ShantanuT01/DACTYL-Pretraining huggingface dataset:
Quantum mechanics of composite systems, gives rise to certain special states called entangled states. A physical system, that is in an entangled state displays an intricate correlation between its subsystems. There are also some composite quantum states (classically correlated states or separable states) that are not entangled. It is generally claimed, often without a rigorous proof to support, that these intricate correlations of an entangled state cannot occur in a classical system. This expository article, provides an elementary proof that entangled states cannot arise in the setting of classical mechanics. In addition, a detailed description of the origin of entanglement in quantum systems is included. The mathematical concepts that are necessary for this purpose are presented. The absence of entanglement in the classical setting is due to the fact that every pure classical state of a composite system is a product state, that is, a tensor product of two pure states of the subsystems. In contrast, there are pure composite quantum states that cannot be expressed in the form of a product state or even by a convex sum of product states. Roughly speaking, this is because classical states are positive valued functions on the phase-space while quantum states are positive linear operators. The structure of the tensor product between two commutative spaces of scalar valued functions is drastically different from that of the tensor product between two non-commutative spaces of linear operators. In other words, entanglement is a non-commutative phenomenon.
We present a quantitative morphological analysis using HST NICMOS H160- and ACS I775- band imaging of 25 spectroscopically confirmed submillimetre galaxies (SMGs) which have redshifts between z=0.7-3.4. Our analysis also employs a comparison sample of more typical star-forming galaxies at similar redshifts (such as LBGs) which have lower far-infrared luminosities. This is the first large-scale study of the morphologies of SMGs in the near-infrared at ~0.1" resolution (<1kpc). We find that the half light radii of the SMGs (r_h=2.3+/-0.3 and 2.8+/-0.4kpc in the observed I- and H-bands respectively) and asymmetries are not statistically distinct from the comparison sample of star-forming galaxies. However, we demonstrate that the SMG morphologies differ more between the rest-frame UV and optical-bands than typical star-forming galaxies and interpret this as evidence for structured dust obscuration. We show that the composite observed H-band light profile of SMGs is better fit with a Sersic index with n~2, suggesting the stellar structure of SMGs is best described by a spheroid/elliptical galaxy light distribution. We also compare the sizes and stellar masses of SMGs to local and high-redshift populations, and find that the SMGs have stellar densities which are comparable to local early-type galaxies, as well as luminous, red and dense galaxies at z~1.5 which have been proposed as direct SMG descendants, although the SMG stellar masses and sizes are systematically larger. Overall, our results suggest that the physical processes occuring within the galaxies are too complex to be simply characterised by the rest-frame UV/optical morphologies which appear to be essentially decoupled from all other observables, such as bolometric luminosity, stellar or dynamical mass.
We consider a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects which is introduced in [2]. It is comprised of phase-field equation to describe tumor growth, which is coupled to a reaction-diffusion type equation for generic nutrient for the tumor. An additional equation couples the concentration of prostate-specific antigen (PSA) in the prostatic tissue and it obeys a linear reaction-diffusion equation. The system completes with homogeneous Dirichlet boundary conditions for the tumor variable and Neuman boundary condition for the nutrient and the concentration of PSA. Here we investigate the long time dynamics of the model. We first prove that the initial-boundary value problem generates a strongly continuous semigroup on a suitable phase space that admits the global attractor in a proper phase space. Moreover, we also discuss the convergence of a solution to a single stationary state and obtain a convergence rate estimate under some conditions on the coefficients.
