ShantanuT01/DACTYL-Pretraining huggingface dataset:
Due to the internal structure of the nucleon, we should expect, in general, that the effective meson nucleon parameters may change in nuclear medium. We study such changes by using a chiral confining model of the nucleon. We use density-dependent masses for all mesons except the pion. Within a Dirac-Brueckner analysis, based on the relativistic covariant structure of the NN amplitude, we show that the effect of such a density dependence in the NN interaction on the saturation properties of nuclear matter, while not large, is quite significant. Due to the density dependence of the $g_{\sigma NN}$, as predicted by the chiral confining model, we find, in particular, a looping behavior of the binding energy at saturation as a function of the saturation density. A simple model is described, which exhibits looping and which is shown to be mainly caused by the presence of a peak in the density dependence of the medium modified $\sigma N$ coupling constant at low density.   The effect of density dependence of the coupling constants and the meson masses tends to improve the results for $E/A$ and density of nuclear matter at saturation. From the present study we see that the relationship between binding energy and saturation density may not be as universal as found in nonrelativistic studies and that more model dependence is exhibited once medium modifications of the basic nuclear interactions are considered.
Let $s_a(n)$ denote the sum of digits of an integer $n$ in the base $a$ expansion. Answering, in a extended form, a question of Deshouillers, Habsieger, Laishram, and Landreau, we show that, provided $a$ and $b$ are multiplicatively independent, any positive real number is a limit point of the sequence $\{s_b(n)/s_a(n)\}_{n=1}^{\infty}$. We also provide upper and lower bounds for the counting functions of the corresponding subsequences.
We prove an asymptotic Cram\'er's theorem, that is, if the sequence $(X_{n}+ Y_{n})_{n\geq 1}$ converges in law to the standard normal distribution and for every $n\geq 1$ the random variables $X_{n}$ and $Y_{n}$ are independent, then $(X_{n})_{n\geq 1}$ {\it and } $(Y_{n}) _{n\geq 1}$ converge in law to a normal distribution. Then we compare this result with recent criteria for the central convergence obtained in terms of Malliavin derivatives.
The two--dimensional topological BF model is considered in the Landau gauge in the framework of perturbation theory. Due to the singular behaviour of the ghost propagator at long distances, a mass term to the ghost fields is introduced as infrared regulator. Relying on the supersymmetric algebraic structure of the resulting massive theory, we study the infrared and ultraviolet renormalizability of the model, with the outcome that it is perturbatively finite.
By considering a set of $N$ anyonic oscillators ( non-local, intrinsic two-dimensional objects interpolating between fermionic and bosonic oscillators) on a two-dimensional lattice, we realize the $SU_q(N)$ quantum algebra by means of a generalized Schwinger construction. We find that the deformation parameter $q$ of the algebra is related to the anyonic statistical parameter $\nu$ by $q=exp({\rm i}\pi\nu)$.
The most complete list of visual binary systems with known orbital elements is compiled. It is based on OARMAC and ORB6 data and contains 3139 orbits for 2278 pairs. A refined subset of high quality orbits with available distance was also compiled. Relations between and distributions along different observational parameters are constructed, and an analysis of selection effects is made. Dynamical, photometric and spectral masses of systems are estimated, and reasons for discrepancies between them are discussed.
Future neutron-antineutron ($n$-$\bar n$) oscillation experiments, such as at the European Spallation Source and the Deep Underground Neutrino Experiment, aim to find first evidence of baryon number violation. We investigate implications of an improved $n$-$\bar n$ oscillation search for baryogenesis via interactions of $n$-$\bar n$ mediators, parameterized by an effective field theory (EFT). We find that even in a minimal EFT setup, there is overlap between the parameter space probed by $n$-$\bar n$ oscillation and the region that can realize the observed baryon asymmetry of the universe. The mass scales of exotic new particles are in the TeV-PeV regime, inaccessible at the LHC or its envisioned upgrades. Given the innumerable high energy theories that can match to, or resemble, the minimal EFT that we discuss, future $n$-$\bar n$ oscillation experiments could probe many viable theories of baryogenesis beyond the reach of other experiments.
We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such system and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states.
