ShantanuT01/DACTYL-Pretraining huggingface dataset:
Structural stability of paramagnetic (PM) body-centered cubic (bcc) Fe under pressure is investigated based on first-principles phonon calculations. Spin configurations of the PM phase are approximated using a binary special quasi-random structure (SQS) with a supercell approach. The behavior of phonon modes can be associated with pressure-induced phase transitions to the face-centered cubic (fcc) and hexagonal close-packed (hcp) structures as follows: For the PM phase, it is found that the low-frequency transverse mode at the N point (N$_4^-$ mode), which corresponds to a bcc-hcp phase transition pathway, exhibits strong softening under isotropic volume compression. The frequency of this mode becomes zero by $2\%$ volume decrease within the harmonic approximation. This result is not consistent with the experimental fact that phase transition from the PM bcc to hcp phases does not occur under volume compression. The seeming contradiction can be explained only when anharmonic behavior of the N$_4^-$ mode is taken into consideration; a potential energy curve along the N$_4^-$ mode becomes closer to a double-well shape for the PM phase under the volume compression. On the other hand, softening of the longitudinal mode at the 2/3[111] point under the volume compression is also found for the PM phase, which indicates the pressure-induced bcc-fcc phase transition along this mode. Such behaviors are not seen in ferromagnetic (FM) bcc Fe, implying that the magnetic structure plays essential roles on the phase transition mechanism.
The universality phenomenon asserts that the distribution of the eigenvalues of random matrix with i.i.d. zero mean, unit variance entries does not depend on the underlying structure of the random entries. For example, a plot of the eigenvalues of a random sign matrix, where each entry is +1 or -1 with equal probability, looks the same as an analogous plot of the eigenvalues of a random matrix where each entry is complex Gaussian with zero mean and unit variance. In the current paper, we prove a universality result for sparse random n by n matrices where each entry is nonzero with probability $1/n^{1-\alpha}$ where $0<\alpha\le1$ is any constant. One consequence of the sparse universality principle is that the circular law holds for sparse random matrices so long as the entries have zero mean and unit variance, which is the most general result for sparse random matrices to date.
Bismuth donors ion-implanted in $^{28}$Si and $^\text{nat}$Si are studied using magnetic resonance spectroscopy based on spin dependent recombination. The hyperfine clock transition, at which the linewidth is significantly narrowed, is observed for the bismuth donors. The experimental results are modeled quantitatively by molecular orbital theory for a coupled pair consisting of a bismuth donor and a spin dependent recombination readout center, including the effect of hyperfine and Zeeman interactions.
We report a direct observation of radiation pressure, exerted on cold rubidium atoms while bouncing on an evanescent-wave atom mirror. We analyze the radiation pressure by imaging the motion of the atoms after the bounce. The number of absorbed photons is measured for laser detunings ranging from {190 MHz} to {1.4 GHz} and for angles from {0.9 mrad} to {24 mrad} above the critical angle of total internal reflection. Depending on these settings, we find velocity changes parallel with the mirror surface, ranging from 1 to {18 cm/s}. This corresponds to 2 to 31 photon recoils per atom. These results are independent of the evanescent-wave optical power.
The present Letter, deals with the statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002) and Phys. Rev E {\bf 72}, 036108 (2005)], which predicts the probability distribution $p(E) \propto \exp_{\kappa} (-I)$, where, $I \propto \beta E -\beta \mu$, is the collision invariant, and $\exp_{\kappa}(x)=(\sqrt{1+ \kappa^2 x^2}+\kappa x)^{1/\kappa}$, with $\kappa^2<1$. This, experimentally observed distribution, at low energies behaves as the Maxwell-Boltzmann exponential distribution, while at high energies presents power law tails. Here we show that the function $\exp_{\kappa}(x)$ and its inverse $\ln_{\kappa}(x)$, can be obtained within the one-particle relativistic dynamics, in a very simple and transparent way, without invoking any extra principle or assumption, starting directly from the Lorentz transformations. The achievements support the idea that the power law tailed distributions are enforced by the Lorentz relativistic microscopic dynamics, like in the case of the exponential distribution which follows from the Newton classical microscopic dynamics.
