ShantanuT01/DACTYL-Pretraining huggingface dataset:
We develop a new, unified approach to the following two classical questions on elliptic PDE: the strong maximum principle for equations with non-Lipschitz nonlinearities, and the at most exponential decay of solutions in the whole space or exterior domains. Our results apply to divergence and nondivergence operators with locally unbounded lower-order coefficients, in a number of situations where all previous results required bounded ingredients. Our approach, which allows for relatively simple and short proofs, is based on a (weak) Harnack inequality with optimal dependence of the constants in the lower-order terms of the equation and the size of the domain, which we establish.
We propose a simple model for studying small-x physics in which we take only the collinearly enhanced part of leading and subleading kernels, for all possible transverse momentum orderings. The small-x equation reduces to a second order differential equation in t=log k^2/Lambda^2 space, whose perturbative and strong-coupling features are investigated both analytically and numerically. For two-scale processes, we clarify the transition mechanism between the perturbative, non Regge regime and the strong-coupling Pomeron behavior.
Hanle effect is ubiquitous in the study of spin-related phenomena and has been used to determine spin lifetime, precession and transport in semiconductors. Here, we report an experimental observation of anomalous Hanle effect in individual self-assembled InAs/GaAs quantum dots where we find that a sizeable photo-created electron spin polarization can be maintained in transverse fields as high as 1T until it abruptly collapses. The striking broadening of the Hanle curve by a factor of ~20 and its bistability upon reversal of the magnetic sweep direction points to a novel dynamical nuclear spin polarization mechanism where the effective nuclear magnetic field compensates the transverse applied field. This interpretation is further supported by the measurement of actual electron Zeeman splitting which exhibits an abrupt increase at the Hanle curve collapse. Strong inhomogeneous quadrupolar interactions typical for strained quantum dots are likely to play a key role in polarizing nuclear spins perpendicular to the optically injected spin orientation.
In this paper, we investigate theoretically the quantum state transfer in a laser driven hybrid optomechanical cavity with two Duffing-like anharmonic movable end mirrors containing an ensemble of identical two-level trapped atoms. The quantum state transfer from the Bogoliubov modes of the two anharmonic oscillators to the atomic mode results in the atomic quadrature squeezing beyond the standard quantum limit of 3 dB which can be controlled by both the optomechanical and atom-field coupling strengths. Interestingly, the generated atomic squeezing can be made robust against the noise sources by means of the Duffing anharmonicity. Moreover, the results reveal that the presence of the Duffing anharmonicity provides the possibility of transferring strongly squeezed states between the two mechanical oscillators in a short operating time and with a high fidelity.
A model independent discussion of $\Delta-$production in $pp \to pp \pi^0$ is presented and the $\Delta-$contributions to the 16 $pp \to pp\pi^0$ partial wave amplitudes are identified taking the $Ds$ and $Sd$ channels also into consideration.
In this note we relate about the problem of evaluate the dimension of linear systems through fat points defined on generic $K3$ surfaces.
The recent distance determinations by HIPPARCOS have allowed to locate very precisely a reasonable set of subdwarfs in the HR diagram. A detailed comparison with evolutionary models is now possible and it has been recently claimed that the observed lower part of the main-sequence is cooler than the computed one. In this paper we show that microscopic diffusion could be the physical explanation of such a systematic shift. We emphazise the fact that, as diffusion alters surface abundances, the initial metal content of the stellar material is higher than the present one. A "calibration" procedure is necessary when comparing observed and theoretical HR diagram, to take into account this effect.
In hep-th/0312098 it was argued that by extending the ``$a$-maximization'' of hep-th/0304128 away from fixed points of the renormalization group, one can compute the anomalous dimensions of chiral superfields along the flow, and obtain a better understanding of the irreversibility of RG flow in four dimensional supersymmetric field theory. According to this proposal, the role of the running couplings is played by certain Lagrange multipliers that are introduced in the construction. We show that one can choose a parametrization of the space of couplings in which the Lagrange multipliers can indeed be identified with the couplings, and discuss the consequences of this for weakly coupled gauge theory.
