ShantanuT01/DACTYL-Pretraining huggingface dataset:
Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of $S(t)$, $S_1(t)$, and $\zeta\left(1/2+\mathrm{i}t\right)$ while comparing them with recently proven unconditional ones. As a corollary we obtain a conditional explicit bound on gaps between consecutive zeros of the Riemann zeta-function.
A class of non abelian affine Toda models arising from the axial gauged two-loop WZW model is presented. Their zero curvature representation is constructed in terms of a graded Kac-Moody algebra. It is shown that the discrete multivacua structure of the potential together with non abelian nature of the zero grade subalgebra allows soliton solutions with non trivial electric and topological charges.   The dressing transformation is employed to explicitly construct one and two soliton solutions and their bound states in terms of the tau functions. A discussion of the classical spectra of such solutions and the time delays are given in detail.
The effect of strain on the magnetic order and band structure of single-layer CrAsS$_4$ has been investigated by first-principles calculations based on density functional theory. We found that single-layer CrAsS$_4$ was an antiferromagnetic (AFM) semiconductor, and would have a phase transition from AFM state to ferromagnetic (FM) state by applying a uniaxial tensile strain of 2.99\% along the y-direction or compressive strain of 1.76\% along the x-direction. The underlying physical mechanism of strain-dependent magnetic stability was further elucidated as the result of the competition between the direct exchange and indirect superexchange interactions. Moreover, band gap exhibit a abrupt change along with phase transition of magnetic order. Our study provides an intuitional approach to design strain-modulated spintronic devices.
We present new measurements of the evolution of the galaxy stellar mass functions (GSMF) and UV luminosity functions (UV LF) for galaxies from $z=6-9$ within the Frontier Field cluster MACSJ0416.1-2403 and its parallel field. To obtain these results, we derive the stellar masses of our sample by fitting synthetic stellar population models to their observed spectral energy distribution with the inclusion of nebular emission lines. This is the deepest and farthest in distance mass function measured to date and probes down to a level of M$_{*} = 10^{6.8}M_{\odot}$. The main result of this study is that the low-mass end of our GSMF to these limits and redshifts appears to become steeper from $-1.98_{-0.07}^{+0.07}$ at $z=6$ to $-2.38_{-0.88}^{+0.72}$ at $z=9$, steeper than previously observed mass functions at slightly lower redshifts, and we find no evidence of turnover in the mass range probed. We furthermore demonstrate that the UV LF for these system also appears to show a steepening at the highest redshifts, without any evidence of turnover in the luminosity range probed. Our $M_{\mathrm{UV}}-M_{*}$ relation exhibit shallower slopes than previously observed and are in accordance with a constant mass-to-light ratio. Integrating our GSMF, we find that the stellar mass density increases by a factor of $\sim15_{-6}^{+21}$ from $z=9$ to $z=6$. We estimate the dust-corrected star formation rates (SFRs) to calculate the specific star formation rates ($\mathrm{sSFR}=\mathrm{SFR/M_{*}}$) of our sample, and find that for a fixed stellar mass of $5\times10^{9}M_{\odot}$, sSFR $\propto(1+z)^{2.01\pm0.16}$. Finally, from our new measurements, we estimate the UV luminosity density ($\rho_{\textrm{UV}}$) and find that our results support a smooth decline of $\rho_{\textrm{UV}}$ towards high redshifts.
Exoplanets have sparked interest in extremely high signal-to-noise ratio spectroscopic observations of very bright stars, in a regime where flux calibrators, in particular DA white dwarfs, are not available. We argue that A-type stars offer a useful alternative and reliable space-based spectrophotometry is now available for a number of bright ones in the range 3<V<8 mag. By means of comparing observed spectrophotometry and model fluxes, we identify 18 new very-bright trustworthy A-type flux standards for the optical range (400-800 nm), and provide scaled model fluxes for them. Our tests suggest that the absolute fluxes for these stars in the optical are reliable to within 3%. We limit the spectral range to 400-800 nm, since our models have difficulties to reproduce the observed fluxes in the near-infrared and, especially, in the near-UV, where the discrepancies rise up to ~ 10%. Based on our model fits, we derive angular diameters with an estimated accuracy of about 1%.