In this paper infinite families of examples of irreducible free and nearly free curves in the complex projective plane which are not rational curves and whose local singularites can have an arbitrary number of branches are given. All these examples answer negatively to some conjectures proposed by A. Dimca and G. Sticlaru. Our examples say nothing about the most remarkable conjecture by A. Dimca and G. Sticlaru, i.e. every rational cuspidal plane curve is either free or nearly free.
One of the most prominent characteristics of two-dimensional Quantum Hall systems are chiral edge modes. Their existence is a consequence of the bulk-boundary correspondence and their stability guarantees the quantization of the transverse conductance. In this work, we study two microscopic models, the Hofstadter lattice model and an extended version of Haldane's Chern insulator. Both models host Quantum Hall phases in two dimensions. We transfer them to lattice implementations of fractals with a dimension between one and two and study the existence and robustness of their edge states. Our main observation is that, contrary to their two-dimensional counterpart, there is no universal behavior of the edge modes in fractals. Instead, their presence and stability critically depends on details of the models and the lattice realization of the fractal.
We use 15 years of $\gamma$-ray data from INTEGRAL/SPI in a refined investigation of the morphology of the Galactic bulge positron annihilation signal. Our spatial analysis confirms that the signal traces the old stellar population in the bulge and reveals for the first time that it traces the boxy bulge and nuclear stellar bulge. Using a 3D smoothing kernel, we find that the signal is smeared out over a characteristic length scale of $150 \pm 50\,$pc, suggesting either annihilation in situ at astrophysical sources kicked at formation or positron propagation away from sources. The former is disfavoured by its requiring kick velocities different between the Galactic nucleus ($\gtrsim 50\,\mathrm{km\,s^{-1}}$) and wider bulge ($\lesssim 15\,\mathrm{km\,s^{-1}}$) source. Positron propagation prior to annihilation can explain the overall phenomenology of the 511 keV signal for positrons injection energies $\lesssim 1.4\,$MeV, suggesting a nucleosynthesis origin.
This is the first in a series of papers describing the {\it Optical Redshift Survey} (ORS), a redshift survey of optically selected galaxies covering 98\% of the sky above $|b| = 20^\circ$ (8.09 ster). The survey is drawn from the UGC, ESO, and ESGC galaxy catalogues, and contains two sub-samples, one complete to a $B$ magnitude of 14.5, the other complete to a $B$ major axis diameter of $1.9^\prime$. The entire sample consists of 8457 objects, of which redshifts are now available for 8286; 171 objects remain without measured redshifts. The ORS provides the most detailed and homogeneous sampling of the large-scale galaxy distribution to date in these areas. The density field of bright optical galaxies is well-defined to $8000 \kms$, and is dominated by the Virgo, Telescopium-Pavo-Indus, Hydra-Centaurus, Pisces-Perseus, and Coma-A1367 Superclusters. The dense sampling provided by ORS allows a detailed analysis of the galaxy density field, and will be used to test its dependence on morphology and other galaxy parameters.
Let $\Omega$ be a bounded domain of $\mathbb{R}^N$ whose boundary is a $\mathbb{C}^2$ compact manifolds. In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we adopted powers of the distance function $\delta(x)$ to the boundary $\partial\Omega$.
By the geometry of the 3-fold quadric we show that the coarse moduli space of genus g ineffective spin hyperelliptic curves with two marked points is a rational variety for every $g \geq 2$.