Our recent search for the presence of a magnetic field in the bright early A-type supergiant HD92207 using FORS2 in spectropolarimetric mode indicated the presence of a longitudinal magnetic field of the order of a few hundred Gauss. Assuming the ideal case of a non-variable star, this discovery has recently been questioned in one work trying to demonstrate the importance of non-photon noise in FORS2 observations. The assumption of non-variability of HD92207 can, however, not be held since substantial profile variations of diverse lines on a time scale of minutes or maybe even a fraction of a minute are detected in FORS2 spectra. The presence of short-term spectral variability in blue supergiants, which are considered as type II supernova progenitors, has not been a subject of systematic studies before and is critical for the current theoretical understanding of their physics. Given the detected short term variability, the question of the presence of a magnetic field cannot be answered without proper modeling of the impact of such a variability on the measurements of the magnetic field. Since the short-term periodicity does not fit into the currently known domain of non-radially pulsating supergiants, its confirmation is of great importance for models of stellar evolution.
The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalized to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be of broad interest for undergraduate teaching in statistical mechanics.
We demonstrate that the Magnus force acting on magnetic skyrmions can be efficiently tuned via modulation of the spin-orbit interaction strength. We show that the skyrmion Hall effect, which is a direct consequence of the non-vanishing Magnus force on the magnetic structure can be suppressed in certain limits. Our calculations show that the emergent magnetic fields in the presence of spin-orbit coupling (SOC) renormalize the Lorentz force on itinerant electrons and thus influence the topological transport. In particular, we show that for a N\'eel-type skyrmion and Bloch-type antiskyrmion, the skyrmion Hall effect (SkHE) can vanish by tuning appropriately the strength of Rashba and Dresselhaus SOCs, respectively. Our results open up alternative directions to explore in a bid to overcome the parasitic and undesirable SkHE for spintronic applications.
Global magnetic fields of active solar-like stars are nowadays routinely detected with spectropolarimetric measurements and are mapped with Zeeman-Doppler imaging (ZDI). However, due to the cancellation of opposite field polarities, polarimetry captures only a tiny fraction of the magnetic flux and cannot assess the overall stellar surface magnetic field if it is dominated by a small-scale component. Analysis of Zeeman broadening in high-resolution intensity spectra can reveal these hidden complex magnetic fields. Historically, there were very few attempts to obtain such measurements for G dwarf stars due to the difficulty of disentangling Zeeman effect from other broadening mechanisms affecting spectral lines. Here we developed a new magnetic field diagnostic method based on relative Zeeman intensification of optical atomic lines with different magnetic sensitivity. Using this technique we obtained 78 field strength measurements for 15 Sun-like stars, including some of the best-studied young solar twins. We find that the average magnetic field strength $Bf$ drops from 1.3-2.0 kG in stars younger than about 120 Myr to 0.2-0.8 kG in older stars. The mean field strength shows a clear correlation with the Rossby number and with the coronal and chromospheric emission indicators. Our results suggest that magnetic regions have roughly the same local field strength $B\approx3.2$ kG in all stars, with the filling factor $f$ of these regions systematically increasing with stellar activity. Comparing our results with the spectropolarimetric analyses of global magnetic fields in the same stars, we find that ZDI recovers about 1% of the total magnetic field energy in the most active stars. This figure drops to just 0.01% for the least active targets.
This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential equations with order of convergence 1/2. We obtain explicit expressions for all the constants involved. At the price of some extra assumptions on the time marginals and an exponential bound in time, we loosen the usual boundedness and Lipschitz assumptions. We conclude with an application of our result to Temperature-Accelerated Molecular Dynamics.
Dissipation and fluctuations of one-body observables in heavy-ion reactions around the Coulomb barrier are investigated with a microscopic stochastic mean-field approach. By projecting the stochastic mean-field dynamics on a suitable collective path, transport coefficients associated with the relative distance between colliding nuclei and a fragment mass are extracted. Although microscopic mean-field approach is know to underestimate the variance of fragment mass distribution, the description of the variance is much improved by the stochastic mean-field method. While fluctuations are consistent with the empirical (semiclassical) analysis of the experimental data, concerning mean values of macroscopic variables the semiclassical description breaks down below the Coulomb barrier.