The correspondence between conformal covariant fields in Minkowski's space-time and isometric fields in the five dimensional anti-deSitter space-time is extended to a six-dimensional bulk space and its regular sub-manifolds, so as to include the analysis of evaporating Schwarzschild's black holes without loss of quantum unitarity.
We have investigated the effects of the neutron-proton interaction in several doubly odd deformed nuclei within the framework of the particle-rotor model. In this paper, we show some selected results of our study which evidence the importance of the tensor-force effects.
We study and compare characteristics of sunspot group latitude distribution in two catalogs: the extended Greenwich (1874--2014) and Schwabe ones (1825--1867). We demonstrate that both datasets reveal similar links between latitude and amplitude characteristics of the 11-year cycle: the latitude dispersion correlates with the current activity and the mean latitude of sunspots in the cycle's maximum is proportional to its amplitude, It agrees with conclusions that we made in previous papers for the Greenwich catalog.   We show that the latitude properties of sunspot distribution are much more stable against loss of observational data than traditional amplitude indices of activity. Therefore, the found links can be used for estimates of quality of observations and independent normalizing of activity levels in a gappy pre-Greenwich data. We demonstrate it using the Schwabe catalog as an example.   In addition, we show that the first part of the Schwabe data probably contains errors in determination of sunspot latitudes that lead to overestimation of the sunspot latitude dispersions.
Global regular axially symmetric solutions with large swirl in a cylinder with periodic conditions on the top and on the bottom are proved. On the lateral part of its boundary the boundary slip conditions are assumed. The proof is obtained step by step extending a local solution and showing that the initial data are not increasing.
We discuss dynamical response theory of driven-dissipative quantum systems described by Markovian Master Equations generating semi-groups of maps. In this setting thermal equilibrium states are replaced by non-equilibrium steady states and dissipative perturbations are considered besides the Hamiltonian ones. We derive explicit expressions for the linear dynamical response functions for generalized dephasing channels and for Davies thermalizing generators. We introduce the notion of maximal harmonic response and compute it exactly for a single qubit channel. Finally, we analyze linear response near dynamical phase transitions in quasi-free open quantum systems. It is found that the effect of the dynamical phase transition shows up in a peak at the edge of the spectrum in the imaginary part of the dynamical response function.
Relativistic models developed for the exclusive and inclusive QuasiElastic (QE) electron scattering have been extended to Charged-Current (CC) and Neutral-Current (NC) neutrino-nucleus scattering. The results of different descriptions of Final-State Interactions (FSI) are compared.
In this paper we propose the most general classification of point-like and line-like extrinsic topological defects in (2+1)-dimensional Abelian topological states. We first map generic extrinsic defects to boundary defects, and then provide a classification of the latter. Based on this classification, the most generic point defects can be understood as domain walls between topologically distinct boundary regions. We show that topologically distinct boundaries can themselves be classified by certain maximal subgroups of mutually bosonic quasiparticles, called Lagrangian subgroups. We study the topological properties of the point defects, including their quantum dimension, localized zero modes, and projective braiding statistics.
I review the status of the search for extremely metal-poor halo stars with the Hamburg/ESO objective-prism survey (HES). 2194 candidate metal-poor turn-off stars and 6133 giants in the magnitude range 14 < B < 17.5 have been selected from 329 (out of 380) HES fields, covering an effective area of 6400 square degrees in the southern extragalactic sky. Moderate-resolution follow-up observations for 3200 candidates have been obtained so far, and ~200 new stars with [Fe/H] <- 3.0 have been found, which trebles the total number of such extremely low-metallicity stars identified by all previous surveys.   We use VLT-UT2/UVES, Keck/HIRES, Subaru/HDS, TNG/SARG, and Magellan/MIKE for high-resolution spectroscopy of HES metal-poor stars. I provide an overview of the scientific aims of these programs, and highlight several recent results.