The \textit{Spitzer}/Infrared Spectrograph spectra of three spectroscopically anomalous galaxies (IRAS~F10398+1455, IRAS~F21013-0739 and SDSS~J0808+3948) are modeled in terms of a mixture of warm and cold silicate dust, and warm and cold carbon dust. Their unique infrared (IR) emission spectra are characterized by a steep $\simali$5--8$\mum$ emission continuum, strong emission bands from polycyclic aromatic hydrocarbon (PAH) molecules, and prominent silicate emission. The steep $\simali$5--8$\mum$ emission continuum and strong PAH emission features suggest the dominance of starbursts, while the silicate emission is indicative of significant heating from active galactic nuclei (AGNs). With warm and cold silicate dust of various compositions ("astronomical silicate," amorphous olivine, or amorphous pyroxene) combined with warm and cold carbon dust (amorphous carbon, or graphite), we are able to closely reproduce the observed IR emission of these %spectroscopically anomalous galaxies. We find that the dust temperature is the primary cause in regulating the steep $\sim$5--8$\mum$ continuum and silicate emission, insensitive to the exact silicate or carbon dust mineralogy and grain size $a$ as long as $a\simlt1\mum$. More specifically, the temperature of the $\simali$5--8$\mum$ continuum emitter (which is essentially carbon dust) of these galaxies is $\sim$250--400$\K$, much lower than that of typical quasars which is $\sim$640$\K$. Moreover, it appears that larger dust grains are preferred in quasars. The lower dust temperature and smaller grain sizes inferred for these three galaxies compared with that of quasars could be due to the fact that they may harbor a young/weak AGN which is not maturely developed yet.
We discuss the theory of jet events in high-energy photon-proton interactions using a model which gives a good description of the data available on total inelastic $\gamma p$ cross sections up to $\sqrt{s}$=210 GeV. We show how to calculate the jet cross sections and jet multiplicities and give predictions for these quantities for energies appropriate for experiments at the HERA $ep$ collider and for very high energy cosmic ray observations.
We study the competition between a random potential and a commensurate potential on interacting fermionic and bosonic systems using a variety of methods. We focus on one dimensional interacting fermionic systems but higher dimensional bosonic and fermionic extensions, as well as classical equivalents are also discussed. Our methods which include bosonization, replica variational method, functional renormalization group (RG) and perturbation around the atomic limit, go beyond conventional perturbative expansions around the Luttinger liquid in one dimension. All these methods agree on the prediction in these systems of a phase, the Mott glass, intermediate between the Anderson Insulator (compressible, with a pseudogap in the optical conductivity) and the Mott Insulator (incompressible with a gap in the optical conductivity). The Mott glass, which was unexpected from a perturbative renormalization group point of view has a pseudogap in the conductivity while remaining incompressible. Having derived the existence of the Mott Glass phase in one dimension, we show qualitatively that its existence can also be expected in higher dimension. We discuss the relevance of this phase to experimental systems such as disordered classical elastic systems and dirty bosons.
We describe a microcanonical approach for polymer models that combines atmospheric methods with urn theory. We show that Large Deviation Properties of urn models can provide quite deep mathematical insight by analyzing the Random Walk Range problem in $\mathbb{Z}^{d}$. We also provide a new mean field theory for the Range Problem that is exactly solvable by analogy with the Bagchi-Pal urn model.
The inverse first-passage problem for a Wiener process $(W_t)_{t\ge0}$ seeks to determine a function $b{}:{}\mathbb{R}_+\to\mathbb{R}$ such that \[\tau=\inf\{t>0| W_t\ge b(t)\}\] has a given law. In this paper two methods for approximating the unknown function $b$ are presented. The errors of the two methods are studied. A set of examples illustrates the methods. Possible applications are enlighted.
We have been using Keck laser guide star adaptive optics to monitor the orbits of ultracool binaries, providing dynamical masses at lower luminosities and temperatures than previously available and enabling strong tests of theoretical models. (1) We find that model color-magnitude diagrams cannot reliably be used to infer masses as they do not accurately reproduce the colors of ultracool dwarfs of known mass. (2) Effective temperatures inferred from evolutionary model radii can be inconsistent with temperatures derived from fitting observed spectra with atmospheric models by at most 100-300 K. (3) For the single pair of field brown dwarfs with a precise mass (3%) and age determination (~25%), the measured luminosities are ~2-3x higher than predicted by model cooling rates (masses inferred from Lbol and age are 20-30% larger than measured). Finally, as the sample of binaries with measured orbits grows, novel tests of brown dwarf formation theories are made possible (e.g., testing theoretical eccentricity distributions).