Full sky surveys of peculiar velocity are arguably the best way to map the large scale structure out to distances of a few times 100 Mpc/h. Using the largest and most accurate ever catalog of galaxy peculiar velocities "Cosmicflows-2", the large scale structure has been reconstructed by means of the Wiener filter and constrained realizations assuming as a Bayesian prior model the LCDM model with the WMAP inferred cosmological parameters. The present paper focuses on studying the bulk flow of the local flow field, defined as the mean velocity of top-hat spheres with radii ranging out to R=500 Mpc/h. The estimated large scale structures, in general, and the bulk flow, in particular, are determined by the tension between the observational data and the assumed prior model. A prerequisite for such an analysis is the requirement that the estimated bulk flow is consistent with the prior model. Such a consistency is found here. At R=50(150) Mpc/h the estimated bulk velocity is 250+/-21 (239+/-38) km/s. The corresponding cosmic variance at these radii is 126(60)km/s, which implies that these estimated bulk flows are dominated by the data and not by the assumed prior model. The estimated bulk velocity is dominated by the data out to R~200 Mpc/h, where the cosmic variance on the individual Supergalactic Cartesian components (of the r.m.s. values) exceeds the variance of the Constrained Realizations by at least a factor of 2. The supergalactic SGX and SGY components of the CMB dipole velocity are recovered by the Wiener filter velocity field down to a very few km/s. The SGZ component of the estimated velocity, the one that is most affected by the Zone of Avoidance, is off by 126 km/s (an almost 2 sigma discrepancy).
We present the results of an abundance analysis of three G and two K dwarfs in the Praesepe open cluster based on high-resolution, moderate signal-to-noise-ratio spectra obtained with the ARC 3.5-m Telescope at Apache Point Observatory. Using a Principle Component Analysis and the BACCHUS automated spectral analysis code, we determined stellar parameters and abundances of up to 24 elements for each of our targets, which range in temperature from 6000 to 4600 K. The average derived iron abundance for the three G stars is 0.17+/-0.07 dex, consistent with the 0.12+/-0.04 dex derived by Boesgaard et al. (2013) for their sample of 11 solar-type Praesepe members, which included these G stars. To investigate the efficacy of using automated routines to derive the abundances of cooler main-sequence stars, we compared the abundances of the K dwarfs to those of the G dwarfs. Our abundances are consistent to <=0.1~dex for 13 of the 18 elements we report for all five of the stars, providing more evidence that G and K stars in a given open cluster are chemically homogeneous. The median difference between the mean G and K stars abundances is 0.08+/-0.05 dex, despite serious challenges with the noisier data for the fainter K dwarfs. Our results are encouraging for chemical tagging, as they indicate that it may be possible to use automated abundance determination techniques to identify chemically related main-sequence stars across larger temperature ranges than are usually considered in these experiments.
Let $(X_j)_{j\geq1}$ be a multivariate long-range dependent Gaussian process. We study the asymptotic behavior of the corresponding sequential empirical process indexed by a class of functions. If some entropy condition is satisfied we have weak convergence to a linear combination of Hermite processes.
Understanding the role of electron correlations in strong spin-orbit transition-metal oxides is key to the realisation of numerous exotic phases including spin-orbit assisted Mott insulators, correlated topological solids, and prospective new high-temperature superconductors. To date, most attention has been focussed on the $5d$ iridium-based oxides. Here, we instead consider the Pt-based delafossite oxide PtCoO$_2$. Our transport measurements, performed on single-crystal samples etched to well-defined geometries using focussed ion-beam techniques, yield a room-temperature resistivity of only 2.1~$\mu\Omega$cm, establishing PtCoO$_2$ as the most conductive oxide known. From angle-resolved photoemission and density-functional theory, we show that the underlying Fermi surface is a single cylinder of nearly hexagonal cross-section, with very weak dispersion along k$_z$. Despite being predominantly composed of $d$-orbital character, the conduction band is remarkably steep, with an average effective mass of only 1.14$m_e$. Moreover, the sharp spectral features observed in photoemission remain well-defined with little additional broadening for over 500~meV below E$_F$, pointing to suppressed electron-electron scattering. Together, our findings establish PtCoO$_2$ as a model nearly-free electron system in a $5d$ delafossite transition-metal oxide.