The dynamics of a binary system with non conserved order parameter under a plain shear flow with rate $\gamma $ is solved analytically in the large-N limit. A phase transition is observed at a critical temperature $T_c(\gamma)$. After a quench from a high temperature equilibrium state to a lower temperature $T$ a non-equilibrium stationary state is entered when $T>T_c(\gamma)$, while aging dynamics characterizes the phases with $T\leq T_c(\gamma)$. Two-time quantities are computed and the off-equilibrium generalization of the fluctuation-dissipation theorem is provided.
We show that invariance properties of the Lagrangian of an incommensurate system, as described by the Frenkel Kontorova model, imply the existence of a generalized angular momentum which is an integral of motion if the system remains floating. The behavior of this quantity can therefore monitor the character of the system as floating (when it is conserved) or locked (when it is not). We find that, during the dynamics, the non-linear couplings of our model cause parametric phonon excitations which lead to the appearance of Umklapp terms and to a sudden deviation of the generalized momentum from a constant value, signalling a dynamical transition from a floating to a pinned state. We point out that this transition is related but does not coincide with the onset of sliding friction which can take place when the system is still floating.
The study of the evolution of star-forming galaxies requires the determination of accurate kinematics and scaling relations out to high redshift. In this paper we select a sample of 18 galaxies at z~1, observed in the H-alpha emission-line with KMOS, to derive accurate kinematics using a novel 3D analysis technique. We use the new code 3D-Barolo, that models the galaxy emission directly in the 3D observational space, without the need to extract kinematic maps. This technique's major advantage is that it is not affected by beam smearing and thus it enables the determination of rotation velocity and intrinsic velocity dispersion, even at low spatial resolution. We find that: 1) the rotation curves of these z~1 galaxies rise very steeply within few kiloparsecs and remain flat out to the outermost radius and 2) the H-alpha velocity dispersions are low, ranging from 15 to 40 km/s, which leads to V/sigma = 3-10. These characteristics are similar to those of disc galaxies in the local Universe. Finally, we also report no significant evolution of the stellar-mass Tully-Fisher relation. Our results show that disc galaxies are kinematically mature and rotation-dominated already at z~1.
We compute the class of the effective divisors on $\overline{\mathcal{M}}_{g,n}$, which are set theoretically equal to the locus of moduli points $[C,p_1,\dots ,p_n]$ where $C$ lies on a quadric under the map given by the linear series $|K_C-p_1-\dots -p_n|$. Using this divisor class we show that the moduli spaces $\overline{\mathcal{M}}_{16,8}$ and $\overline{\mathcal{M}}_{17,8}$ are of general type. We also note that the divisor classes computed in the papers \cite{FV1} and \cite{FV2} can be used to show that $\overline{\mathcal{M}}_{12,10}$ is of general type as well.
The discovery of 2-dimensional (2D) materials, such as CrI3, that retain magnetic ordering at monolayer thickness has resulted in a surge of research in 2D magnetism from both pure and applied perspectives. Here, we report a magneto-Raman spectroscopy study on multilayered CrI3, focusing on two new features in the spectra which appear at temperatures below the magnetic ordering temperature and were previously assigned to high frequency magnons. We observe a striking evolution of the Raman spectra with increasing magnetic field in which clear, sudden changes in intensities of the modes are attributed to the interlayer ordering changing from antiferromagnetic to ferromagnetic at a critical magnetic field. Our work highlights the sensitivity of the Raman modes to weak interlayer spin ordering in CrI3. In addition, we theoretically examine potential origins for the new modes, which we deduce are unlikely single magnons.
We define a Deligne-Mumford stack X_{D,r} which depends on a scheme X, an effective Cartier divisor D\subset X, and a positive integer r. Then we show that the Abramovich-Vistoli moduli stack of stable maps into X_{D,r} provides compactifications of the locally closed substacks of \bar{M}_{g,n}(X,\beta) corresponding to relative stable maps.