Making statistical predictions requires tackling two problems: one must assign appropriate probability distributions and then one must calculate a variety of expected values. The method of maximum entropy is commonly used to address the first problem. Here we explore its use to tackle the second problem. We show how this use of maximum entropy leads to the Bogoliuvob variational principle which we generalize, apply to density functional theory, and use it to develop a mean field theory for classical fluids. Numerical calculations for Argon gas are compared with experimental data.
In the powerful, high redshift radio galaxies, it is believed that the dominant source of ionization for the interstellar gas is the hard radiation field associated with the active nucleus. The photon source is generally external to the clouds being ionized and so the geometrical perspective from which the gas is observed and the presence and distribution of dust must be properly accounted for in the diagnostic process. In this paper, we examine the formation of the three strong lines: CIV$\lambda$1549, Ly$\alpha$ and CIII]$\lambda$1909 which are often observed in the nuclear and extended emission from these sources. We find that the observed trends, in particular the high CIV$\lambda$1549/Ly$\alpha$ ratio, are often better explained by geometrical (viewing angle) effects than by the presence of large quantities of dust either within or outside the excited clouds. We show that neutral condensations along the line-of-sight, by reflecting photons near the wavelength of Ly$\alpha$, can increase the observed CIV/Ly$\alpha$ ratio. The existence of HI absorption clouds (i.e., mirrors) external to the emission region leads also to the presence of large, diffuse haloes of what appears to be pure, narrow Ly$\alpha$ emission.
Much effort has been spent in recent years on restoring uniqueness of McKean-Vlasov SDEs with non-smooth coefficients. As a typical instance, the velocity field is assumed to be bounded and measurable in its space variable and Lipschitz-continuous with respect to the distance in total variation in its measure variable, see [Jourdain, Mishura-Veretennikov]. In contrast with those works, we consider in this paper a Fokker-Planck equation driven by an infinite-dimensional noise, inspired by the diffusion models on the Wasserstein space studied in [Konarovskyi, Marx]. We prove that well-posedness of that equation holds for a drift function that might be only bounded and measurable in its measure argument, provided that a trade-off is respected between the regularity in the finite-dimensional component and the regularity in the measure argument. In this regard, we show that the higher the regularity of b with respect to its space variable is, the lower regularity we have to assume on b with respect to its measure variable in order to restore uniqueness.
We verify the Invariance Conjectures of tautological equations in genus two. In particular, a uniform derivation of all known genus two equations is given.
We investigate the dependence of the local galaxy stellar-to-halo mass relation (SHMR) on galaxy morphology. We use data from the Sloan Digital Sky Survey DR7 with morphological classifications from Galaxy Zoo, and compare with the EAGLE cosmological simulation. At fixed halo mass in the mass range $10^{11.7}-10^{12.9}M_{\odot}$, the median stellar masses of SDSS disc galaxies are up to a factor of 1.4 higher than the median masses of their elliptical counterparts. However, when we switch from the stellar masses from Kauffmann et al. to those calculated by Chang et al. or Brinchmann et al., the median SHMR from discs and ellipticals coincide in this mass range. For halo masses larger than $10^{13}M_{\odot}$, discs are less massive than ellipticals in same-mass haloes, regardless of whose stellar mass estimates we use. However, we find that for these high halo masses the results for discs may be affected by central/satellite misclassifications. The EAGLE simulation predicts that discs are up to a factor of 1.5 more massive than elliptical galaxies residing in same-mass haloes less massive than $10^{13}M_{\odot}$, in agreement with the Kauffmann et al. data. Haloes with masses between $10^{11.5}$ and $10^{12}M_{\odot}$, that host disc galaxies, were assembled earlier than those hosting ellipticals. This suggests that the discs are more massive because they had more time for gas accretion and star formation. In $10^{12}-10^{12.5}M_{\odot}$ haloes, the central black holes in elliptical galaxies grew faster and became more massive than their counterparts in disc galaxies. This suggests that in this halo mass range the ellipticals are less massive because AGN feedback ejected more of the halo's gas reservoir, reducing star formation, and suppressing the (re)growth of stellar discs.