Atomic level defects such as dislocations play key roles in determining the macroscopic properties of crystalline materials. Their effects are important and wide-reaching, and range from increased chemical reactivity to enhanced mechanical properties to vastly increased rates of crystal growth. Dislocations have therefore been widely studied using traditional techniques such as X-ray diffraction (XRD) and optical imaging. More recently, advances in microscopy have allowed their direct visualization. Atomic force microscopy (AFM) has enabled the 2D study of single dislocations while transmission electron microscopy (TEM), which was initially limited to 2D projections of thin specimens, can now visualize strain fields in 3D with near atomic resolution. However, these techniques can- not offer in situ, 3D imaging of the formation or movement of dislocations during dynamic processes such as crystal growth and dissolution. Here, we describe how Bragg Coherent Diffraction Imaging (BCDI) can be used to visualize in 3D the entire network of dislocations present within an individual crystal. Using calcite (CaCO3) single crystals, we also use BCDI to monitor the propagation of the dislocation network during repeated growth and dissolution cycles, and show how this is intimately linked to the growth and dissolution mechanisms. These investigations demonstrate the potential of BCDI for studying the mechanisms underlying the response of crystalline materials to external stimuli.
In this paper, we consider the family of pattern-replacement equivalence relations referred to as the "indices and values adjacent" case. Each such equivalence is determined by a partition $P$ of a subset of $S_c$ for some $c$. In 2010, Linton, Propp, Roby, and West posed a number of open problems in the area of pattern-replacement equivalences. Five, in particular, have remained unsolved until now, the enumeration of equivalence classes under the $\{123, 132\}$-equivalence, under the $\{123, 321\}$-equivalence, under the $\{123, 132, 213\}$ equivalence, and under the $\{123, 132, 213, 321\}$-equivalence. We find formulas for three of the five equivalences and systems of representatives for the equivalence classes of the other two. We generalize our results to hold for all replacement partitions of $S_3$, as well as for an infinite family of other replacement partitions. In addition, we characterize the equivalence classes in $S_n$ under the $S_c$-equivalence, finding a generalization of Stanley's results on the $\{12, 21\}$-equivalence.   To do this, we introduce a notion of confluence that often allows one to find a representative element in each equivalence class under a given equivalence relation. Using an inclusion-exclusion argument, we are able to use this to count the equivalence classes under equivalence relations satisfying certain conditions.
The harmonic sawtooth map w(x) of the unit interval onto itself is defined where it is shown that its fixed points are enumerated by generating functions involving the golden ratio in their parameters. The appropriately scaled Mellin transform of w(x) is an analytic continuation of the Riemann zeta function {\zeta}(s) valid for all -Re(s) not an integer. The series expansion of the inverse scaling function which makes the Mellin transform of w(x) equal to the zeta function has coefficients enumerating the Large Schroder Numbers S_n, the number of perfect matchings in a triangular grid of n squares. A finite-sum approximation to is examined and an associated function is found which solves a reflection formula. The reflection function is singular at s = 0 and the residue at this point changes sign from negative to positive between the values of N = 176 and N = 177. The Gauss map h(x) is recalled so that its fixed points and Mellin transform can be contrasted to those of w(x). The geometric counting function of the fractal string associated to the lengths of the harmonic sawtooth map components happens to coincide with the counting function for the number of Pythagorean triangles of the form {(a,b,b+1):(b+1)<=x}. The volume of the inner tubular neighborhood of the boundary of the map with radius {\epsilon} is shown to have the particuarly simple closed-form. Also, the Minkowski content is shown to be 2 and the Minkowski dimension to be 1/2 and thus not invertible. Some definitions from the theory of fractal strings and membranes are also recalled.