We study the evolution of quantum fluctuations of a scalar field which is coupled to the geometry, in an exponentially expanding universe.   We derive an expression for the spectrum of intrinsic perturbations, and it is shown that the intrinsic degrees of freedom are well behaved in the infra-red part of the spectrum. We conclude that quantum fluctuations do not change the dynamics of the spacetime in a way which makes its evolution non-perturbative and stochastic.   This result contradicts previous derivations which are based on the study of a quantum field on a fixed geometry.
The Navarro-Frenk-White (NFW) density profile is often used to model gravitational lenses. For low values of the characteristic convergence ($\kappa_s \ll 1$) of this model - corresponding to galaxy and galaxy group mass scales - a high numerical precision is required in order to accurately compute several quantities in the strong lensing regime. An alternative for fast and accurate computations is to derive analytic approximations in this limit. In this work we obtain analytic solutions for several lensing quantities for elliptical (ENFW) and pseudo-elliptical (PNFW) NFW lens models on the typical scales where gravitational arcs are expected to be formed, in the $\kappa_s \ll 1$ limit, establishing their domain of validity. We derive analytic solutions for the convergence and shear for these models, obtaining explicit expressions for the iso-convergence contours and constant distortion curves (including the tangential critical curve). We also compute the deformation cross section, which is given in closed form for the circular NFW model and in terms of a one-dimensional integral for the elliptical ones. In addition, we provide a simple expression for the ellipticity of the iso-convergence contours of the pseudo-elliptical models and the connection of characteristic convergences among the PNFW and ENFW models. We conclude that the set of solutions derived here is generally accurate for $\kappa_s \lesssim 0.1$. For low ellipticities, values up to $\kappa_s \simeq 0.18$ are allowed. On the other hand, the mapping between PNFW and the ENFW models is valid up to $\kappa_s \simeq 0.4$. The solutions derived in this work can be used to speed up numerical codes and ensure their accuracy in the low $\kappa_s$ regime, including applications to arc statistics and other strong lensing observables. (Abridged)
Thresholds for beam damage have been assessed for La$_{0.7}$Sr$_{0.3}$MnO$_3$ and SrTiO$_3$ as a function of electron probe current and exposure time at 80 and 200 kV acceleration voltage. The materials were exposed to an intense electron probe by aberration corrected scanning transmission electron microscopy (STEM) with simultaneous acquisition of electron energy loss spectroscopy (EELS) data. Electron beam damage was identified by changes of the core loss fine structure after quantification by a refined and improved model based approach. At 200 kV acceleration voltage, damage in SrTiO$_3$ was identified by changes both in the EEL fine structure and by contrast changes in the STEM images. However, the changes in the STEM image contrast as introduced by minor damage can be difficult to detect under several common experimental conditions. No damage was observed in SrTiO$_3$ at 80 kV acceleration voltage, independent of probe current and exposure time. In La$_{0.7}$Sr$_{0.3}$MnO$_3$, beam damage was observed at both 80 and 200 kV acceleration voltages. This damage was observed by large changes in the EEL fine structure, but not by any detectable changes in the STEM images. The typical method to validate if damage has been introduced during acquisitions is to compare STEM images prior to and after spectroscopy. Quantifications in this work show that this method possibly can result in misinterpretation of beam damage as changes of material properties.
Following recent work in which events which may correspond to a bound tetraneutron ($^4$n) were observed, it is pointed out that from the theoretical perspective the two-body nucleon-nucleon force cannot by itself bind four neutrons, even if it can bind a dineutron.   A very strong phenomenological four-nucleon (4N) force is needed in order to bind the tetraneutron. Such a 4N force, if it existed, would bind $^4$He by about 100 MeV. Alternative experiments such as ($^8$He,$^4$n) are proposed to search for the tetraneutron.
