ShantanuT01/DACTYL-Pretraining huggingface dataset:
Motivated by recent works on the origin of inertial mass, we revisit the relationship between the mass of charged particles and zero-point electromagnetic fields. To this end we first introduce a simple model comprising a scalar field coupled to stochastic or thermal electromagnetic fields. Then we check if it is possible to start from a zero bare mass in the renormalization process and express the finite physical mass in terms of a cut-off. In scalar QED this is indeed possible, except for the problem that all conceivable cut-offs correspond to very large masses. For spin-1/2 particles (QED with fermions) the relation between bare mass and renormalized mass is compatible with the observed electron mass and with a finite cut-off, but only if the bare mass is not zero; for any value of the cut-off the radiative correction is very small.
The Thirring model with imaginary mass (or the sine-Gordon model with imaginary coupling) is deeply related to all the flows between minimal conformal theories. We solve this model explicitely using the Bethe ansatz. We find that there are Left and Right moving massless excitations with non trivial LR scattering. We compute the S matrix and recover the result conjectured by Fendley et al.
We report on observational evidence of an extra-tidal clumpy structure around NGC 288 from an homogeneous coverage of a large area with the Pan-STARRS PS1 database. The extra-tidal star population has been disentangled from that of the Milky Way field by using a cleaning technique that successfully reproduced the stellar density, luminosity function and colour distributions of MW field stars. We have produced the cluster stellar density radial profile and a stellar density map from independent approaches, from which we found results in excellent agreement : the feature extends up to 3.5 times the cluster tidal radius. Previous works based on shallower photometric data sets have speculated on the existence of several long tidal tails, similar to that found in Pal 5. The present outcome shows that NGC 288 could hardly have such tails, but favours the notion that interactions with the MW tidal field has been a relatively inefficient process for stripping stars off the cluster. These results point to the need of a renewed overall study of the external regions of Galactic globular clusters (GGCs) in order to reliably characterise them. Hence, it will be possible to investigate whether there is any connection between detected tidal tails, extra-tidal stellar populations, extent diffuse halo-like structures with the GGCs' dynamical histories in the Galaxy.
We study truncated moment sequences of distribution mixtures, especially from Gaussian and log-normal distributions and their Carath\'eodory numbers. For $\mathsf{A} = \{a_1,\dots,a_m\}$ continuous (sufficiently differentiable) functions on $\mathbb{R}^n$ we give a general upper bound of $m-1$ and a general lower bound of $\left\lceil \frac{2m}{(n+1)(n+2)}\right\rceil$. For polynomials of degree at most $d$ in $n$ variables we find that the number of Gaussian and log-normal mixtures is bounded by the Carath\'eodory numbers in \cite{didio17Cara}. Therefore, for univariate polynomials $\{1,x,\dots,x^d\}$ at most $\left\lceil\frac{d+1}{2}\right\rceil$ distributions are needed. For bivariate polynomials of degree at most $2d-1$ we find that $\frac{3d(d-1)}{2}+1$ Gaussian distributions are sufficient. We also treat polynomial systems with gaps and find, e.g., that for $\{1,x^2,x^3,x^5,x^6\}$ 3 Gaussian distributions are enough for almost all truncated moment sequences. For log-normal distributions the number is bounded by half of the moment number. We give an example of continuous functions where more Gaussian distributions are needed than Dirac delta measures. We show that any inner truncated moment sequence has a mixture which contains any given distribution.
We construct in this paper a multi-brne model with Minkowski and AdS spacetime alternated in the fifth dimension and study the gravity on the brane of our universe. We will show that in this model there are both the graviton-like resonant states which generates the "quasi-localized gravity" and the resonant states of the massive KK mode. This model gives rise to gravity which deviates from the Newton gravitational potential at small and large scale which, however can be shown to be consistent with the observations in the absence of fine-tuning of the model parameters.
