ShantanuT01/DACTYL-Pretraining huggingface dataset:
In crystalline color superconductivity, quark pairs form at non-zero total momentum. This crystalline order potentially enlarges the domain of color superconductivity in cold dense quark matter. We present a perturbative calculation of the parameters governing the crystalline phase and show that this is indeed the case. Nevertheless, the enhancement is modest, and to lowest order is independent of the strength of the color interaction.
With the help of the Bohr--Sommerfeld quantization rule, the area spectrum of a charged, spherically symmetric spacetime is obtained by studying an adiabatic invariant action variable. The period of the Einstein-Maxwell system, which is related to the surface gravity of a given spacetime, is determined by the Kruskal--like coordinates.   It is shown that the area spectrum of the Reissner-Nordstr\"{o}m black hole is evenly spaced and the spacing is the same as that of a Schwarzschild black hole, which indicates that the area spectrum of a black hole is independent of its parameters. In contrast to the quasi-normal mode analysis, we do not impose the small charge limit as the general area gap $8\pi $ is obtained.
For the L2 supercritical generalized Korteweg-de Vries equation, we proved in a previous article the existence and uniqueness of an N-parameter family of N-solitons. Recall that, for any N given solitons, we call N-soliton a solution of the equation which behaves as the sum of these N solitons asymptotically as time goes to infinity. In the present paper, we also construct an N-parameter family of N-solitons for the supercritical nonlinear Schr\"odinger equation, in dimension 1 for the sake of simplicity. Nevertheless, we do not obtain any classification result; but recall that, even in subcritical and critical cases, no general uniqueness result has been proved yet.
We give a condition that ensures that a fibered category over a field admits a universal morphism to a profinite gerbe. This fundamental gerbe generalizes both Nori's fundamental group scheme and Deligne's relative fundamental groupoid. Using a simplified notion of essentially finite bundle, we also give a tannakian construction. As an application, we show how the fundamental gerbe enables to formulate a version of Grothendieck's section conjecture in arbitrary characteristic. We then study various natural quotients of the fundamental gerbe.
We calculate form factors of half-BPS operators in N=4 super Yang-Mills theory at tree level and one loop using novel applications of recursion relations and unitarity. In particular, we determine the expression of the one-loop form factors with two scalars and an arbitrary number of positive-helicity gluons. These quantities resemble closely the MHV scattering amplitudes, including holomorphicity of the tree-level form factor, and the expansion in terms of two-mass easy box functions of the one-loop result. Next, we compare our result for these form factors to the calculation of a particular periodic Wilson loop at one loop, finding agreement. This suggests a novel duality relating form factors to periodic Wilson loops.
We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move sub-diffusively, such that the mean square displacement of each trap grows as $t^{\gamma}$ with $0\leq \gamma \leq 1$. Starting from a continuous time random walk (CTRW) description of the motion of the particle and of the traps, we derive lower and upper bounds for $P(t)$ and show that for $\gamma \leq 2/(d+2)$ these bounds coincide asymptotically, thus determining asymptotically exact results. The asymptotic decay law in this regime is exactly that obtained for immobile traps. This means that for sufficiently subdiffusive traps, the moving $A$ particle sees the traps as essentially immobile, and Lifshitz or trapping tails remain unchanged. For $\gamma > 2/(d+2)$ and $d\leq 2$ the upper and lower bounds again coincide, leading to a decay law equal to that of a stationary particle. Thus, in this regime the moving traps see the particle as essentially immobile. For $d>2$, however, the upper and lower bounds in this $\gamma$ regime no longer coincide and the decay law for the survival probability of the $A$ particle remains ambiguous.