Bulk magnetism in solids is fundamentally quantum mechanical in nature. Yet in many situations, including our everyday encounters with magnetic materials, quantum effects are masked, and it often suffices to think of magnetism in terms of the interaction between classical dipole moments. Whereas this intuition generally holds for ferromagnets, even as the size of the magnetic moment is reduced to that of a single electron spin (the quantum limit), it breaks down spectacularly for antiferromagnets, particularly in low dimensions. Considerable theoretical and experimental progress has been made in understanding quantum effects in one-dimensional quantum antiferromagnets, but a complete experimental description of even simple two-dimensional antiferromagnets is lacking. Here we describe a comprehensive set of neutron scattering measurements that reveal a non-spin-wave continuum and strong quantum effects, suggesting entanglement of spins at short distances in the simplest of all two-dimensional quantum antiferromagnets, the square lattice Heisenberg system.
We study the vertical structure of polytropic, $P\propto \rho^\Gamma$, centrifugally-supported gaseous discs embedded in cold dark matter (CDM) halos. At fixed radius $R$, the shape of the vertical density profile depends only weakly on whether the disc is self-gravitating (SG) or not (NSG). The disc thickness, set by the midplane sound speed and circular velocity, $(c_s/V_c)R$, in the NSG case, and by the sound speed and surface density, $c_s^2/G\Sigma$, in SG discs, is smaller than either of these scales. SG discs are typically Toomre unstable, NSG discs are stable. Exponential discs in CDM halos with roughly flat circular velocity curves generally "flare" outwards. For the polytropic equation of state of the EAGLE simulations, discs whose mass and size match observational constraints are stable (NSG) for $M_d< 3\times 10^9\, M_\odot$ and unstable (SG) at higher masses, if fully gaseous. We test these analytic results using a set of idealized SPH simulations and find excellent agreement. Our results clarify the role of the gravitational softening on the thickness of simulated discs, and on the onset of radial instabilities. EAGLE low-mass discs are non-self-gravitating so the softening plays no role in their vertical structure. High-mass discs, on the other hand, are expected to be self-gravitating and unstable, and may be artificially thickened and stabilized unless gravity is well resolved. Simulations with spatial resolution high enough to not compromise the vertical structure of a disc also resolve the onset of their instabilities, but the converse is not true: resolving instabilities does not guarantee that the vertical structure is resolved.
Concurrence introduced by Hill and Wootters [Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive entangled states and vanishes for all separable states. We present an extension of entanglement measure to general continuous variable states of multiple degrees of freedom by generalizing the Lagrange's identity and wedge product framework proposed by Bhaskara et al. [Quantum Inf. Process. 16, 118 (2017)] for pure discrete variable systems in arbitrary dimensions. A family of faithful entanglement measures is constructed that admit necessary and sufficient conditions for separability across arbitrary bipartitions presented by Vedral et al. [Phys. Rev. Lett. 16 2275 (1997)]. The computed entanglement measure in the present approach for general Gaussian states, pair coherent states and non Gaussian continuous variable Bell states, matches with known results. We also quantify entanglement of phase randomized squeezed states and superposition of squeezed states. Our results also simplify several results in quantum entanglement theory.
We present measurements of the Fe-K line for nine Seyfert I galaxies using Chandra High Energy Transmission Grating Spectrometer (HETGS) data. The centroid energies are narrowly dispersed (6.403 +/- 0.062 keV) and indicate an origin of the line cores in cold matter. If {\it all} the lines in this sample were the peaks of a relativistically broadened disk line, it would require unrealistically fine tuning. However, at least three of the nine AGN clearly show a complex Fe-K line with an underlying broad component, possibly from a disk. In the others, an apparently narrow Fe-K line (even if it is resolved by Chandra) may still be due to the peak of a disk line. To distinguish this scenario from an origin in distant matter requires variability information.