In this paper we showed that under two assumptions we are able to define interesting functions that we call generalized local coefficients. We showed that in the quasi-split case generalized local coefficients are up to a positive constant the same as Shahidi's local coefficients. We provide a proof that the non quasi-split group $GL_m(D)$, for a central division algebra $D$ satisfies those assumptions. We also showed that generalized local coefficients satisfy nice properties, like the relation to Plancherel measures and multiplicativity inherited by that of intertwining operators. Generalized local coefficients are only defined for representations that are $(Y,\varphi)$-generic which is a generalization of generic representations in the quasi-split case. Here $Y$ denotes a nilpotent element in the Lie algebra of the group and $\varphi$ is a co-character related to $Y$.
Coronal seismology is extensively used to estimate properties of the corona, e.g. the coronal magnetic field strength are derived from oscillations observed in coronal loops. We present a three-dimensional coronal simulation including a realistic energy balance in which we observe oscillations of a loop in synthesised coronal emission. We use these results to test the inversions based on coronal seismology.   From the simulation of the corona above an active region we synthesise extreme ultraviolet (EUV) emission from the model corona. From this we derive maps of line intensity and Doppler shift providing synthetic data in the same format as obtained from observations. We fit the (Doppler) oscillation of the loop in the same fashion as done for observations to derive the oscillation period and damping time.   The loop oscillation seen in our model is similar to imaging and spectroscopic observations of the Sun. The velocity disturbance of the kink oscillation shows an oscillation period of 52.5s and a damping time of 125s, both being consistent with the ranges of periods and damping times found in observation. Using standard coronal seismology techniques, we find an average magnetic field strength of $B_{\rm kink}=79$G for our loop in the simulation, while in the loop the field strength drops from some 300G at the coronal base to 50G at the apex. Using the data from our simulation we can infer what the average magnetic field derived from coronal seismology actually means. It is close to the magnetic field strength in a constant cross-section flux tube that would give the same wave travel time through the loop.   Our model produced not only a realistic looking loop-dominated corona, but also provides realistic information on the oscillation properties that can be used to calibrate and better understand the result from coronal seismology.
This paper establishes the well-posedness of reflected backward stochastic differential equations in the non-convex domains that satisfy a weaker version of the star-shaped property. The main results are established (i) in a Markovian framework with H\"older-continuous generator and terminal condition and (ii) in a general setting under a smallness assumption on the input data. We also investigate the connections between this well-posedness result and the theory of martingales on manifolds.
We show that almost every matroid contains the rank-3 whirl $\mathcal{W}^3$ or the complete-graphic matroid $M(K_4)$ as a minor.
Emil Artin defined a zeta function for algebraic curves over finite fields and made a conjecture about them analogous to the famous Riemann hypothesis. This and other conjectures about these zeta functions would come to be called the Weil conjectures, which were proved by Weil for curves and later, by Deligne for varieties over finite fields. Much work was done in the search for a proof of these conjectures, including the development in algebraic geometry of a Weil cohomology theory for these varieties, which uses the Frobenius operator on a finite field. The zeta function is then expressed as a determinant, allowing the properties of the function to relate to those of the operator. The search for a suitable cohomology theory and associated operator to prove the Riemann hypothesis is still on. In this paper, we study the properties of the derivative operator $D = \frac{d}{dz}$ on a particular weighted Bergman space of entire functions. The operator $D$ can be naturally viewed as the `infinitesimal shift of the complex plane'. Furthermore, this operator is meant to be the replacement for the Frobenius operator in the general case and is used to construct an operator associated to any suitable meromorphic function. We then show that the meromorphic function can be recovered by using a regularized determinant involving the above operator. This is illustrated in some important special cases: rational functions, zeta functions of curves over finite fields, the Riemann zeta function, and culminating in a quantized version of the Hadamard factorization theorem that applies to any entire function of finite order. Our construction is motivated in part by [23] on the infinitesimal shift of the real line, as well as by earlier work of Deninger [10] on cohomology in number theory and a conjectural `fractal cohomology theory' envisioned in [25] and [28].
