ShantanuT01/DACTYL-Pretraining huggingface dataset:
We describe a simple scheme to construct a low-energy effective Hamiltonian H_eff for highly correlated systems containing non-metals like O, P or As (O in what follows) and a transition-metal (M) as the active part in the electronic structure, eliminating the O degrees of freedom from a starting Hamiltonian that contains all M d orbitals and all non-metal p orbitals. We calculate all interaction terms between d electrons originating from Coulomb repulsion, as a function of three parameters (F_0, F_2 and F_4) and write them in a basis of orbitals appropriate for cubic, tetragonal, tetrahedral or hexagonal symmetry around M. The approach is based on solving exactly (numerically if necessary) a MO_n cluster containing the transition-metal atom and its n nearest O atoms (for example a CoO_6 cluster in the case of the cobaltates, or a CuO_n cluster in the case of the cuprates, in which n depends on the number of apical O atoms), and mapping them into many-body states of the same symmetry containing d holes only. We illustrate the procedure for the case of Na_xCoO_2. The resulting H_eff, including a trigonal distortion D, has been studied recently and its electronic structure agrees well with angle-resolved photoemission spectra [A. Bourgeois, A. A. Aligia, and M. J. Rozenberg, Phys. Rev. Lett. 102, 066402 (2009)]. Although H_eff contains only 3d t_2g holes, the highly correlated states that they represent contain an important amount not only of O 2p holes but also of 3d e_g holes. When more holes are added, a significant redistribution of charge takes place. As a consequence of these facts, the resulting values of the effective interactions between t_2g states are smaller than previously assumed, rendering more important the effect of D in obtaining only one sheet around the center of the Brillouin zone for the Fermi surface (without additional pockets).
The Kitaev material $\alpha$-RuCl$_3$ is among the most prominent candidates to host a quantum spin-liquid state endowed with fractionalized excitations. Recent experimental and theoretical investigations have separately revealed the importance of both the magnetoelastic coupling and the magnetic anisotropy, in dependence of the applied magnetic field direction. In this combined theoretical and experimental research, we investigate the anisotropic magnetic and magnetoelastic properties for magnetic fields applied along the main crystallographic axes as well as for fields canted out of the honeycomb plane. We found that the magnetostriction anisotropy is unusually large compared to the anisotropy of the magnetization, which is related to the strong magnetoelastic $\widetilde{\Gamma'}$-type coupling in our \textit{ab-initio} derived model. We observed large, non-symmetric magnetic anisotropy for magnetic fields canted out of the honeycomb $ab$-plane in opposite directions, namely towards the $+c^*$ or $-c^*$ axes, respectively. The observed directional anisotropy is explained by considering the relative orientation of the magnetic field with respect to the co-aligned RuCl$_6$ octahedra. Magnetostriction measurements in canted fields support this non-symmetric magnetic anisotropy, however these experiments are affected by magnetic torque effects. Comparison of theoretical predictions with experimental findings allow us to recognize the significant contribution of torque effects in experimental setups where $\alpha$-RuCl$_3$ is placed in canted magnetic fields.
This paper presents a study of the specific merger rate as a function of group membership, local environment, and redshift in a very large, $500h^{-1} Mpc$, cosmological N-body simulation, the \textit{Millennium Simulation}. The goal is to provide environmental diagnostics of major merger populations in order to test simulations against observations and provide further constraints on major merger driven galaxy evolution scenarios. A halo sample is defined using the maximum circular velocity, which is both well defined for subhalos and closely correlated with galaxy luminosity. Subhalos, including the precursors of major mergers, are severely tidally stripped. Major mergers between subhalos are therefore extremely rare. Tidal stripping also suppresses dynamical friction, resulting in long major merger time scales when the more massive halo does not host other subhalos. In contrast, when other subhalos are present major merger time scales are several times shorter. This enhancement is likely due to inelastic unbound collisions between subhalos. Following these results, we predict that major mergers in group environments are dominated by mergers involving the central galaxy, that the specific merger rate is suppressed in groups, and that the frequency of fainter companions is enhanced for mergers and their remnants. We also observe an `assembly bias' in the major merger rate in that mergers of galaxy-like halos are slightly suppressed in overdense environments while mergers of group-like halos are slightly enhanced. A dynamical explanation for this trend is advanced which calls on both tidal effects and interactions between bound halos beyond the virial radii of locally dynamically dominant halos.