TeV $\gamma$-ray detections in flaring states without activity in X-rays from blazars have attracted much attention due to the irregularity of these "orphan" flares. Although the synchrotron self-Compton model has been very successful in explaining the spectral energy distribution and spectral variability of these sources, it has not been able to describe these atypical flaring events. On the other hand, an electron-positron pair plasma at the base of the AGN jet was proposed as the mechanism of bulk acceleration of relativistic outflows. This plasma in quasi-themal equilibrium called Wein fireball emits radiation at MeV-peak energies serving as target of accelerated protons. In this work we describe the "orphan" TeV flares presented in blazars 1ES 1959+650 and Mrk421 assuming geometrical considerations in the jet and evoking the interactions of Fermi-accelerated protons and MeV-peak target photons coming from the Wein fireball. After describing successfully these "orphan" TeV flares, we correlate the TeV $\gamma$-ray, neutrino and UHECR fluxes through p$\gamma$ interactions and calculate the number of high-energy neutrinos and UHECRs expected in IceCube/AMANDA and TA experiment, respectively. In addition, thermal MeV neutrinos produced mainly through electron-positron annihilation at the Wein fireball will be able to propagate through it. By considering two- (solar, atmospheric and accelerator parameters) and three-neutrino mixing, we study the resonant oscillations and estimate the neutrino flavor ratios as well as the number of thermal neutrinos expected on Earth.
We investigate the relation of the stellar initial mass function (IMF) and the dense core mass function (CMF), using stellar masses and positions in 14 well-studied young groups. Initial column density maps are computed by replacing each star with a model initial core having the same star formation efficiency (SFE). For each group the SFE, core model, and observational resolution are varied to produce a realistic range of initial maps. A clumpfinding algorithm parses each initial map into derived cores, derived core masses, and a derived CMF. The main result is that projected blending of initial cores causes derived cores to be too few and too massive. The number of derived cores is fewer than the number of initial cores by a mean factor 1.4 in sparse groups and 5 in crowded groups. The mass at the peak of the derived CMF exceeds the mass at the peak of the initial CMF by a mean factor 1.0 in sparse groups and 12.1 in crowded groups. These results imply that in crowded young groups and clusters, the mass distribution of observed cores may not reliably predict the mass distribution of protostars which will form in those cores.
The visual A component of the Gliese 586AB system is a double-lined spectroscopic binary consisting of two cool stars with the exceptional orbital eccentricity of 0.976. Such an extremely eccentric system may be important for our understanding of low-mass binary formation. We present a total of 598 high-resolution echelle spectra from our robotic facility STELLA from 2006-2012 which we used to compute orbital elements of unprecedented accuracy. The orbit constrains the eccentricity to 0.97608+/-0.00004 and the orbital period to 889.8195+/-0.0003d. The masses of the two components are 0.87+/-0.05 Msun and 0.58+/-0.03 Msun if the inclination is 5+/-1.5degr as determined from adaptive-optics images, that is good to only 6% due to the error of the inclination although the minimum masses reached a precision of 0.3%. The flux ratio Aa:Ab in the optical is betwee n 30:1 in Johnson-B and 11:1 in I. Radial velocities of the visual B-component (K0-1V) appear constant to within 130 m/s over six years. Sinusoidal modulations of Teff of Aa with an amplitude of apprx 55 K are seen with the orbital period. Component Aa appears warmest at periastron and coolest at apastron, indicating atmospheric changes induced by the high orbital eccentricity. No light variations larger than approximately 4 mmag are detected for A, while a photometric period of 8.5+/-0.2 d with an amplitude of 7 mmag is discovered for the active star B, which we interpret to be its rotation period. We estimate an orbital period of approx 50,000 yr for the AB system. The most likely age of the AB system is >=2 Gyr, while the activity of the B component, if it were a single star, would imply 0.5 Gyr. Both Aa and B are matched with single-star evolutionary tracks of their respective mass.
The sextic oscillator is proposed as a two-parameter solvable $\gamma$-independent potential in the Bohr Hamiltonian. It is shown that closed analytical expressions can be derived for the energies and wavefunctions of the first few levels and for the strength of electric quadrupole transitions between them. Depending on the parameters this potential has a minimum at $\beta=0$ or at $\beta>0$, and might also have a local maximum before reaching its minimum. A comparison with the spectral properties of the infinite square well and the $\beta^4$ potential is presented, together with a brief analysis of the experimental spectrum and E2 transitions of the $^{134}$Ba nucleus.