We prove a conjecture of Andras Gyarfas, that for all k,t, every graph with clique number at most k and sufficiently large chromatic number has an odd hole of length at least t.
Electric polarization phenomena in insulating systems have long been described in mean field theory by the (static) Clausius-Mossotti or (dynamic) Lorentz-Lorenz polarizabilities. It is here shown, in the strong coupling regime, that a thermodynamic phase instability exists in these models. The resulting thermodynamic phase diagram coincides with that obtained from Dicke-Preparata model of thermal superradiance.
We present models that predict spectra of old- and intermediate-aged stellar populations at 2.51\AA\ (FWHM) with varying [\alpha/Fe] abundance. The models are based on the MILES library and on corrections from theoretical stellar spectra. The models employ recent [Mg/Fe] determinations for the MILES stars and BaSTI scaled-solar and \alpha-enhanced isochrones. We compute models for a suite of IMF shapes and slopes, covering a wide age/metallicity range. Using BaSTI, we also compute "base models" matching The Galactic abundance pattern. We confirm that the \alpha-enhanced models show a flux excess with respect to the scaled-solar models blue-ward $\sim$4500\AA, which increases with age and metallicity. We also confirm that both [MgFe] and [MgFe]' indices are [\alpha/Fe]-insensitive. We show that the sensitivity of the higher order Balmer lines to [\alpha/Fe] resides in their pseudo-continua, with narrower index definitions yielding lower sensitivity. We confirm that the \alpha-enhanced models yield bluer (redder) colours in the blue (red) spectral range. To match optical colours of massive galaxies we require both \alpha-enhancement and a bottom-heavy IMF. The comparison of Globular Cluster line-strengths with our predictions match the [Mg/Fe] determinations from their individual stars. We obtain good fits to both full spectra and indices of galaxies with varying [\alpha/Fe]. Using thousands of SDSS galaxy spectra we obtain a linear relation between a proxy for the abundance, [Z$_{\rm Mg}$/Z$_{\rm Fe}$]$_{\rm SS(BaSTI)}$, using solely scaled-solar models and the [Mg/Fe] derived with models with varying abundance ([Mg/Fe]=0.59[Z$_{\rm Mg}$/Z$_{\rm Fe}$]$_{\rm SS(BaSTI)}$). Finally we provide a user-friendly, web-based facility, which allows composite populations with varying IMF and [\alpha/Fe] ( http://miles.iac.es ).
The inversion of 3/2$^{-}$ and 5/2$^{-}$ levels in heavier Cu isotopes is one of the most visible example of shell-evolution, caused by the strong monopole attraction between the nucleons occupying the orbitals $\pi 0f_{5/2}$ and $\nu 0g_{9/2}$. The tensor part of the nucleon-nucleon interaction is expected to be the driving force behind this monopole migration. In shell model framework, usually spin-tensor decomposition is used to get the information of individual force components to the shell evolution, however, in the present scenario, this method can not apply on \textit{pfg} model space due to the missing spin-orbit partners $ 0f_{7/2}$ and $ 0g_{7/2}$. Therefore, we have analytically obtained the tensor force two-body matrix elements (TBMEs) for this model space using Yukawa potential, and subtract it from effective interaction jj44b \cite{}. The interaction without tensor part, named as jj44a, have been used for calculation of Ni, Zn, Ge and Cu isotopes with various physics viewpoints. In most of the cases, the theoretical results are in good agreement with the experiment only when tensor force is included to the interaction jj44a.
We review the stabilisation of complex structure moduli in Type IIA orientifolds, especially on $T^6 / (\mathbb{Z}_2 \times \mathbb{Z}_6^\prime \times \Omega \mathcal{R})$ with discrete torsion, via deformations of $\mathbb{Z}_2 \times \mathbb{Z}_2$ orbifold singularities. While D6-branes in SO(2N) and USp(2N) models always preserve supersymmetry and thus give rise to flat directions, in an exemplary Pati-Salam model with only U(N) gauge groups ten out of the 15 deformation moduli can be stabilised at the orbifold point.
