ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we initiate the study of equivariant wave maps from 2d hyperbolic space into rotationally symmetric surfaces. This problem exhibits markedly different phenomena than its Euclidean counterpart due to the exponential volume growth of concentric geodesic spheres on the domain.   In particular, when the target is the 2-sphere, we find a family of equivariant harmonic maps indexed by a parameter that measures how far the image of each harmonic map wraps around the sphere. These maps have energies taking all values between zero and the energy of the unique co-rotational Euclidean harmonic map, Q, from the Euclidean plane to the 2-sphere, given by stereographic projection. We prove that the harmonic maps are asymptotically stable for values of the parameter smaller than a threshold that is large enough to allow for maps that wrap more than halfway around the sphere. Indeed, we prove Strichartz estimates for the operator obtained by linearizing around such a harmonic map. However, for harmonic maps with energies approaching the Euclidean energy of Q, asymptotic stability via a perturbative argument based on Strichartz estimates is precluded by the existence of gap eigenvalues in the spectrum of the linearized operator.   When the target is 2d hyperbolic space, we find a continuous family of asymptotically stable equivariant harmonic maps with arbitrarily small and arbitrarily large energies. This stands in sharp contrast to the corresponding problem on Euclidean space, where all finite energy solutions scatter to zero as time tends to infinity.
We describe the evolution of the carbon dust shells around Very Late Thermal Pulse (VLTP) objects as seen at infrared wavelengths. This includes a 20-year overview of the evolution of the dust around Sakurai's object (to which Olivier made a seminal contribution) and FG Sge. VLTPs may occur during the endpoint of as many as 25% of solar mass stars, and may therefore provide a glimpse of the possible fate of the Sun.
We consider a magnetic operator of Aharonov-Bohm type with Dirichlet boundary conditions in a planar domain. We analyse the behavior of its eigenvalues as the singular pole moves in the domain. For any value of the circulation we prove that the k-th magnetic eigenvalue converges to the k-th eigenvalue of the Laplacian as the pole approaches the boundary. We show that the magnetic eigenvalues depend in a smooth way on the position of the pole, as long as they remain simple. In case of half-integer circulation, we show that the rate of convergence depends on the number of nodal lines of the corresponding magnetic eigenfunction. In addition, we provide several numerical simulations both on the circular sector and on the square, which find a perfect theoretical justification within our main results, together with the ones in [Bonnaillie-No\"el, V., Helffer, B., Exp. Math. 20 (2011), no. 3, 304-322; MR2836255 (2012i:35274)].
Broad emission lines, particularly broad iron-K lines, are now commonly seen in the X-ray spectra of luminous AGN and Galactic black hole binaries. Sensitive NuSTAR spectra over the energy range of 3-78 keV and high frequency reverberation spectra now confirm that these are relativistic disc lines produced by coronal irradiation of the innermost accretion flow around rapidly spinning black holes. General relativistic effects are essential in explaining the observations. Recent results are briefly reviewed here.
The $L-\sigma$ relation of HII galaxies (HIIGx) calibrated by a distance indicator is a reliable standard candle for measuring the Hubble constant $H_0$. The most straightforward calibration technique anchors them with the first tier of distance ladders from the same galaxies. Recently another promising method that uses the cosmological model-independent Cosmic Chronometers (CC) as a calibrator has been proposed. We promote this technique by removing the assumptions about the cosmic flatness and using a non-parametric Artificial Neural Network for the data reconstruction process. We observe a correlation between the cosmic curvature density parameter and the slope of the $L-\sigma$ relation, thereby improving the reliability of the calibration. Using the calibrated HIIGx Hubble diagram, we obtain a Type Ia Supernovae Hubble diagram free of the conventional assumption about $H_0$. Finally we get a value of $H_0=65.9_{-2.9}^{+3.0} \mathrm{km s^{-1} Mpc^{-1}}$, which is compatible with latest Planck18 measurement.