Let $S(\sigma,t)=\frac{1}{\pi}\arg\zeta(\sigma+it)$ be the argument of the Riemann zeta-function at the point $\sigma+it$ in the critical strip. For $n\geq 1$ and $t>0$, we define \begin{equation*} S_{n}(\sigma,t) = \int_0^t S_{n-1}(\sigma,\tau) \,d\tau + \delta_{n,\sigma\,}, \end{equation*} where $\delta_{n,\sigma}$ is a specific constant depending on $\sigma$ and $n$. Let $0\leq \beta<1$ be a fixed real number. Assuming the Riemann hypothesis, we establish lower bounds for the maximum of $S_n(\sigma,t+h)-S_n(\sigma,t)$ near the critical line, on the interval $T^\beta\leq t \leq T$ and in a small range of $h$. This improves some results of the first author and generalizes a result of the authors on $S(t)$. We also give new omega results for $S_n(t)$, improving a result by Selberg.
The Erd\H{o}s-Hajnal Conjecture states that for every $H$ there exists a constant $\epsilon(H)>0$ such that every graph $G$ that does not contain $H$ as an induced subgraph contains a clique or a stable set of size at least $|V(G)|^{\epsilon(H)}$. The Conjecture is still open. Some time ago its directed version was formulated (see:\cite{alon}). In the directed version graphs are replaced by tournaments, and cliques and stable sets by transitive subtournaments. If the Conjecture is not true then the smallest counterexample is a prime tournament. For a long time the Conjecture was known only for finitely many prime tournaments. Recently in \cite{bcc} and \cite{choromanski2} the Conjecture was proven for the families of galaxies and constellations that contain infinitely many prime tournaments. In \cite{bcc} the Conjecture was also proven for all $5$-vertex tournaments. We say that a tournament $H$ has the $EH$-property if it satisfies the Conjecture. In this paper we introduce the so-called \textit{strong EH-property} which enables us to prove the Conjecture for new prime tournaments, but what is even more interesting, provides a mechanism to combine tournaments satisfying the Conjecture to get bigger tournaments that do so and are not necessarily nonprime. We give several examples of families of tournaments constructed according to this procedure. The only procedure known before used to construct bigger tournaments satisfying the Conjecture from smaller tournaments satisfying the Conjecture was the so-called \textit{substitution procedure} (see: \cite{alon}). However an outcome of this procedure is always a nonprime tournament and, from what we have said before, prime tournaments are those that play crucial role in the research on the Conjecture. Our method may be potentially used to prove the Conjecture for several new classes of tournaments.
We consider a system of interacting diffusions labeled by a geographic space that is given by the hierarchical group $\Omega_N$ of order $N\in\mathbb{N}$. Individuals live in colonies and are subject to resampling and migration as long as they are active. Each colony has a seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. The migration kernel has a hierarchical structure: individuals hop between colonies at a rate that depends on the hierarchical distance between the colonies. The seed-bank has a layered structure: when individuals become dormant they acquire a colour that determines the rate at which they become active again. The latter allows us to model seed-banks whose wake-up times have a fat tail. We analyse a system of coupled stochastic differential equations that describes the population in the large-colony-size limit. For fixed $N\in\mathbb{N}$, the system exhibits a dichotomy between coexistence and clustering. We identify the range of parameters controlling the migration and the seed-bank for which clustering prevails. We carry out a multi-scale renormalisation analysis in the hierarchical mean-field limit $N\to\infty$. We show that block averages on hierarchical space-time scale $k \in \mathbb{N}$ perform a diffusion with a renormalised diffusion function that depends on $k$. In the clustering regime, after an appropriate scaling with $k$, this diffusion function converges to the Fisher-Wright diffusion function as $k\to\infty$, irrespective of the diffusion function controlling the resampling. For several subclasses of parameters we identify the speed at which the scaled renormalised diffusion function converges to the Fisher-Wright diffusion as $k\to\infty$. We show that the seed-bank reduces the speed compared to the model without seed-bank.
Yang's pure space equations (C.N. Yang, Phys. Rev. Lett. v.33, p.445 (1974)) generalize Einstein's gravitational equations, while coming from gauge theory. We study these equations from a number of vantage points: summarizing the work done previously, comparing them with the Einstein equations and investigating their properties. In particular, the initial value problem is discussed and a number of results are presented for these equations with common energy-momentum tensors.