Knowledge of the elemental abundances of symbiotic giants is essential to address the role of chemical composition in the evolution of symbiotic binaries, to map their parent population, and to trace their mass transfer history. However, there are few symbiotic giants for which the photospheric abundances are fairly well determined. This is the second in a series of papers on chemical composition of symbiotic giants determined from high-resolution (R ~ 50000) near-IR spectra. Results are presented for the late-type giant star in the AE Ara, BX Mon, KX TrA, and CL Sco systems. Spectrum synthesis employing standard local thermal equilibrium (LTE) analysis and stellar atmosphere models were used to obtain photospheric abundances of CNO and elements around the iron peak (Sc, Ti, Fe, and Ni). Our analysis resulted in sub-solar metallicities in BX Mon, KX TrA, and CL Sco by [Fe/H] ~ -0.3 or -0.5 depending on the value of microturbulence. AE Ara shows metallicity closer to solar by ~0.2 dex. The enrichment in 14N isotope found in all these objects indicates that the giants have experienced the first dredge-up. In the case of BX Mon first dredge-up is also confirmed by the low 12C/13C isotopic ratio of ~8.
Let p be an odd prime. Let K = \Q(zeta) be the p-cyclotomic number field. Let v be a primitive root mod p and sigma : zeta --> zeta^v be a \Q-isomorphism of the extension K/\Q generating the Galois group G of K/\Q. For n in Z, the notation v^n is understood by v^n mod p with 1 \leq v^n \leq p-1. Let P(X) = \sum_{i=0}^{p-2} v^{-i}X^i \in \Z[X] be the Stickelberger polynomial. P(sigma) annihilates the class group C of K. There exists a polynomial Q(X) \in \Z[X] such that P(sigma)(sigma-v) = p\times Q(sigma) and such that Q(sigma) annihilates the p-class group C_p of K (the subgroup of exponent p of C). In the other hand sigma^{(p-1)/2}+1 annihilates the relative class group of K. The simultaneous application of these results brings some informations on the structure of the class group C, give some explicit congruences in \Z[v] mod p for the p-class group C_p of K and some explicit congruences in \Z[v] mod h for the h-class group of K for all the prime divisors h \not = p of the class number h(K). We detail at the end the case of class number of quadratic and biquadratic fields contained in the cyclotomic field K and give a general MAPLE algorithm.
A fundamental concept in physics is the Fermi surface, the constant-energy surface in momentum space encompassing all the occupied quantum states at absolute zero temperature. In 1960, Luttinger postulated that the area enclosed by the Fermi surface should remain unaffected even when electron-electron interaction is turned on, so long as the interaction does not cause a phase transition. Understanding what determines the Fermi surface size is a crucial and yet unsolved problem in strongly interacting systems such as high-$T_{c}$ superconductors. Here we present a precise test of the Luttinger theorem for a two-dimensional Fermi liquid system where the exotic quasi-particles themselves emerge from the strong interaction, namely for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs' Fermi wavevector down to very low electron densities, we show that the Luttinger theorem is obeyed over a significant range of interaction strengths, in the sense that the Fermi sea area is determined by the density of the \textit{minority carriers} in the lowest Landau level. Our data also address the ongoing debates on whether or not CFs obey particle-hole symmetry, and if they are Dirac particles. We find that particle-hole symmetry is obeyed, but the measured Fermi sea area differs quantitatively from that predicted by the Dirac model for CFs.
We present a brief, observational review about the study of the cooling behaviour of accretion-heated neutron stars and the inferences about the neutron-star crust and core that have been obtained from these studies. Accretion of matter during outbursts can heat the crust out of thermal equilibrium with the core and after the accretion episodes are over, the crust will cool down until crust-core equilibrium is restored. We discuss the observed properties of the crust cooling sources and what has been learned about the physics of neutron-star crusts. We also briefly discuss those systems that have been observed long after their outbursts were over, i.e, during times when the crust and core are expected to be in thermal equilibrium. The surface temperature is then a direct probe for the core temperature. By comparing the expected temperatures based on estimates of the accretion history of the targets with the observed ones, the physics of neutron-star cores can be investigated. Finally, we discuss similar studies performed for strongly magnetized neutron stars in which the magnetic field might play an important role in the heating and cooling of the neutron stars.