Contrary to common belief, there are perspectives for generalizing the notion of positive and negative frequency in minisuperspace quantum cosmology, even when the wave equation does not admit symmetries. We outline a strategy in doing so when the potential is positive. Also, an underlying unitarity structure shows up. Starting in the framework of the Klein-Gordon type quantization, I am led to a result that relies on global features on the model, and that is possibly related to structures encountered in the refined algebraic quantization scheme.
In this paper we discuss applications of our earlier work in studying certain Galois groups and splitting fields of rational functions in $\mathbb Q\left(X_0(N)\right)$ using Hilbert's irreducibility theorem and modular forms. We also consider computational aspect of the problem using MAGMA and SAGE.
We extend the well-known static duality \cite{girardeau1960relationship, cheon1999fermion} between 1-D Bosons and 1-D Fermions to the dynamical version. By utilizing this dynamical duality we find the duality of non-equilibrium work distributions between interacting 1-D bosonic (Lieb-Liniger model) and 1-D fermionic (Cheon-Shigehara model) systems with dual contact interactions. As a special case, the work distribution of the Tonks-Girardeau (TG) gas is identical to that of 1-D free fermionic system even though their momentum distributions are significantly different. In the classical limit, the work distributions of Lieb-Liniger models (Cheon-Shigehara models) with arbitrary coupling strength converge to that of the 1-D noninteracting distinguishable particles, although their elemetary excitations (quasi-particles) obey different statistics, e.g. the Bose-Einstein, the Fermi-Dirac and the fractional statistics. We also present numerical results of the work distributions of Lieb-Liniger model with various coupling strengths, which demonstrate the convergence of work distributions in the classical limit.
We report the initial results from an ongoing multi-year spectroscopic survey of novae in M33. The survey resulted in the spectroscopic classification of six novae (M33N 2006-09a, 2007-09a, 2009-01a, 2010-10a, 2010-11a, and 2011-12a) and a determination of rates of decline (t_2 times) for four of them (2006-09a, 2007-09a, 2009-01a, and 2010-10a). When these data are combined with existing spectroscopic data for two additional M33 novae (2003-09a and 2008-02a) we find that 5 of the 8 novae with available spectroscopic class appear to be members of either the He/N or Fe IIb (hybrid) classes, with only two clear members of the Fe II spectroscopic class. This initial finding is very different from what would be expected based on the results for M31 and the Galaxy where Fe II novae dominate, and the He/N and Fe IIb classes together make up only ~20% of the total. It is plausible that the increased fraction of He/N and Fe IIb novae observed in M33 thus far may be the result of the younger stellar population that dominates this galaxy, which is expected to produce novae that harbor generally more massive white dwarfs than those typically associated with novae in M31 or the Milky Way.
Recent results based on the analysis of radio galaxies and their hot X-ray emitting atmospheres suggest that non-radiating particles dominate the energy budget in the lobes of FRI radio galaxies, in some cases by a factor of more than 1000, while radiating particles dominate the energy budget in FRII radio galaxy lobes. This implies a significant difference in the radiative efficiency of the two morphological classes. To test this hypothesis, we have measured the kinetic energy flux for a sample of 3C FRII radio sources using a new method based on the observed parameters of the jet terminal hotspots, and compared the resulting Q(jet) - L(radio) relation to that obtained for FRI radio galaxies based on X-ray cavity measurements. Contrary to expectations, we find approximate agreement between the Q(jet) - L(radio) relations determined separately for FRI and FRII radio galaxies. This result is ostensibly difficult to reconcile with the emerging scenario in which the lobes of FRI and FRII radio galaxies have vastly different energy budgets. However, a combination of lower density environment, spectral ageing and strong shocks driven by powerful FRII radio galaxies may reduce the radiative efficiency of these objects relative to FRIs and couteract, to some extent, the higher radiative efficiency expected to arise due to the lower fraction of energy in non-radiating particles. An unexpected corollary is that extrapolating the Q(jet) - L(radio) relation determined for low power FRI radio galaxies provides a reasonable approximation for high power sources, despite their apparently different lobe compositions.
