis arises from a phonon avalanche effect.
(abridged) In this work we present the results of an optical and IR study for the curious B[e] star CD-42 11721. This object has a doubtful evolutionary stage, being either a pre-main sequence star (HAeB[e]) or an evolved star (sgB[e]). Our optical investigation could be splitted in two parts, a qualitative study based on the identification of the numerous emission lines present in the spectra and the classification of their line profiles, which indicate a non-spherically symmetric circumstellar environment, and a quantitative analysis of numerous forbidden lines, e.g. [OI], [OII], [NII] and [SII]. Assuming a typical circumstellar scenario for a sgB[e], i.e. a fast, low-density polar wind and a slow, high-density disc forming equatorial wind, we can reproduce very well the line luminosities of the forbidden lines. From this analysis, we can determine the mass loss rate of the star lying in the range from 4.4 x 10^(-6) to 2.2 x 10^(-5) M_sun/yr, depending on the considered redenning. Our IR study could also be splitted in two parts: the identification of several features in the SWS ISO spectrum, and the modeling of the SED of CD-42 11721. The first part shows the presence of a mixed chemistry, i.e. C- and O-rich dust in the same circumstellar medium. We have tried to model the SED, by using a numerical code written by us which considers a spherical circumstellar scenario. Although the answer concerning the evolutionary stage of CD-42 11721 is still not very clear, we believe that our analysis will improve the discussion about the nature of this curious star.
In this paper the notion of the rigid frame of reference within special relativity is analysed. Three definitions of rigidity are formulated. By using several examples of non-inertial frames, it is shown that these definitions are not equivalent. It is also shown that so called M\"oller rigid non-inertial frames are locally rigid, but do not exhibit global rigidity. The physical meaning of this phenomenon is discussed, as well as its relation to the non-Euclidean nature of space in non-inertial frames of reference. (russian version)
We review the basic concepts of perturbative quantum chromodynamics (QCD) and relativistic hydrodynamics, and their applications to hadron production in high energy nuclear collisions. We discuss results from the Relativistic Heavy Ion Collider (RHIC) in light of these theoretical approaches. Perturbative QCD and hydrodynamics together explain a large amount of experimental data gathered during the first decade of RHIC running, although some questions remain open. We focus primarily on practical aspects of the calculations, covering basic topics like perturbation theory, initial state nuclear effects, jet quenching models, ideal hydrodynamics, dissipative corrections, freeze-out and initial conditions. We conclude by comparing key results from RHIC to calculations.
We study theoretically the spin dynamics of the ferric wheel, an antiferromagnetic molecular ring. For a single nuclear or impurity spin coupled to one of the electron spins of the ring, we calculate nuclear and electronic spin correlation functions and show that nuclear magnetic resonance (NMR) and electron spin resonance (ESR) techniques can be used to detect coherent tunneling of the Neel vector in these rings. The location of the NMR/ESR resonances gives the tunnel splitting and its linewidth an upper bound on the decoherence rate of the electron spin dynamics. We illustrate the experimental feasibility of our proposal with estimates for Fe_10 molecules.
We study mesoscopic fluctuations in a system in which there is a continuous connection between two distinct Fermi liquids, asking whether the mesoscopic variation in the two limits is correlated. The particular system studied is an Anderson impurity coupled to a finite mesoscopic reservoir described by random matrix theory, a structure which can be realized using quantum dots. We use the slave boson mean field approach to connect the levels of the uncoupled system to those of the strong coupling Nozi\`eres Fermi liquid. We find strong but not complete correlation between the mesoscopic properties in the two limits and several universal features.
It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and continuous. This may be interesting in some questions of stochastic calculus, in particular, in a methodical proof of multidimensional Ito's formula based on the product rule.