Effective Chiral Lagrangian is derived from QCD in the framework of Field Correlator Method. It contains the effects of both confinement and chiral symmetry breaking due to a special structure of the resulting quark mass operator. It is shown that this Lagrangian describes light pseudoscalar mesons, and Gell-Mann-Oakes-Renner relations for pions, eta and K mesons are reproduced. Spectrum of radial excitations of pions and K mesons is found and compared to experimentally known masses.
Let $\mathcal C_Q$ be the cyclic group of order $Q$, $n$ a divisor of $Q$ and $r$ a divisor of $Q/n$. We introduce the set of $(r,n)$-free elements of $\mathcal C_Q$ and derive a lower bound for the the number of elements $\theta \in \mathbb F_q$ for which $f(\theta)$ is $(r,n)$-free and $F(\theta)$ is $(R,N)$-free, where $ f, F \in \mathbb F_q[x]$. As an application, we consider the existence of $\mathbb F_q$-primitive points on curves like $y^n=f(x)$ and find, in particular, all the odd prime powers $q$ for which the elliptic curves $y^2=x^3 \pm x$ contain an $\mathbb F_q$-primitive point.
Artin's Conjecture on Primitive Roots states that a non-square nonunit integer $a$ is a primitive root modulo $p$ for the positive proportion of $p$. This conjecture remains open, but on average, there are many results due to P. J. Stephens. There is a natural generalization of the conjecture for composite moduli. We can consider $a$ as the primitive root modulo, $(\mathbb{Z}/n\mathbb{Z})^{*}$ if $a$ is an element of the maximal exponent in the group. The behavior is more complex for composite moduli, and the corresponding average results are provided by S. Li and C. Pomerance, and recently by the author. P. J. Stephens included the second moment results in his work, but for composite moduli, there were no such results previously. We prove that the corresponding second moment results in this case.
This paper is concerned with the ergodic problem for viscous Hamilton-Jacobi equations having superlinear Hamiltonian, inward-pointing drift, and positive potential which vanishes at infinity. Assuming some radial symmetry of the drift and the potential outside a ball, we establish sharp estimates of the generalized principal eigenvalue with respect to a perturbation of the potential.
After an introduction to the Standard-Model description of CP violation and a brief look at the present status of this phenomenon in the kaon system, a classification of non-leptonic B-decays is given and the formalism of $B^0_{d,s}$--$\bar{B^0_{d,s}}$ mixing is discussed. We then turn to the $B$-factory benchmark modes, CP violation in charged B decays, and the $B_s$-meson system. Finally, we focus both on $B\to\pi K$ decays, which play an important role to probe the CKM angle $\gamma$, and on the $B_d\to\pi^+\pi^-$, $B_s\to K^+K^-$ system, which allows an interesting determination of $\beta$ and $\gamma$.
Integral field spectroscopy (IFS) is presented for star forming regions in M33. A central area of 300 x 500 pc^2 and the external HII region IC 132, at a galactocentric distance {\sim} 19arcmin (4.69 kpc) were observed with the Potsdam Multi Aperture Spectrophotometer (PMAS) instrument at the 3.5 m telescope of the Calar Alto Hispano- Alem\'an observatory (CAHA). The spectral coverage goes from 3600 A to 1{\mu}m to include from [OII]{\lambda}3727 A to the near infrared lines required for deriving sulphur electron temperature and abundance diagnostics. Local conditions within individual HII regions are presented in the form of emission line fluxes and physical conditions for each spatial resolution element (spaxel) and for segments with similar H{\alpha} surface brightness. A clear dichotomy is observed when comparing the central to outer disc HII regions. While the external HII region has higher electron temperature plus larger H{\beta} equivalent width, size and excitation, the central region has higher extinction and metal content. The dichotomy extends to the BPT diagnostic diagrams that show two orthogonal broad distributions of points. By comparing with pseudo-3D photoionization models we conclude that the bulk observed differences are probably related to a different ionization parameter and metallicity. Wolf-Rayet features are detected in IC 132, and resolved into two concentrations whose integrated spectra were used to estimate the characteristic number of WR stars. No WR features were detected in the central HII regions despite their higher metallicity.