We study the Cauchy problem for the parabolic infinity Laplace equation. We prove a new comparison principle and obtain uniqueness of viscosity solutions in the class of functions with a polinomial growth at infinity, improving previous results obtained assuming a linear growth.
In relativistic, Poynting dominated outflows, acceleration and collimation are intimately connected. An important point is that the Lorentz force is nearly compensated by the electric force therefore the acceleration zone spans a large range of scales. We derived the asymptotic equations describing relativistic, axisymmetric MHD flows far beyond the light cylinder. These equations do not contain either intrinsic small scales (like the light cylinder radius) or terms that nearly cancel each other (like the electric and magnetic forces) therefore they could be easily solved numerically. They also suit well for qualitative analysis of the flow and in many cases, they could even be solved analytically or semi-analytically. We show that there are generally two collimation regimes. In the first regime, the residual of the hoop stress and the electric force is counterbalanced by the pressure of the poloidal magnetic field so that at any distance from the source, the structure of the flow is the same as the structure of an appropriate cylindrical equilibrium configuration. In the second regime, the pressure of the poloidal magnetic field is negligible small so that the flow could be conceived as composed from coaxial shrinking magnetic loops. In the two collimation regimes, the flow is accelerated in different ways. We study in detail the structure of jets confined by the external pressure with a power law profile. In particular, we obtained simple scalings for the extent of the acceleration zone, for the terminal Lorentz factor and for the collimation angle.
We study the thermodynamic properties of an ideal gas of fermions in a harmonic oscillator confining potential. The analogy between this problem and the de Haas-van Alphen effect is discussed and used to obtain analytical results for the chemical potential and specific heat in the case of both isotropic and anisotropic potentials. Step-like behaviour in the chemical potential, first noted in numerical studies, is obtained analytically and shown to result in an oscillatory behaviour of the specific heat when the particle number is varied. The origin of these oscillations is that part of the thermodynamic potential responsible for the de Haas-van Alphen-type effect. At low temperatures we show analytically that there are significant deviations in the specific heat from the expected linear temperature dependence, again as a consequence of the de Haas-van Alphen part of the thermodynamic potential. Results are given for one, two, and three spatial dimensions. In the anisotropic case we show how the specific heat jumps as the ratio of oscillator frequencies varies.
Under zero magnetic field, a quadrupolar order parameter at q_Q=(1/2,1/2,1/2) in a typical antiferro-quadrupole (AFQ) ordering compound CeB6 has been observed for the first time by means of a resonant X-ray scattering (RXS) te\ chnique. The RXS is observed at the 2p->5d dipole transition energy of the Ce L3-edge. Using this RXS technique to observe the pure order parameter of the AFQ state, the magnetic phase diagram of Phase II is first determined.
We describe a program to measure surface brightness fluctuation (SBF) distances to galaxies observed in the Next Generation Virgo Cluster Survey (NGVS), a photometric imaging survey covering $104~deg^2$ of the Virgo cluster in the ${u}^*,g,i,z$ bandpasses with the Canada-France Hawaii Telescope. We describe the selection of the sample galaxies, the procedures for measuring the apparent $i$-band SBF magnitude $\bar{i}$, and the calibration of the absolute $\bar{M}_i$ as a function of observed stellar population properties. The multi-band NGVS data set provides multiple options for calibrating the SBF distances, and we explore various calibrations involving individual color indices as well as combinations of two different colors. Within the color range of the present sample, the two-color calibrations do not significantly improve the scatter with respect to wide-baseline, single-color calibrations involving $u^{*}$. We adopt the ${u}^*{-}z$ calibration as reference for the present galaxy sample, with an observed scatter of 0.11 mag. For a few cases that lack good ${u}^*$ photometry, we use an alternative relation based on a combination of $g{-}i$ and $g{-}z$ colors, with only a slightly larger observed scatter of 0.12 mag. The agreement of our measurements with the best existing distance estimates provides confidence that our measurements are accurate. We present a preliminary catalog of distances for 89 galaxies brighter than $B_T\approx13.0$ mag within the survey footprint, including members of the background M and W Clouds at roughly twice the distance of the main body of the Virgo cluster. The extension of the present work to fainter and bluer galaxies is in progress.