We investigate the global properties of the radiation emitted by the accretion disk around Kerr black holes. Using the Kerr blackbody (KERRBB) numerical model, we build an analytic approximation of the disk emission features focusing on the pattern of the produced radiation as a function of the black hole spin, mass, accretion rate and viewing angle. The assumption of having a geometrically thin disk limits our analysis to systems emitting below ~0.3 of the Eddington luminosity. We apply this analytical model to four blazars (whose jets are pointing at us) at high redshift that show clear signatures of disk emission. For them, we derive the black hole masses as a function of spin. If these jetted sources are powered by the black hole rotation, they must have high spin values, further constraining their masses.
We evaluate the performance of modern nuclear energy density functionals for predicting inner and outer fission barrier heights and energies of fission isomers of even-even actinides. For isomer energies and outer barrier heights, we find that the self-consistent theory at the HFB level is capable of providing quantitative agreement with empirical data.
Thermoelectric power due to coherent electron transmission through a quantum dot is theoretically studied. In addition to the known features related to resonant peaks, we show that a novel significant structure appears between the peaks. This structure arises from the so-called transmission zero, which is characteristic of coherent transmission through several quantum levels. Because of sensitivity to phase-breaking effect in quantum dots, this novel structure indicates degree of coherency in the electron transmission.
In this work we consider a problem related to the equilibrium statistical mechanics of spin glasses, namely the study of the Gibbs measure of the random energy model. For solving this problem, new results of independent interest on sums of spacings for i.i.d. Gaussian random variables are presented.   Then we give a precise description of the support of the Gibbs measure below the critical temperature.
Using the Space Telescope Imaging Spectrograph, we have obtained ultraviolet (UV) spectra from $\sim 1200$ to 2000 \AA\ of known Lyman continuum (LyC) emitting galaxies at low redshift ($z \sim 0.3-0.4$) with varying absolute LyC escape fractions (fesc $\sim 0.01 - 0.72$). Our observations include in particular the galaxy J1243+4646, which has the highest known LyC escape fraction at low redshift. While all galaxies are known Lyman alpha emitters, we consistently detect an inventory of additional emission lines, including CIV 1550, HeII 1640, OIII] 1666, and CIII] 1909, whose origin is presumably essentially nebular. CIV 1550 emission is detected above 4 $\sigma$ in six out of eight galaxies, with equivalent widths of EW(CIV)$=12-15$ Ang for two galaxies, which exceeds the previously reported maximum emission in low-$z$ star-forming galaxies. We detect CIV 1550 emission in all LyC emitters with escape fractions fesc $> 0.1$ and find a tentative increase in the flux ratio CIV 1550/ CIII] 1909 with fesc. Based on the data, we propose a new criterion to select and classify strong leakers (galaxies with fesc $> 0.1$): CIV 1550/ CIII] 1909 $> 0.75$. Finally, we also find HeII 1640 emission in all the strong leakers with equivalent widths from 3 to 8 Ang rest frame. These are among the highest values observed in star-forming galaxies and are primarily due to a high rate of ionizing photon production. The nebular HeII 1640 emission of the strong LyC emitters does not require harder ionizing spectra at $>54$ eV compared to those of typical star-forming galaxies at similarly low metallicity.