A number of experimental small-angle scattering (SAS) data are characterized by a succession of power-law decays with arbitrarily decreasing values of scattering exponents. To describe such data, here we develop a new theoretical model based on 3D fat fractals (sets with fractal structure, but nonzero volume) and show how one can extract structural information about the underlying fractal structure. We calculate analytically the monodisperse and polydisperse SAS intensity (fractal form factor and structure factor) of a newly introduced model of fat fractals and study its properties in momentum space. The system is a 3D deterministic mass fractal built on an extension of the well-known Cantor fractal. The model allows us to explain a succession of power-law decays and respectively, of generalized power-law decays (superposition of maxima and minima on a power-law decay) with arbitrarily decreasing scattering exponents in the range from zero to three. We show that within the model, the present analysis allows us to obtain the edges of all the fractal regions in the momentum space, the number of fractal iteration and the fractal dimensions and scaling factors at each structural level in the fractal. We applied our model to calculate an analytical expression for the radius of gyration of the fractal. The obtained quantities characterizing the fat fractal are correlated to variation of scaling factor with the iteration number.
In a recent paper [E. P. Pokatilov et al, PRB 65, 075316 (2002) the Raman selection rules in spherical nanocrystals with a degenerate valence band are analyzed. Some precisions are given here.
We combine the latest spectrally stacked data of 21-cm emission from the ALFALFA survey with an updated version of the Dark Sage semi-analytic model to investigate the relative contributions of secular and environmental astrophysical processes on shaping the HI fractions and quiescence of galaxies in the local Universe. We calibrate the model to match the observed mean HI fraction of all galaxies as a function of stellar mass. Without consideration of stellar feedback, disc instabilities, and active galactic nuclei, we show how the slope and normalisation of this relation would change significantly. We find Dark Sage can reproduce the relative impact that halo mass is observed to have on satellites' HI fractions and quiescent fraction. However, the model satellites are systematically gas-poor. We discuss how this could be affected by satellite--central cross-contamination from the group-finding algorithm applied to the observed galaxies, but that it is not the full story. From our results, we suggest the anti-correlation between satellites' HI fractions and host halo mass, seen at fixed stellar mass and fixed specific star formation rate, can be attributed almost entirely to ram-pressure stripping of cold gas. Meanwhile, stripping of hot gas from around the satellites drives the correlation of quiescent fraction with halo mass at fixed stellar mass. Further detail in the modelling of galaxy discs' centres is required to solidify this result, however. We contextualise our results with those from other semi-analytic models and hydrodynamic simulations.
Here $f(R)$-cosmology is discussed using a different approach. This model explains early-inflation, emergence of cosmic background radiation at the exit from inflation, cosmic deceleration during radiation-dominance followed by deceleration due to curvature-induced matter and acceleration in the very late universe due to curvature-induced phantom dark energy. This model predicts collapse in the future universe. Further, a possible avoidence of collapse as well as revival of very early universe is suggested.
Recently, the authors and de Wolff introduced the imaginary projection of a polynomial $f\in\mathbb{C}[\mathbf{z}]$ as the projection of the variety of $f$ onto its imaginary part, $\mathcal{I}(f) \ = \ \{\text{Im}(\mathbf{z}) \, : \, \mathbf{z} \in \mathcal{V}(f) \}$. Since a polynomial $f$ is stable if and only if $\mathcal{I}(f) \cap \mathbb{R}_{>0}^n \ = \ \emptyset$, the notion offers a novel geometric view underlying stability questions of polynomials. In this article, we study the relation between the imaginary projections and hyperbolicity cones, where the latter ones are only defined for homogeneous polynomials. Building upon this, for homogeneous polynomials we provide a tight upper bound for the number of components in the complement $\mathcal{I}(f)^{c}$ and thus for the number of hyperbolicity cones of $f$. And we show that for $n \ge 2$, a polynomial $f$ in $n$ variables can have an arbitrarily high number of strictly convex and bounded components in $\mathcal{I}(f)^{c}$.
We study the photoproduction of vector mesons off proton and off nuclear targets. We work within the colour dipole model in an approach that includes subnucleon degrees of freedom, so-called hot spots, whose positions in the impact-parameter plane change event-by-event. The key feature of our model is that the number of hot spots depends on the energy of the photon--target interaction. Predictions are presented for exclusive and dissociative production of $\rho^{0}$, $\mathrm{J/}\psi$, and $\Upsilon(1S)$ off protons, as well as for coherent and incoherent photoproduction of $\rho^{0}$ off nuclear targets, where Xe, Au, and Pb nuclei are considered. We find that the mass dependence of dissociative production off protons as a function of the energy of the interaction provides a further handle to search for saturation effects at HERA, the LHC and future colliders. We also find that the coherent photonuclear production of $\rho^{0}$ is sensitive to fluctuations in the subnucleon degrees of freedom at RHIC and LHC energies.