Treating the QCD Wilson loop as amplitude for the propagation of the first quantized particle we develop the second quantization of the same propagation. The operator of the particle position $\hat{\cal X}_{\mu}$ (the endpoint of the "open string") is introduced as a limit of the large $N$ Hermitean matrix. We then derive the set of equations for the expectation values of the vertex operators $\VEV{ V(k_1)\dots V(k_n)} $. The remarkable property of these equations is that they can be expanded at small momenta (less than the QCD mass scale), and solved for expansion coefficients. This provides the relations for multiple commutators of position operator, which can be used to construct this operator. We employ the noncommutative probability theory and find the expansion of the operator $\hat{\cal X}_\mu $ in terms of products of creation operators $ a_\mu^{\dagger}$. In general, there are some free parameters left in this expansion. In two dimensions we fix parameters uniquely from the symplectic invariance. The Fock space of our theory is much smaller than that of perturbative QCD, where the creation and annihilation operators were labelled by continuous momenta. In our case this is a space generated by $d = 4$ creation operators. The corresponding states are given by all sentences made of the four letter words. We discuss the implication of this construction for the mass spectra of mesons and glueballs.
The generalized Kneser graph $K(n,k,t)$ for integers $k>t>0$ and $n>2k-t$ is the graph whose vertices are the $k$-subsets of $\{1,\dots,n\}$ with two vertices adjacent if and only if they share less than $t$ elements. We determine the treewidth of the generalized Kneser graphs $K(n,k,t)$ when $t\ge 2$ and $n$ is sufficiently large compared to $k$. The imposed bound on $n$ is a significant improvement of a previously known bound. One consequence of our result is the following. For each integer $c\ge 1$ there exists a constant $K(c)\ge 2c$ such that $k\ge K(c)$ implies for $t=k-c$ that $$tw(K(n,k,t))=\binom{n}{k}-\binom{n-t}{k-t}-1$$ if and only if $n\ge (t+1)(k+1-t)$ .
We study magnetic order in the Heisenberg antiferromagnet on the checkerboard lattice, a two-dimensional version of the pyrochlore network with strong geometric frustration. By employing the semiclassical (1/S) expansion we find that quantum fluctuations of spins induce a long-range order that breaks the four-fold rotational symmetry of the lattice. The ordered phase is a valence-bond crystal. We discuss similarities and differences with the extreme quantum case S = 1/2 and find a useful phenomenology to describe the bond-ordered phases.
We present spatially-resolved dynamics for six strongly lensed star-forming galaxies at z=1.7-3.1, each enlarged by a linear magnification factor ~8. Using the Keck laser guide star AO system and the OSIRIS integral field unit spectrograph we resolve kinematic and morphological detail in our sample with an unprecedented fidelity, in some cases achieving spatial resolutions of ~100 pc. With one exception our sources have diameters ranging from 1-7 kpc, star formation rates of 2-40 Msun/yr (uncorrected for extinction) and dynamical masses of 10^(9.7-10.3) Msun. With this exquisite resolution we find that four of the six galaxies display coherent velocity fields consistent with a simple rotating disk model, which can only be recovered with the considerably improved spatial resolution and sampling from the combination of adaptive optics and strong gravitational lensing. Our model fits imply ratios for the systemic to random motion, V sin(i)/sigma, ranging from 0.5-1.3 and Toomre disk parameters Q<1. The large fraction of well-ordered velocity fields in our sample is consistent with data analyzed for larger, more luminous sources at this redshift. Our high resolution data further reveal that all six galaxies contain multiple giant star-forming HII regions whose resolved diameters are in the range 300 pc - 1.0 kpc, consistent with the Jeans length expected in the case of dispersion support. The density of star formation in these regions is ~100 times higher than observed in local spirals; such high values are only seen in the most luminous local starbursts. The global dynamics and demographics of star formation in these HII regions suggest that vigorous star formation is primarily governed by gravitational instability in primitive rotating disks.