We calculate survival probability of a special state which couples randomly to a regular or chaotic environment. The environment is modelled by a suitably chosen random matrix ensemble. The exact results exhibit non--perturbative features as revival of probability and non--ergodicity. The role of background complexity and of coupling complexity is discussed as well.
We prove a Gaussian upper bound for the fundamental solutions of a class of ultra-parabolic equations in divergence form. The bound is independent on the smoothness of the coefficients and generalizes some classical results by Nash, Aronson and Davies. The class considered has relevant applications in the theory of stochastic processes, in physics and in mathematical finance.
We establish a small time large deviation principle and a Varadhan type asymptotics for Brownian motion with singular drift on $\bR^d$ with $d\geq 3$ whose infinitesimal generator is $\frac12 \Delta + \mu \cdot \nabla$, where each $\mu_i$ of $\mu = (\mu_1, \cdots, \mu_d)$ is a measure in some suitable Kato class.
In this paper, we consider the existence of static solutions to the nonlinear Chern-Simons-Schr\"odinger system \begin{equation}\label{eqabstr} \left\{\begin{array}{ll} -ihD_0\Psi-h^2(D_1D_1+D_2D_2)\Psi+V\Psi=|\Psi|^{p-2}\Psi,\\ \partial_0A_1-\partial_1A_0=-\frac 12ih[\overline{\Psi}D_2\Psi-\Psi\overline{D_2\Psi}],\\ \partial_0A_2-\partial_2A_0=\frac 12ih[\overline{\Psi}D_1\Psi-\Psi\overline{D_1\Psi}],\\ \partial_1A_2-\partial_2A_1=-\frac12|\Psi|^2,\\ \end{array} \right. \end{equation} where $p>2$ and non-radial potential $V(x)$ satisfies some certain conditions. We show that for every positive integer $k$, there exists $h_0>0$ such that for $0<h<h_0$, problem \eqref{eqabstr} has a nontrivial static solution $(\Psi_h, A_0^h, A_1^h,A_2^h)$. Moreover, $\Psi_h$ is a positive non-radial function with $k$ positive peaks, which approach to the local maximum point of $V(x)$ as $h\to 0^+$.
Galactic halos are of great importance for our understanding of both the dark matter nature and primordial non-Gaussianity in the perturbation spectrum, a powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. In this paper we analyze {\it Planck} data towards the galaxy M104 (Sombrero) and find an asymmetry in the microwave temperature which extends up to about $1 \degr$ from the galactic center. This frequency-independent asymmetry is consistent with that induced by the Doppler effect due to the galactic rotation and we find a probability of less than about $0.2\%$ that it is due to a random fluctuation of the microwave background. In addition, {\it Planck} data indicate the relatively complex dynamics of the M104 galactic halo, and this appears to be in agreement with previous studies. In view of our previous analysis of the dark halos of nearby galaxies, this finding confirms the efficiency of the method used in revealing and mapping the dark halos around relatively nearby edge-on galaxies.
We suggest the nondestructive method for determination of the dielectric constant of substrate-deposited thin films by capacitance measurement with two parallel wires placed on top of the film. The exact analytical formula for the capacitance of such system is derived. The functional dependence of the capacitance on dielectric constants of the film, substrate, and environment media and on the distance between the wires permits to measure the dielectric constant of thin films for the vast set of parameters where previously proposed approximate methods are less efficient.
We investigate the clustering properties of galaxies in the recently completed ELAIS-S1 redshift survey through their spatial two point autocorrelation function. We used a sub-sample of the ELAIS-S1 catalog covering approximately 4 deg^2 and consisting of 148 objects selected at 15 micron with a flux >0.5 mJy and redshift z<0.5. We detected a positive signal in the correlation function that, in the range of separations 1-10 h mpc is well approximated by a power law with a slope gamma = 1.4 and a correlation length s =5.4 h mpc. This result is in good agreement with the redshift-space correlation function measured in more local samples of mid infrared selected galaxies like the IRAS PSC$z$ redshift survey. This suggests a lack of significant clustering evolution of infrared selected objects out to $z=0.5$ that is further confirmed by the consistency found between the correlation functions measured in a local (z<0.2) and a distant (0.2<z<0.5) subsample of ELAIS-S1 galaxies. We also confirm that optically selected galaxies in the local redshift surveys, especially those of the SDSS sample, are significantly more clustered than infrared objects.