The surface of topological insulators is proposed as a promising platform for spintronics and quantum information applications. In particular, when time- reversal symmetry is broken, topological surface states are expected to exhibit a wide range of exotic spin phenomena for potential implementation in electronics. Such devices need to be fabricated using nanoscale artificial thin films. It is of critical importance to study the spin behavior of artificial topological MBE thin films associated with magnetic dopants, and with regards to quantum size effects related to surface-to-surface tunneling as well as experimentally isolate time-reversal breaking from non-intrinsic surface electronic gaps. Here we present observation of the first (and thorough) study of magnetically induced spin reorientation phenomena on the surface of a topological insulator. Our results reveal dramatic rearrangements of the spin configuration upon magnetic doping contrasted with chemically similar nonmagnetic doping as well as with quantum tunneling phenomena in ultra-thin high quality MBE films. While we observe that the spin rearrangement induced by quantum tunneling occurs in a time-reversal invariant fashion, we present critical and systematic observation of an out-of-plane spin texture evolution correlated with magnetic interactions, which breaks time-reversal symmetry, demonstrating microscopic TRB at a Kramers' point on the surface.
The cyanides $M$CN, $M$=Cu, Ag, Au, have experimentally a structure with hexagonally packed, infinite -$M$-CN-$M$-CN- chains. Following our earlier study for AuCN, we now predict that all three $M$CN could have an alternative $M_3$C$_3$N$_3$ sheet structure of comparable energy with the known one. The valence isoelectronic systems $M$C$_2$ versus $M_3$C$_6$, $M$=Be-Ba; Zn-Hg are also studied. Now, the known dicarbides have the CaC$_2$ or MgC$_2$ chain structures. The predicted sheets lie energetically below the chains for $M$ = Zn, Cd, and Hg. All these systems are experimentally unknown. Indeed, they are clearly endothermic, compared to the elements. For some sheet structures the densities of states suggests rather small band gaps and even metallic character. When available, the experimental geometries agree well with the calculated ones for both cyanides and dicarbides.
A ${\rm{TS}}(v,\lambda)$ is a pair $(V,\mathcal{B})$ where $V$ contains $v$ points and $\mathcal{B}$ contains $3$-element subsets of $V$ so that each pair in $V$ appears in exactly $\lambda$ blocks. A $2$-block intersection graph ($2$-BIG) of a ${\rm{TS}}(v,\lambda)$ is a graph where each vertex is represented by a block from the ${\rm{TS}}(v,\lambda)$ and each pair of blocks $B_i,B_j\in \mathcal{B}$ are joined by an edge if $|B_i\cap B_j|=2$. Using constructions for ${\rm{TS}}(v,\lambda)$ given by Schreiber, we show that there exists a ${\rm{TS}}(v,\lambda)$ for $v\equiv 0$ or $4\pmod{12}$ whose $2$-BIG is Hamiltonian.
We study the relevance of strange degrees of freedom for nucleon structure functions. For this purpose we employ the three flavor generalization of the collective quantization approach to the chiral soliton of the bosonized Nambu-Jona-Lasinio model. Contrary to many other soliton models the hadronic tensor is tractable in this model. By applying the Bjorken limit to the hadronic tensor we extract the leading twist contributions to the nucleon structure functions at the low energy scale at which the model is assumed to approximate QCD. After transforming to the infinite momentum frame and performing the DGLAP evolution program to these structure functions we compare with available data for deep inelastic electron-nucleon scattering.
We present the optimal convergence and shear estimators for lensing reconstruction from the cosmic microwave background temperature field. This generalizes the deflection estimator, is sensitive to non-lensing modes, provides internal consistency checks, and is always at least as optimal. Previously, these estimators were only known in the squeezed limit. This paper decomposes convergence and shear fields into cosine and sine waves and the lensed correlation function is then Taylor expanded in the wave amplitudes. Maximizing the likelihood function gives the optimal estimators for the convergence and shear fields.   This method has the potential to improve the lensing reconstruction of the cosmic microwave background polarization field: the shear and convergence can be optimally combined to form a deflection estimator, or used separately to separate non-lensing modes, or utilize lensing of non-Gaussian secondary foregrounds.