Convection in the cores of massive stars becomes anisotropic when they rotate. This anisotropy leads to a misalignment of the thermal gradient and the thermal flux, which in turn results in baroclinicity and circulation currents in the upper radiative zone. We show that this induces a much stronger meridional flow in the radiative zone than previously thought. This drives significantly enhanced mixing, though this mixing does not necessarily reach the surface. The extra mixing takes on a similar form to convective overshooting, and is relatively insensitive to the rotation rate above a threshold, and may help explain the large overshoot distances inferred from observations. This has significant consequences for the evolution of these stars by enhancing core-envelope mixing.
We report ambipolar transport properties in black phosphorus using an electric-double-layer transistor (EDLT) configuration. The transfer curve clearly exhibits ambipolar transistor behavior with an ON-OFF ratio of 5*10^3. The band gap was determined as = 0.35 eV from the transfer curve, and Hall-effect measurements revealed that the hole mobility was ~ 190 cm^2/Vs at 170 K, which is one order of magnitude larger than the electron mobility. By inducing an ultra-high carrier density of ~ 10^14 cm^-2, an electric-field-induced transition from the insulating state to the metallic state was realized, due to both electron and hole doping. Our results suggest that black phosphorus will be a good candidate for the fabrication of functional devices, such as lateral p-n junctions and tunnel diodes, due to the intrinsic narrow band gap.
We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method and a genera lization of virial theorem, which consists in scaling the wave function, we calculate the binding energies of the 1S, $2P^-$ and $3D^-$ levels. We compare the computed energy spectra with those obtained via a generalization of the mesh point technique as well as the shifted 1/N method. We show that the variational solutions present a very good behavior in the weak and strong magnetic field regimes.
The "Magnificent Seven" (M7) are a group of radio-quiet Isolated Neutron Stars (INSs) discovered in the soft X-rays through their purely thermal surface emission. Owing to the large inferred magnetic fields ($B\approx 10^{13}$ G), radiation from these sources is expected to be substantially polarised, independently on the mechanism actually responsible for the thermal emission. A large observed polarisation degree is, however, expected only if quantum-electrodynamics (QED) polarisation effects are present in the magnetised vacuum around the star. The detection of a strongly linearly polarised signal would therefore provide the first observational evidence of QED effects in the strong-field regime. While polarisation measurements in the soft X-rays are not feasible yet, optical polarisation measurements are within reach also for quite faint targets, like the M7 which have optical counterparts with magnitudes $\approx 26$--$28$. Here, we report on the measurement of optical linear polarisation for the prototype, and brightest member, of the class, RX\, J1856.5$-$3754 ($V\sim 25.5$), the first ever for one of the M7, obtained with the Very Large Telescope. We measured a polarisation degree $\mathrm{P.D.} =16.43\% \pm5.26\%$ and a polarisation position angle $\mathrm{P.A.}=145\fdg39\pm9\fdg44$, computed east of the North Celestial Meridian. The $\mathrm{P.D.}$ that we derive is large enough to support the presence of vacuum birefringence, as predicted by QED.
The Ewens-Pitman sampling model (EP-SM) is a distribution for random partitions of the set $\{1,\ldots,n\}$, with $n\in\mathbb{N}$, which is index by real parameters $\alpha$ and $\theta$ such that either $\alpha\in[0,1)$ and $\theta>-\alpha$, or $\alpha<0$ and $\theta=-m\alpha$ for some $m\in\mathbb{N}$. For $\alpha=0$ the EP-SM reduces to the celebrated Ewens sampling model (E-SM), which admits a well-known compound Poisson perspective in terms of the log-series compound Poisson sampling model (LS-CPSM). In this paper, we consider a generalization of the LS-CPSM, which is referred to as the negative Binomial compound Poisson sampling model (NB-CPSM), and we show that it leads to extend the compound Poisson perspective of the E-SM to the more general EP-SM for either $\alpha\in(0,1)$, or $\alpha<0$. The interplay between the NB-CPSM and the EP-SM is then applied to the study of the large $n$ asymptotic behaviour of the number of blocks in the corresponding random partitions, leading to a new proof of Pitman's $\alpha$ diversity. We discuss the proposed results, and conjecture that analogous compound Poisson representations may hold for the class of $\alpha$-stable Poisson-Kingman sampling models, of which the EP-SM is a noteworthy special case.