We present a method to simultaneously infer the interstellar extinction parameters $A_0$ and $R_0$, stellar effective temperature $T_{\rm eff}$, and distance modulus $\mu$ in a Bayesian framework. Using multi-band photometry from SDSS and UKIDSS, we train a forward model to emulate the colour-change due to physical properties of stars and the interstellar medium for temperatures from 4000 to 9000 K and extinctions from 0 to 5 mag. We introduce a Hertzsprung-Russel diagram prior to account for physical constraints on the distribution of stars in the temperature-absolute magnitude plane. This allows us to infer distances probabilistically. Influences of colour information, priors and model parameters are explored. Residual mean absolute errors (MAEs) on a set of objects for extinction and temperature are 0.2 mag and 300 K, respectively, for $R_0$ fixed to 3.1. For variable $R_0$, we obtain MAEs of 0.37 mag, 412.9 K and 0.74 for $A_0$, $T_{\rm eff}$ and $R_0$, respectively. Distance moduli are accurate to approximately 2 mag. Quantifying the precisions of individual parameter estimates with $68\%$ confidence interval of the posterior distribution, we obtain 0.05 mag, 66 K, 2 mag and 0.07 for $A_0$, $T_{\rm eff}$, $\mu$ and $R_0$, respectively, although we find that these underestimate the accuracy of the model. We produce two-dimensional maps in extinction and $R_0$ that are compared to previous work. Furthermore we incorporate the inferred distance information to compute fully probabilistic distance profiles for individual lines of sight. The individual stellar AP estimates, combined with inferred 3D information will make possible many Galactic science and modelling applications. Adapting our method to work with other surveys, such as Pan-STARRS and Gaia, will allow us to probe other regions of the Galaxy.
We study the effects of including a running coupling constant in high-density QCD evolution. For fixed coupling constant, QCD evolution preserves the initial dependence of the saturation momentum $Q_s$ on the nuclear size $A$ and results in an exponential dependence on rapidity $Y$, $Q^2_s(Y) = Q^2_s(Y_0) \exp{[ \bar\alpha_s d (Y-Y_0) ]}$. For the running coupling case, we re-derive analytical estimates for the $A$- and $Y$-dependences of the saturation scale and test them numerically. The $A$-dependence of $Q_s$ vanishes $\propto 1/ \sqrt{Y}$ for large $A$ and $Y$. The $Y$-dependence is reduced to $Q_s^2(Y) \propto \exp{(\Delta^\prime\sqrt{Y+X})}$ where we find numerically $\Delta^\prime\simeq 3.2$. We study the behaviour of the gluon distribution at large transverse momentum, characterizing it by an anomalous dimension $1-\gamma$ which we define in a fixed region of small dipole sizes. In contrast to previous analytical work, we find a marked difference between the fixed coupling ($\gamma \simeq 0.65$) and running coupling ($\gamma \sim 0.85$) results. Our numerical findings show that both a scaling function depending only on the variable $r Q_s$ and the perturbative double-leading-logarithmic expression, provide equally good descriptions of the numerical solutions for very small $r$-values below the so-called scaling window.
The decay of $\Lambda_c^+$ into $\pi^+\pi^0\Lambda(1405)$ with the $\Lambda(1405)$ decay into $\pi^0\Sigma^0$ through a triangle diagram is studied. This process is initiated by $ \Lambda_c^+ \to \pi^+ \bar{K}^*N $, then the $\bar{K}^*$ decays into $\bar{K} \pi$ and $\bar{K} N$ produce the $\Lambda(1405)$ through a triangle loop containing $\bar{K}^*N\bar{K}$ which develops a singularity around $1890$ MeV. This process is prohibited by the isospin symmetry, but the decay into this channel is enhanced by the contribution of the triangle diagram, which is sensitive to the mass of the internal particles. We find a narrow peak in the $\pi^0\Sigma^0$ invariant mass distribution, which originates from the $\Lambda(1405)$ amplitude, but is tied to the mass differences between the charged and neutral $\bar{K}$ or $N$ states. The observation of the unavoidable peak of the triangle singularity in the isospin-violating $\Lambda(1405)$ production would provide further support for hadronic molecular picture of the $\Lambda(1405)$ and further information on the $\bar{K} N $ interaction.