It is becoming clear that determination of the abundance of Si using lines of Si II and Si III can lead to quite discordant results in mid to late B-type stars. The difference between the Si abundances derived from the two ion states can exceed one dex in some cases.   We have carried out a study intended to clarify which kinds of B stars exhibit this discrepancy, to try to identify regularities in the phenomenon, and to explore possible explanations such as abundance stratification by comparing models to observed spectra.   We used spectra from the ESPaDOnS spectropolarimeter and FEROS spectrograph, supplemented with spectra from the ESO and ELODIE archives, of magnetic Bp, HgMn, and normal B-type stars ranging in effective temperature from about 10500 to 15000 K. Using these spectra, we derived abundances using the spectrum synthesis program ZEEMAN which can take into account the influence of magnetic fields. For each star, accurate abundances of Si II, Si III, Ti, Cr, and Fe were derived.   All magnetic Bp stars in our sample show a discordance between the derived abundances of the first and second ions of silicon, with the latter being between 0.6 - 1.7 dex higher. The same behaviour is observed in the non-magnetic stars but to a much smaller extent: Si III is enhanced by between 0.3 - 0.8 dex compared to Si II.We do not detect the discrepancy in three stars, HD 22136 (normal), HD 57608 (HgMn) and HD 27295 (HgMn); these are the only stars in our sample for which the microturbulence parameter is significantly different from zero, and which therefore probably have convection occurring in their atmospheres.   We find that vertical stratification of silicon in the atmospheres of B-type stars may provide an explanation of this phenomenon, but our detailed stratification models do not completely explain the discrepancies, which may, in part, be due to non-LTE effects.
In this paper, we study a compound Korteweg-de Vries-Burgers equation with a higher-order nonlinearity. A class of solitary wave solutions is obtained by means of a series expansion.
Quantum entanglement is among the most fundamental, yet from classical intuition also most surprising properties of the fully quantum nature of physical reality. We report several experiments performed on IBM's Quantum Experience demonstrating envariance -- entanglement assisted invariance. Envariance is a recently discovered symmetry of composite quantum systems, which is at the foundational origin of physics and a quantum phenomenon of pure states. These very easily reproducible and freely accessible experiments on Quantum Experience provide simple tools to study the properties of envariance, and we illustrate this for several cases with "quantum universes" consisting of up to five qubits.
In this short research note, we aim to establish an interesting extension of a summation due to Ramanujan.The result is derived with the help of an extension of Gauss's summation theorem available in the literature.
The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change with time. We study existence, uniqueness and maximal regularity of solutions in Sobolev spaces. In contrast to the previous results we use only the continuity assumption on the operators in the main part of the equation.
We introduce a family of paired-composite-fermion trial wave functions for any odd Cooper-pair angular momentum. These wave functions are parameter-free and can be efficiently projected into the lowest Landau level. We use large-scale Monte Carlo simulations to study three cases: Firstly, the Moore-Read phase, which serves us as a benchmark. Secondly, we explore the pairing associated with the anti-Pfaffian and the particle-hole-symmetric Pfaffian. Specifically, we assess whether their trial states feature exponentially decaying correlations and thus represent gapped phases of matter. For Moore-Read and anti-Pfaffian we find decay lengths of $\xi_\text{Moore-Read}=1.30(5)$ and $\xi_\text{anti-Pfaffian}=1.38(14)$, in units of the magnetic length. By contrast, for the case of PH-Pfaffian, we find no evidence of a finite length scale for up to $56$ particles.
We propose universal SSE method for simulation of Heisenberg model with arbitrary spin and Bose Hubbard model with interaction. We report on the first calculations of soft-core bosons with interaction by the SSE method. Moreover we develop a simple procedure for increase efficiency of the algorithm. From calculation of integrated autocorrelation times we conclude that the method is efficient for both models and essentially eliminates the critical slowing down problem.
Following work by W\"unsch and collaborators, we investigate a self-enrichment scenario for second generation star formation in globular clusters wherein wind material from first generation massive stars rapidly radiatively cools. Radiative energy loss allows retention of fast winds within the central regions of clusters, where it fuels star formation. Secondary star formation occurs in $\sim3-5$ Myr, before supernovae, producing uniform iron abundances in both populations. We derive the critical criteria for radiative cooling of massive star winds and the second generation mass as a function of cluster mass, radius, and metallicity. We derive a critical condition on $M/R$, above which second generation star formation can occur. We speculate that above this threshold the strong decrease in the cluster wind energy and momentum allows ambient gas to remain from the cluster formation process. We reproduce large observed second generation fractions of $\sim30-80\%$ if wind material mixes with ambient gas. Importantly, the mass of ambient gas required is only of order the first generation's stellar mass. Second generation helium enrichment $\Delta Y$ is inversely proportional to mass fraction in the second generation; a large second generation can form with $\Delta Y\sim0.001-0.02$, while a small second generation can reach $\Delta Y\sim0.16$. Like other self-enrichment models for the second generation, we are not able to simultaneously account for both the full range of the Na-O anticorrelation and the second generation fraction.