Measurements of the ionized Ca II K line are one of the major resources for long-term studies of solar and stellar activity. They also play a critical role in many studies related to solar irradiance variability, particularly as a ground-based proxy to model the solar ultraviolet flux variation that may influence the Earth's climate. Full disk images of the Sun in Ca II K have been available from various observatories for more than 100 years and latter synoptic Sun-as-a-star observations in Ca II K began in the early 1970s. One of these instruments, the Integrated Sunlight Spectrometer (ISS) has been in operation at Kitt Peak (Arizona) since late 2006. The ISS takes daily observations of solar spectra in nine spectra bands, including the Ca II K and H line s. We describe recent improvements in data reduction of Ca II K observations, and present time variations of nine parameters derived from the profile of this spectral line.
We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analogue of Floquet theory for cellular automata.
Magnetars are neutron stars (NSs) with extreme magnetic fields of strength $5 \times 10^{13}$ - $10^{15}$ G. They exhibit transient, highly energetic events, such as short X-ray flashes, bursts and giant flares, all of which are powered by their enormous magnetic energy. Quiescent magnetars have X-ray luminosities between $10^{29}$ and $10^{35}$ erg/s, and are further classified as either persistent or transient magnetars. Their X-ray emission is modulated with the rotational period of the NS, with a typical relative amplitude (so-called pulsed fraction) between 10-58 per cent, implying that the surface temperature is significantly non-uniform despite the high thermal conductivity of the star's crust. Here, we present the first 3D magneto-thermal MHD simulations of magnetars with strong toroidal magnetic fields. We show that these models, combined with ray propagation in curved space-time, accurately describe the light-curves of most transient magnetars in quiescence and allow us to further constrain their rotational orientation. We find that the presence of a strong toroidal magnetic field explains the observed asymmetry in the surface temperature, and is the main cause of the strong modulation of thermal X-ray emission in quiescence.
A brief review of jet physics is presented with an emphasis upon open theoretical problems (non-perturbative domain; hadronization and confinement) and new phenomena (hadroproduction in heavy ion collisions).
A natural and very important development of constrained system theory is a detail study of the relation between the constraint structure in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation, especially the relation between the constraint structure with the symmetries of the Lagrangian action. An important preliminary step in this direction is a strict demonstration, and this is the aim of the present article, that the symmetry structures of the Hamiltonian action and of the Lagrangian action are the same. This proved, it is sufficient to consider the symmetry structure of the Hamiltonian action. The latter problem is, in some sense, simpler because the Hamiltonian action is a first-order action. At the same time, the study of the symmetry of the Hamiltonian action naturally involves Hamiltonian constraints as basic objects. One can see that the Lagrangian and Hamiltonian actions are dynamically equivalent. This is why, in the present article, we consider from the very beginning a more general problem: how the symmetry structures of dynamically equivalent actions are related. First, we present some necessary notions and relations concerning infinitesimal symmetries in general, as well as a strict definition of dynamically equivalent actions. Finally, we demonstrate that there exists an isomorphism between classes of equivalent symmetries of dynamically equivalent actions.
We present time-series uvby-beta photometry of 41 classical Cepheid stars. A brief discussion of the comparison between the presented data and previous photometric data has been done.
The symbiotic star AG Dra experienced a double-peaked outburst of 0.6 magnitudes in April and May 2016. Photometry and spectroscopy through the outburst showed the B-V colour index varying linearly with the V magnitude and enabled the temperature variation of the hot star to be calculated from the changing flux in the H beta and He II 4686A emission lines.