V532 Oph has been found to be a member of the rare, hydrogen-deficient R Coronae Borealis (RCB) stars from new photometric and spectroscopic data reported in this paper. The lightcurve of V532 Oph shows the sudden, deep, irregularly spaced declines characteristic of RCB stars. Its optical spectrum is typical of a warm (T(eff)~7000 K) RCB star, showing weak or absent hydrogen lines, the C2 Swan bands, and no evidence for 13C. In addition, the star shows small pulsations typical of an RCB star and an infrared excess due to circum- stellar dust. It also appears to be significantly reddened by foreground dust. The distance to V532 Oph is estimated to be 5.5-8.7 kpc. These new data show that this star was misclassified as an eclipsing binary in the General Catalog of Variable Stars. The new data presented here for V532 Oph reveal the power of high-quality, high-cadence all-sky photometric surveys, such as ASAS-3, to identify new RCB candidates on the basis of lightcurve data alone, now that they have been collecting data for durations sufficiently long to reveal multiple declines. Despite their small numbers, RCB stars may be of great importance in understanding the late stages of stellar evolution. In particular, their measured isotopic abundances imply that many, if not most, RCB stars are produced by WD mergers, which may be the low-mass counterparts of the more massive mergers thought to produce type Ia supernovae. Therefore, establishing the population of RCB stars in the Galaxy will help constrain the frequency of these WD mergers.
We introduce a new technique for proving positivity of certain divisor classes on $\bar{M}_{0,n}$ and its weighted variants. Our methods give an unconditional description of the spaces of symmetric weighted pointed rational curves as log canonical models of $\bar{M}_{0,n}$.
We consider quasilinear elliptic systems in divergence form. In general, we cannot expect that weak solutions are locally bounded because of De Giorgi's counterexample. Here we assume a condition on the support of off-diagonal coefficients that "keeps away" the counterexample and allows us to prove local boundedness of weak solutions.
Current constraints on spatial curvature show that it is dynamically negligible: $|\Omega_{\rm K}| \lesssim 5 \times 10^{-3}$ (95% CL). Neglecting it as a cosmological parameter would be premature however, as more stringent constraints on $\Omega_{\rm K}$ at around the $10^{-4}$ level would offer valuable tests of eternal inflation models and probe novel large-scale structure phenomena. This precision also represents the "curvature floor", beyond which constraints cannot be meaningfully improved due to the cosmic variance of horizon-scale perturbations. In this paper, we discuss what future experiments will need to do in order to measure spatial curvature to this maximum accuracy. Our conservative forecasts show that the curvature floor is unreachable - by an order of magnitude - even with Stage IV experiments, unless strong assumptions are made about dark energy evolution and the $\Lambda$CDM parameter values. We also discuss some of the novel problems that arise when attempting to constrain a global cosmological parameter like $\Omega_{\rm K}$ with such high precision. Measuring curvature down to this level would be an important validation of systematics characterisation in high-precision cosmological analyses.
We have compiled a comprehensive library of all X-ray observations of Magellanic pulsars carried out by {\it XMM-Newton}, {\it Chandra}, and {\it RXTE} in the period 1997-2014. In this work, we use the data from 53 high-mass Be/X-ray binaries in the Small Magellanic Cloud to demonstrate that the distribution of spin-period derivatives vs. spin periods of spinning-down pulsars is not at all different than that of the accreting spinning-up pulsars. The inescapable conclusion is that the up and down samples were drawn from the same continuous parent population, therefore Be/X-ray pulsars that are spinning down over periods spanning 18 years are in fact accreting from retrograde disks. The presence of prograde and retrograde disks in roughly equal numbers supports a new evolutionary scenario for Be/X-ray pulsars in their spin period-period derivative diagram.