Size effects on vibrational modes in complex crystals remain largely unexplored, despite their importance in a variety of electronic and energy conversion technologies. Enabled by advances in a four-probe thermal transport measurement method, we report the observation of glass-like thermal conductivity in ~20 nm thick single crystalline ribbons of higher manganese silicide, a complex, anisotropic crystal with a ~10 nm scale lattice constant along the incommensurate c axis. The boundary scattering effect is strong for many vibrational modes because of a strong anisotropy in their group velocities or diffusive nature, while confinement effects are pronounced for acoustic modes with long wavelengths along the c axis. Furthermore, the transport of the non-propagating, diffusive modes is suppressed in the nanostructures by the increased incommensurability between the two substructures as a result of the unusual composition of the nanostructure samples. These unique effects point to diverse, new approaches to suppressing the lattice thermal conductivity in complex materials.
The dynamics of a pair of coupled harmonic oscillators in separate or common thermal environments is studied, focusing on different indicators of quantumness, such as entanglement, twin oscillators correlations and quantum discord. We compare their decay under the effect of dissipation and show, through a phase diagram, that entanglement is more likely to survive asymptotically than twin oscillators correlations.
In the first part of this paper, traditional methods of studying Cepheids are summarized, mentioning Detre's contribution to this field. Then the new directions of Cepheid related research are reviewed with an emphasis on the problems concerning the period-luminosity relationship.
Nuclear mean-field models are briefly reviewed to illustrate its foundation and necessity of state dependence in effective interactions. This state dependence is successfully taken into account by the density dependence, leading to the energy density functional. Recent results for photoabsorption cross sections in spherical and deformed Nd isotopes are shown.
We study the existence theory of solutions of the kinetic Bohmian equation, a nonlinear Vlasov-type equation proposed for the phase-space formulation of Bohmian mechanics. Our main idea is to interpret the kinetic Bohmian equation as a Hamiltonian system defined on an appropriate Poisson manifold built on a Wasserstein space. We start by presenting an existence theory for stationary solutions of the kinetic Bohmian equation. Afterwards, we develop an approximative version of our Hamiltonian system in order to study its associated flow. We then prove existence of solutions of our approximative version. Finally, we present some convergence results for the approximative system, the aim being to establish that, in the limit, the approximative solution satisfies the kinetic Bohmian equation in a weak sense.
In this letter, I develop a new topologically invariant coherent state path integral for spin systems, and apply it to the quantum Heisenberg model on a square lattice. As a result, the quantum nonlinear $\sigma$ model for arbitrary values of spin can be directly obtained. The effective coupling constant and spin wave velocity are modified by $g_s= {2\over S}\sqrt{d+{T_\Lambda\over 2SJ}}$ and $c_s=2JSa \sqrt{d+{T_\Lambda\over 2SJ}}$, where $T_\Lambda$ is a natural temperature scale for the reliability of the theory. The formulation can also be extended to other generalized coherent state path integrals.
The goal of this paper is to derive signatures of synchrotron radiation from state-of-the-art simulation models of collimating relativistic magnetohydrodynamic (MHD) jets featuring a large-scale helical magnetic field. We perform axisymmetric special relativistic MHD simulations of the jet acceleration region using the PLUTO code. The computational domain extends from the slow magnetosonic launching surface of the disk up to 6000^2 Schwarzschild radii allowing to reach highly relativistic Lorentz factors. The Poynting dominated disk wind develops into a jet with Lorentz factors of 8 and is collimated to 1 degree. In addition to the disk jet, we evolve a thermally driven spine jet, emanating from a hypothetical black hole corona. Solving the linearly polarized synchrotron radiation transport within the jet, we derive VLBI radio and (sub-) mm diagnostics such as core shift, polarization structure, intensity maps, spectra and Faraday rotation measure (RM), directly from the Stokes parameters. We also investigate depolarization and the detectability of a lambda^2-law RM depending on beam resolution and observing frequency. We find non-monotonic intrinsic RM profiles which could be detected at a resolution of 100 Schwarzschild radii. In our collimating jet geometry, the strict bi-modality in polarization direction (as predicted by Pariev et al.) can be circumvented. Due to relativistic aberration, asymmetries in the polarization vectors across the jet can hint to the spin direction of the central engine.