The massive and luminous star-forming region W49A is a well known Galactic candidate to probe the physical conditions and chemistry similar to those expected in external starburst galaxies. We aim to probe the physical and chemical structure of W49A on a spatial scale of ~0.8 pc based on the JCMT Spectral Legacy Survey, which covers the frequency range between 330 and 373 GHz. The wide 2x2 arcminutes field and the high spectral resolution of the HARP instrument on JCMT provides information on the spatial structure and kinematics of the cloud. For species where multiple transitions are available, we estimate excitation temperatures and column densities. We detected 255 transitions corresponding to 60 species in the 330-373 GHz range at the center position of W49A. Excitation conditions can be probed for 16 molecules. The chemical composition suggests the importance of shock-, PDR-, and hot core chemistry. Many molecular lines show a significant spatial extent across the maps including high density tracers (e.g. HCN, HNC, CS, HCO+) and tracers of UV-irradiation (e.g. CN and C2H). Large variations are seen between the sub-regions with mostly blue-shifted emission toward the Eastern tail, mostly red-shifted emission toward the Northern clump, and emission peaking around the expected source velocity toward the South-west clump. A comparison of column density ratios of characteristic species observed toward W49A to Galactic PDRs suggests that while the chemistry toward the W49A center is driven by a combination of UV-irradiation and shocks, UV-irradiation dominates for the Northern Clump, Eastern tail, and South-west clump regions. A comparison to a starburst galaxy and an AGN suggests similar C2H, CN, and H2CO abundances (with respect to the dense gas tracer 34CS) between the ~0.8 pc scale probed for W49A and the >1 kpc regions in external galaxies with global star-formation.
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry's phase, can also be found in systems which have slow variables taking values in such a coset space.
We examine the shadow cast by a Kerr black hole pierced by a cosmic string. The observable images depend not only on the black hole spin parameter and the angle of inclination, but also on the deficit angle yielded by the cosmic string. The dependence of the observable characteristics of the shadow on the deficit angle is explored. The imprints in the black hole shadow left by the presence of a cosmic string can serve as a method for observational detection of such strings.
This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken nowadays. The discussion is started by a brief historical report that starts with the studies of thermal machines and combines in theories such as the statistical mechanics of Boltzmann-Gibbs and the Brownian Movement. In this scenario, in the twentieth century, a series of experiments were reported that were not described by the usual model of diffusion. Such experiments paved the way for deeper investigation into anomalous diffusion. These processes are very abundant in physics, and the mechanisms for them to occur are diverse. For this reason, there are many possible ways of modelling the diffusive processes. This article discusses three analytic approaches to investigate anomalous diffusion: fractional diffusion equation, nonlinear diffusion equation and Langevin equation in the presence of fractional, coloured or multiplicative noises. All these formalisms presented different degrees of complexity and for this reason, they have succeeded in describing anomalous diffusion phenomena.
We study a new family of sign-changing solutions to the stationary nonlinear Schr\"odinger equation $$ -\Delta v +q v =|v|^{p-2} v, \qquad \text{in $\mathbb{R}^3$,} $$ with $2<p<\infty$ and $q \ge 0$. These solutions are spiraling in the sense that they are not axially symmetric but invariant under screw motion, i.e., they share the symmetry properties of a helicoid. In addition to existence results, we provide information on the shape of spiraling solutions, which depends on the parameter value representing the rotational slope of the underlying screw motion. Our results complement a related analysis of Del Pino, Musso and Pacard for the Allen-Cahn equation, whereas the nature of results and the underlying variational structure are completely different.
I estimate the accuracies on Higgs boson coupling constants that experiments at the Large Hadron Collider and the International Linear Collider are capable of reaching over the long term.