We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear Schr\"odinger equation (NLS) with initial data below L^2. In particular, we exhibit nonlinear smoothing when the initial data are randomized. Then, we prove local well-posedness of NLS almost surely for the initial data in the support of the canonical Gaussian measures on H^s(T) for each s > -1/3, and global well-posedness for each s > -1/12.
The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems; the case of disorder in 1D with a chiral symmetry is discussed and the relation with exponential functionals of the Brownian motion underlined. Another approach for the analysis of time delay statistics is the random matrix approach, from which we review few results. As a pratical illustration, we briefly outline a theory of nonlinear transport and AC transport developed by B\"uttiker and coworkers, where the concept of Wigner-Smith time delay matrix is a central piece allowing to describe screening properties in out-of-equilibrium coherent conductors.
We give an update on the status of the hadronic light-by-light scattering contribution to the muon g-2. We review recent work by various groups, list some of the open problems and give an outlook on how to better control the uncertainty of this contribution. This is necessary in order to fully profit from planned future muon g-2 experiments to test the Standard Model. Despite some recent developments, we think that the estimate a_{mu}^{HLbL} = (116 \pm 40) x 10^{-11} still gives a fair description of the current situation.
We characterize which systems of sign vectors are the cocircuits of an oriented matroid in terms of the cocircuit graph.
During the last decade, numerous and varied observations, along with increasingly sophisticated numerical simulations, have awakened astronomers to the central role the circumgalactic medium (CGM) plays in regulating galaxy evolution. It contains the majority of the baryonic matter associated with a galaxy, along with most of the metals, and must continually replenish the star forming gas in galaxies that continue to sustain star formation. And while the CGM is complex, containing gas ranging over orders of magnitude in temperature and density, a simple emergent property may be governing its structure and role. Observations increasingly suggest that the ambient CGM pressure cannot exceed the limit at which cold clouds start to condense out and precipitate toward the center of the potential well. If feedback fueled by those clouds then heats the CGM and causes it to expand, the pressure will drop and the "rain" will diminish. Such a feedback loop tends to suspend the CGM at the threshold pressure for precipitation. The coming decade will offer many opportunities to test this potentially fundamental principle of galaxy evolution.
Epitaxial thin films of the heavy fermion superconductor UNi2Al3 with Tc{max}=0.98K were investigated. The transition temperature Tc depends on the current direction which can be related to superconducting gaps opening at different temperatures. Also the influence of the magnetic ordering at TN=5K on R(T) is strongly anisotropic indicating different coupling between the magnetic moments and itinerant charge carriers on the multi-sheeted Fermi surface. The upper critical field Hc2(T) suggests an unconventional spin-singlet superconducting state.