In this paper, we investigate the interior transmission eigenvalue problem for an inhomogeneous media with conductive boundary conditions. We prove the discreteness and existence of the transmission eigenvalues. We also investigate the inverse spectral problem of gaining information about the material properties from the transmission eigenvalues. In particular, we prove that the first transmission eigenvalue is a monotonic function of the refractive index and boundary conductivity parameter eta, and obtain a uniqueness result for constant coefficients. We provide some numerical examples to demonstrate the theoretical results in three dimensions
Mechanism of di-pion transitions $nS\to n'S\pi\pi(n=3,2; n'=2,1)$ in bottomonium and charmonium is studied with the use of the chiral string-breaking Lagrangian allowing for the emission of any number of $\pi(K,\eta),$ and not containing fitting parameters. The transition amplitude contains two terms, $M=a-b$, where first term (a) refers to subsequent one-pion emission: $\Upsilon(nS)\to\pi B\bar B^*\to\pi\Upsilon(n'S)\pi$ and second term (b) refers to two-pion emission: $\Upsilon(nS)\to\pi\pi B\bar B\to\pi\pi\Upsilon(n'S)$. The one-parameter formula for the di-pion mass distribution is derived, $\frac{dw}{dq}\sim$(phase space) $|\eta-x|^2$, where $x=\frac{q^2-4m^2_\pi}{q^2_{max}-4m^2_\pi},$ $q^2\equiv M^2_{\pi\pi}$. The parameter $\eta$ dependent on the process is calculated, using SHO wave functions and imposing PCAC restrictions (Adler zero) on amplitudes a,b. The resulting di-pion mass distributions are in agreement with experimental data.
We report on the impact of magnetoelastic coupling on the magnetocaloric properties of LaFe$_{11.4}$Si$_{1.6}$H$_{1.6}$ in terms of the vibrational density of states, which we determined with $^{57}$Fe nuclear resonant inelastic X-ray scattering measurements and with density-functional-theory based first-principles calculations in the ferromagnetic low-temperature and paramagnetic high-temperature phase. In experiments and calculations, we observe pronounced differences in the shape of the Fe-partial VDOS between non-hydrogenated and hydrogenated samples. This shows that hydrogen does not only shift the temperature of the first-order phase transition, but also affects the elastic response of the Fe-subsystem significantly. In turn, the anomalous redshift of the Fe VDOS, observed by going to the low-volume PM phase, survives hydrogenation. As a consequence, the change in the Fe specific vibrational entropy $\Delta S_\mathrm{lat}$ across the phase transition has the same sign as the magnetic and electronic contribution. DFT calculations show that the same mechanism, which is a consequence of the itinerant electron metamagnetism associated with the Fe subsystem, is effective in both the hydrogenated and he hydrogen-free compounds. Although reduced by 50 % as compared to the hydrogen-free system, the measured change $\Delta S_\mathrm{lat}$ of 3.2\pm1.9 J/kgK across the FM to PM transition contributes with 35 % significantly and cooperatively to the total isothermal entropy change $\Delta S_\mathrm{iso}$. Hydrogenation is observed to induce an overall blueshift of the Fe-VDOS with respect to the H-free compound; this effect, together with the enhanced Debye temperature observed, is a fingerprint of the hardening of the Fe sublattice by hydrogen incorporation. In addition, the mean Debye velocity of sound of LaFe$_{11.4}$Si$_{1.6}$H$_{1.6}$ was determined from the NRIXS and the DFT data.
The scheme previously proposed by the present authors is modified to incorporate the strong interaction by affording the direct product internal symmetry. We do not need to prepare the extra discrete space for the color gauge group responsible for the strong interaction to reconstruct the standard model and the left-right symmetric gauge model(LRSM). The approach based on non-commutative geometry leads us to presents many attractive points such as the unified picture of the gauge and Higgs field as the generalized connection on the discrete space; Minkowski space multipied by N-points discrete space. This approach leads us to unified picture of gauge and Higgs fields as the generalized connection. The standard model needs N=2 discrete space for reconstruction in this formalism. \lr is still alive as a model with the intermediate symmetry of the spontaneously broken SO(10) grand unified theory(GUT). N=3 discrete space is needed for the reconstruction of LRSM to include two Higgs bosons $\phi$ and $\xi$ which are as usual transformed as (2,2*,0)$ and (1,3,-2) under left-handed SU(2)x right-handed SU(2)x U(1), respectively. xi is responsible to make the right handed-neutrino Majorana fermion and so well explains the seesaw mechanism. Up and down quarks have the different masses through the vacuum expectation value of phi.