Dynamic second-order nonlinear susceptibilities, $\chi^{(2)}(2\omega,\omega,\omega)\equiv \chi^{(2)}(\omega)$, are calculated here within a fully first-principles scheme for monolayered molybdenum dichalcogenides, $2H$-MoX$_2$ (X=S,Se,Te). The absolute values of $\chi^{(2)}(\omega)$ across the three chalcogens critically depend on the band gap energies upon uniform strain, yielding the highest $\chi^{(2)}(0)\sim$ 140 pm/V for MoTe$_2$ in the static limit. Under this uniform in-plane stress, $2H$-MoX$_2$ can undergo direct-to-indirect transition of band gaps, which in turn substantially affects $\chi^{(2)}(\omega)$. The tunability of $\chi^{(2)}(\omega)$ by either compressive or tensile strain is demonstrated especially for two important experimental wavelengths, 1064 nm and 800 nm, where resonantly enhanced non-linear effects can be exploited: $\chi^{(2)}$ of MoSe$_2$ and MoTe$_2$ approach $\sim$800 pm/V with -2\% strain at 1064 nm.
We investigated theoretically the effect of covalent edge functionalization, with organic functional groups, on the electronic properties of graphene nanostructures and nano-junctions. Our analysis shows that functionalization can be designed to tune electron affinities and ionization potentials of graphene flakes, and to control the energy alignment of frontier orbitals in nanometer-wide graphene junctions. The stability of the proposed mechanism is discussed with respect to the functional groups, their number as well as the width of graphene nanostructures. The results of our work indicate that different level alignments can be obtained and engineered in order to realize stable all-graphene nanodevices.
Bloch's conjecture for a surface $X$ over an algebraically closed field $k$ states that every homologically trivial correspondence $\Gamma $ acts as 0 on the Albanese kernel $T(X_{\Omega})$, where $\Omega $ is a universal domain containing $k$. Here we prove that, for a complex K3 surface $X$, Bloch's conjecture is equivalent to the existence of a valence for every correspondence. We also give applications of this result to the case of a correspondence associated to an automorphisms of finite order and to the existence of constant cycle curves on $X$. Finally we show that Franchetta's conjecture, as stated by K.O'Grady, holds true for the family of polarized K3 surfacees of genus $g$, if $ 3 \le g \le 6$
Current 6D object pose methods consist of deep CNN models fully optimized for a single object but with its architecture standardized among objects with different shapes. In contrast to previous works, we explicitly exploit each object's distinct topological information i.e. 3D dense meshes in the pose estimation model, with an automated process and prior to any post-processing refinement stage. In order to achieve this, we propose a learning framework in which a Graph Convolutional Neural Network reconstructs a pose conditioned 3D mesh of the object. A robust estimation of the allocentric orientation is recovered by computing, in a differentiable manner, the Procrustes' alignment between the canonical and reconstructed dense 3D meshes. 6D egocentric pose is then lifted using additional mask and 2D centroid projection estimations. Our method is capable of self validating its pose estimation by measuring the quality of the reconstructed mesh, which is invaluable in real life applications. In our experiments on the LINEMOD, OCCLUSION and YCB-Video benchmarks, the proposed method outperforms state-of-the-arts.