In a recent manuscript, we showed how an electron pocket in the shape of a diamond with concave sides could potentially explain changes in sign of the Hall coefficient R_H in the underdoped high-Tc cuprates as a function of magnetic field and temperature. For simplicity, this Fermi surface is assumed to be constructed from arcs of a circle connected at vertices which is an idea borrowed from Banik and Overhauser. Such a diamond-shaped pocket is proposed to be the product of biaxial charge-density wave order, which was subsequently confirmed in x-ray scattering experiments. Since those x-ray scattering experiments were performed, the biaxial Fermi surface reconstruction scheme has garnered widespread support in the scientific literature. It has been shown to accurately account for the cross-section of the Fermi surface pocket observed in quantum oscillation measurements, the sign and behavior of the Hall coefficient, the size of the high magnetic field electronic contribution to the heat capacity and more recently the form of the angle-dependent magnetoresistance.In their comment, Chakravarty and Wang raise several important questions relating to the validity of the Hall coefficient we calculated for such a diamond-shaped Fermi surface pocket. These questions concern specifically (1) whether a change in sign of the Hall coefficient R_H with magnetic field and temperature is dependent on a `special' form for the rounding of the vertices, (2) whether a pocket of such a geometry can produce quantum oscillations in R_H in the absence of other Fermi surface sections and (3) whether a reconstructed Fermi surface consisting of a single pocket is less `natural' than one consisting of multiple pockets. Below we consider each of these in turn.
We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and unifies earlier work. We then consider the "obvious" limit points of the set of Salem numbers produced by our theorems, and show that these are all Pisot numbers, in support of a conjecture of Boyd. We then show that all Pisot numbers arise in this way. Combining this with a theorem of Boyd, we show that all Salem numbers are produced via an interlacing construction.
We present the first microscopic calculation of the spectator fragmentation observed in heavy ion reactions at relativistic energies which reproduces the slope of the kinetic energy spectra of the fragments as well as their multiplicity, both measured by the ALADIN collaboration. In the past both have been explained in thermal models, however with vastly different assumptions about the excitation energy and the density of the system. We show that both observables are dominated by dynamical processes and that the system does not pass a state of thermal equilibrium. These findings question the recent conjecture that in these collisions a phase transition of first order, similar to that between water and vapor, can be observed.
We analyze the entanglement properties of spins (qubits) close to the boundary of spin chains in the vicinity of a quantum critical point and show that the concurrence at the boundary is significantly different from the one of bulk spins. We also discuss the von Neumann entropy of dissipative environments in the vicinity of a (boundary) critical point, such as two Ising-coupled Kondo-impurities or the dissipative two-level system. Our results indicate that the entanglement (concurrence and/or von Neumann entropy) changes abruptly at the point where coherent quantum oscillations cease to exist. The phase transition modifies significantly less the entanglement if no symmetry breaking field is applied and we argue that this might be a general property of the entanglement of dissipative systems. We finally analyze the entanglement of an harmonic chain between the two ends as function of the system size.
Let $X$ be a general complex projective hypersurface in $\mathbb{P}^{n+1}$ of degree $d>1$. A point $P$ not in $X$ is called uniform if the monodromy group of the projection of $X$ from $P$ is isomorphic to the symmetric group. We prove that all the points in $\mathbb{P}^{n+1}$ are uniform for $X$, generalizing a result of Cukierman on general plane curves.
We show that a ``fragmented Bose condensate'' in which two or more distinct single-particle states are macroscopically occupied by the same species of boson is inherently unstable to the formation of a conventional Bose condensate whose macroscopically occupied state is a linear combination of the ``fragments'' with definite relative phases. A related analysis shows that a reproducible relative phase develops when two initially decoupled condensates are placed in contact.
Given a variety defined over a field of characteristic zero and an algebraically integrable foliation of corank less than or equal to two, we show the existence of a categorical quotient, defined on the non-empty open set of stable points, through which every invariant morphism factors uniquely.