The time translation operator for neutrino mass states is often taken to be $e^{-iEt/\hbar}$. This is not relativistically invariant. In kaon mixing, physicists use $e^{-imc^2\tau/\hbar}$ where $\tau$ is the proper time of the kaon state. The factor $mc^2\tau$ is the rest frame value of the four vector product $p_\mu x^\mu$ which is an invariant quantity. If $-i p_\mu x^\mu$ is used in neutrino oscillation formulae instead of $-iEt$, the scale of the $\Delta m^2_{ij}$ is reduced by a factor of two.
We study the directed Abelian sandpile model on a square lattice, with $K$ downward neighbors per site, $K > 2$. The $K=3$ case is solved exactly, which extends the earlier known solution for the $K=2$ case. For $K>2$, the avalanche clusters can have holes and side-branches and are thus qualitatively different from the $K=2$ case where avalance clusters are compact. However, we find that the critical exponents for $K>2$ are identical with those for the $K=2$ case, and the large scale structure of the avalanches for $K>2$ tends to the $K=2$ case.
Top decays into a light Higgs boson and an up or charm quark can reach detectable levels in Standard Model extensions with two Higgs doublets or with new exotic quarks, and in the Minimal Supersymmetric Standard Model. Using both a standard and a neural network analysis we show that the CERN Large Hadron Collider will give 3 sigma evidence of decays with Br(t -> Hc) >= 6.5 10^-5 or set a limit Br(t -> Hc) <= 4.5 10^-5 with a 95% confidence level if these decays are not observed. We also consider limits obtained from single top production associated with a neutral Higgs boson.
The extension of Green's functions techniques to the complex energy plane provides access to fully dressed quasi-particle properties from a microscopic perspective. Using self-consistent ladder self-energies, we find both spectra and lifetimes of such quasi-particles in nuclear matter. With a consistent choice of the group velocity, the nucleon mean-free path can be computed. Our results indicate that, for energies above 50 MeV at densities close to saturation, a nucleon has a mean-free path of 4 to 5 femtometers.
We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By performing an eigenfunction decomposition, we reduce the problem to a system of linear ordinary differential equations which we are able to solve. The solutions are relevant to the characteristic formulation of numerical relativity: (a) as exact solutions against which computations of gravitational radiation can be compared; and (b) in formulating boundary conditions on the $r=2M$ Schwarzschild horizon.
Models in which the 750 GeV resonance ($S$) decays to two light axion-like particles (ALPs $a$), which in turn decay to collimated photons mimicking the observed signal, are motivated by Hidden Valley scenarios and could also provide a mechanism by which a $S \to \gamma \gamma$ signal persists while $S \to Z \gamma,\; ZZ$ and $WW$ remain subdued in the near future. We point out that these Hidden Valley like models invoking $S \to aa \to 4 \gamma$ must also contend with $Z \to a (\to \gamma \gamma) \gamma$ constraints coming from CDF and ATLAS. Within an effective field theory framework, we work out the constraints on the couplings of $S$ to $a$ and gauge bosons coming from photonic $Z$ decays and ensuring that the ALPs decay inside the electromagnetic calorimeter, in two regimes - where $a$ decays primarily to photons, and where $a$ also has hadronic branchings. The analysis is done for both when $S$ has a large as well as a narrow width, and for different relative contributions to the signal coming from $S \to \gamma \gamma$ and $a \to \gamma \gamma$. Results for the particular case where $S$ and $a$ belong to the same complex field are also presented. A $\gamma\gamma$ resonance at the $Z$-pole coming from $Z \to a \gamma$ is expected in this class of models. Taking benchmark ALP masses below around 0.4 GeV and, assuming reasonable values for the fake jet rate and the identification efficiency of the photon-jet, we find the prospects for the discovery of diphotons at the $Z$-pole.