We develop a field theory of quantum magnets and magnetic (semi)metals, which is suitable for the analysis of their universal and topological properties. The systems of interest include collinear, coplanar and general non-coplanar magnets. At the basic level, we describe the dynamics of magnetic moments using smooth vector fields in the continuum limit. Dzyaloshinskii-Moriya interaction is captured by a non-Abelian vector gauge field, and chiral spin couplings related to topological defects appear as higher-rank antisymmetric tensor gauge fields. We distinguish type-I and type-II magnets by their equilibrium response to the non-Abelian gauge flux, and characterize the resulting lattices of skyrmions and hedgehogs, the spectra of spin waves, and the chiral response to external perturbations. The general spin-orbit coupling of electrons is similarly described by non-Abelian gauge fields, including higher-rank tensors related to the electronic Berry flux. Itinerant electrons and local moments exchange their gauge fluxes through Kondo and Hund interactions. Hence, by utilizing gauge fields, this theory provides a unifying physical picture of ``intrinsic'' and ``topological'' anomalous Hall effects, spin-Hall effects, and other correlations between the topological properties of electrons and moments. We predict ``topological'' magnetoelectric effect in materials prone to hosting hedgehogs. Links to experiments and model calculations are provided by deriving the couplings and gauge fields from generic microscopic models, including the Hubbard model with spin-orbit interactions. We establish the possible existence of novel quantum spin liquids that exhibit a fractional magnetoelectric effect, and discuss a few applications to topological magnetic conductors like Mn$_3$Sn and Pr$_2$Ir$_2$O$_7$.
The time-varying gravitational field produced by a Weber bar is used to explore mathematical features of the linearized Einstein equation. We present a self-contained formal framework for the treatment of the linear field, which is applicable to several situations where the standard quadrupolar formulas are not adequate. The expressions for retarded integrals reveal a singularity associated with boundary conditions. Results from the transverse traceless subgauge are compared with the radiation calculated from retarded integrals. Lienard-Wiechert potentials are used in a treatment of the Weber bar as a collection of point particles and further possible applications are outlined. The Riemann tensor clarifies the transition from near-field geodesic forces to tidal forces in the far field.
We study the main properties of the warm inflationary model based on Barrow's solution for the scale factor of the universe. Within this framework we calculate analytically the basic slow roll parameters for different versions of warm inflation. We test the performance of this inflationary scenario against the latest observational data and we verify that the predicted spectral index and the tensor-to-scalar fluctuation ratio are in excellent agreement with those of {\it Planck 2015}. Finally, we find that the current predictions are consistent with those of viable inflationary models.
In this study, we report the epitaxial growth of a series of {\alpha}-Sn films on InSb substrate by molecular beam epitaxy (MBE) with thickness varying from 10 nm to 400 nm. High qualities of the {\alpha}-Sn films are confirmed. An enhanced large magnetoresistance (MR) over 450,000% has been observed compared to that of the bare InSb substrate. Thickness, angle and temperature dependent MR are used to demonstrate the effects of {\alpha}-Sn films on the electrical transport properties.
Let $\mathcal{D} =\Omega \setminus\bar{\omega} \subset \mathbb{R}^2$ be a smooth annular type domain. We consider the simplified Ginzburg-Landau energy $E_\epsilon(u)=\frac{1}{2}\int_{\mathcal{D}} |\nabla u|^2 +\frac{1}{4\epsilon^2}\int_{\mathcal{D}} (1-|u|^2)^2$, where $u: \mathcal{D} \rightarrow \mathbb{C}$, and look for minimizers of $E_\epsilon$ with prescribed degrees $deg(u,\partial \Omega)=p$, $deg(u,\partial \omega)=q$ on the boundaries of the domain. For large $\epsilon$ and for balanced degrees, i.e., $p=q$, we obtain existence of minimizers for {\it thin} domain. We also prove non-existence of minimizers of $E_\epsilon$, for large $\epsilon$, in the case $p\neq q$, $pq>0$ and $\mathcal{D}$ is a circular annulus with large capacity (corresponding to "thin" annulus). Our approach relies on similar results obtained for the Dirichlet energy $E_\infty(u)=\frac{1}{2}\int_{\mathcal{D}}|\nabla u|^2$, the existence result obtained by Berlyand and Golovaty and on a technique developed by Misiats.
We prove a double binomial sum identity which differs from most binomial sum identities in that the summands involve the absolute value function. The identity is of interest because it can be used in proofs of lower bounds for the Hadamard maximal determinant problem. Our proof of the identity uses a two-variable variant of the method of telescoping sums.