KIC 1571511 is a 14d eclipsing binary (EB) in the Kepler dataset. The secondary of this EB is a very low mass star with a mass of 0.14136 +/- 0.00036 M_sun and a radius of 0.17831 +0.00051/-0.00062 R_sun (statistical errors only). The overall system parameters make KIC 1571511B an ideal "benchmark object": among the smallest, lightest and best-described stars known, smaller even than some known exoplanet. Currently available photometry encompasses only a small part of the total: future Kepler data releases promise to constrain many of the properties of KIC 1571511B to unprecedented level. However, as in many spectroscopic single-lined systems, the current error budget is dominated by the modeling errors of the primary and not by the above statistical errors. We conclude that detecting the RV signal of the secondary component is crucial to achieving the full potential of this possible benchmark object for the study of low mass stars.
We consider an open quantum system in contact with fermionic metallic reservoirs in a nonequilibrium setup. For the case of spin, orbital or potential fluctuations, we present a systematic formulation of real-time renormalization group at finite temperature, where the complex Fourier variable of an effective Liouvillian is used as flow parameter. We derive a universal set of differential equations free of divergencies written as a systematic power series in terms of the frequency-independent two-point vertex only, and solve it in different truncation orders by using a universal set of boundary conditions. We apply the formalism to the description of the weak to strong coupling crossover of the isotropic spin-1/2 nonequilibrium Kondo model at zero magnetic field. From the temperature and voltage dependence of the conductance in different energy regimes we determine various characteristic low-energy scales and compare their universal ratio to known results. For a fixed finite bias voltage larger than the Kondo temperature, we find that the temperature-dependence of the differential conductance exhibits non-monotonic behavior in the form of a peak structure. We show that the peak position and peak width scale linearly with the applied voltage over many orders of magnitude in units of the Kondo temperature. Finally, we compare our calculations with recent experiments.
A pseudo ternary diffusion couple technique in a multicomponent system by simplifying the mathematical complications of Onsager formalism is proposed for the estimation of composition dependent values of the interdiffusion coefficients. This is otherwise impossible following the conventional method in a system with more than three components. Other alternative methods estimate the average diffusion coefficients over a composition range of random choice and lack physical significance. This method can be followed in a multicomponent system with any number of components on the condition that only three components develop diffusion profiles keeping others as constant.
Recombination lines involving high principal quantum numbers populate the radio spectrum in large numbers. Low-frequency (<1 GHz) observations of radio recombination lines (RRLs) primarily from carbon and hydrogen offer a new, if not unique, way to probe cold, largely atomic gas and warm, ionised gas in other galaxies. Furthermore, RRLs can be used to determine the physical state of the emitting regions, such as temperature and density. These properties make RRLs, potentially, a powerful tool of extragalactic ISM physics. At low radio frequencies, its conceivable to detect RRLs out to cosmological distances when illuminated by a strong radio continuum. However, they are extremely faint (tau ~ 1e-3 -- 1e-4) and have so far eluded detection outside of the local universe.   With LOFAR observations of the radio quasar 3C 190 (z=1.1946), we aim to demonstrate that the ISM can be explored out to great distances through low-frequency RRLs.   We report the detection of RRLs in the frequency range 112--163 MHz in the spectrum of 3C 190. Stacking 13 a-transitions with principal quantum numbers n=266-301, a peak 6sigma feature of optical depth, tau(peak) = (1.0 +\- 0.2) x 1e-3 and FWHM = 31.2 +/- 8.3 km/s was found at z=1.124. This corresponds to a velocity offset of -9965 km/s with respect to the systemic redshift of 3C 190.   We consider three interpretations of the origin of the RRL emission: an intervening dwarf-like galaxy, an AGN-driven outflow, and the inter-galactic medium. We argue that the RRLs most likely originate in a dwarf-like galaxy (M ~ 1e9 Msun) along the line of sight, although we cannot rule out an AGN-driven outflow. We do find the RRLs to be inconsistent with an inter-galactic medium origin. With this detection, we have opened up a new way to study the physical properties of cool, diffuse gas out to cosmological distances.