We investigate the optical spectral region of spectra of 1000 stars searching for IMF-sensitive features to constrain the low-mass end of the initial mass function (IMF) slope in elliptical galaxies. We use the MILES stellar library in the wavelength range [3500-7500] {\AA} to select indices that are sensitive to cool dwarf stars and that only weakly depend on age and metallicity. In this wavelength range, the response of a change in the effective temperature of the cool red giant population is similar to the response of a change in the number of dwarf stars in the galaxy. We investigate the degeneracy between IMF variation and Teff,RGB and show that it is possible to break it with the new IMF indicators defined here. In particular, we define a CaH1 index around {\lambda}6380 {\AA} that arises purely from cool dwarfs, does not strongly depend on age and is anti-correlated with [a/Fe]. This index allows the determination of the the IMF slope when combined with TiO lines and age- and metallicity-dependent features. The use of several indicators is crucial to break degeneracies between IMF, age, abundance pattern and Teff of the RGB population. We measure line-index strengths of the optical IMF indicators in the SSP models and compare these with index strengths of the same features in stacked SSDSS early-type galaxy spectra with varying velocity dispersions. Using 10 different indicators, we find a clear trend of a steepening IMF with increasing velocity dispersion described by the equation x=(2.3+-0.1)*log{\sigma}200+(2.13+-0.15), where x is the IMF slope and {\sigma}200 is the central stellar velocity dispersion measured in units of 200km/s. We compute the 'IMF mismatch' parameter as the ratio of stellar mass-to-light ratio predicted from the x-{\sigma}200 relation to that inferred from SSP models assuming a Salpeter IMF and find good agreement with independent published results.
General conditions in which disordered, spin liquid, and valence-bond ordered phases occur in quantum Ising antiferromagnets are studied using the prototype Kagome lattice spin models. A range of quantum dynamical processes in the Ising model, with and without total Ising spin conserved, are analytically shown to yield all three characteristic quantum paramagnetic phases in the Kagome system. Special emphasis is given to the XXZ model that can be sensibly compared to the Kagome lattice Heisenberg antiferromagnet. It is explicitly demonstrated that the total-spin-conserving dynamics can yield a resonant valence bond (RVB) liquid phase with very short-ranged correlations, but also a valence-bond ordered phase compatible with the one proposed to explain the seemingly gapless singlet states of the Heisenberg antiferromagnet on the Kagome lattice. Likely consequences for generic spin models are discussed. The analysis combines compact U(1) gauge theory, duality transformations, lattice-field-theoretical methods, and variational approach.
We extend a simple model of a charge trap coupled to a single-electron box to energy ranges and parameters such that it gives new insights and predictions readily observable in many experimental systems. We show that a single background charge is enough to give lines of differential conductance in the stability diagram of the quantum dot, even within undistorted Coulomb diamonds. It also suppresses the current near degeneracy of the impurity charge, and yields negative differential lines far from this degeneracy. We compare this picture to two other accepted explanations for lines in diamonds, based respectively on the excitation spectrum of a quantum dot and on fluctuations of the density-of-states in the contacts. In order to discriminate between these models we emphasize the specific features related to environmental charge traps. Finally we show that our model accounts very well for all the anomalous features observed in silicon nanowire quantum dots.
The temperature dependence of the surface plasmon resonance in small metal spheres is calculated using an electron gas model within the Random Phase Approximation. The calculation is mainly devoted to the study of spheres with diameters up to at least 10 nm, where quantum effects can still be relevant and simple plasmon pole approximation for the dielectric function is no more appropriate. We find a possible blue shift of the plasmon resonance position when the temperature is increased while keeping the size of the sphere fixed. The blue shift is appreciable only when the temperature is a large fraction of the Fermi energy. These results provide a guide for pump and probe experiments with a high time resolution, and tailored to study the excited electron system before thermalisation with the lattice takes place.
Pairing fluctuations are self-consistently incorporated on the same footing as the quadrupole deformations in present state of the art calculations including particle number and angular momentum conservation as well as configuration mixing. The approach is complemented by the use of the finite range density dependent Gogny force which, with a unique source for the particle-hole and particle-particle interactions, guarantees a self-consistent interplay in both channels.   We have applied our formalism to study the role of the pairing degree of freedom in the description of the most relevant observables like spectra, transition probabilities, separation energies, etc. We find that the inclusion of pairing fluctuations mostly affects the description of excited states, depending on the excitation energy and the angular momentum. $E0$ transition probabilities experiment rather big changes while $E2$'s are less affected.   Genuine pairing vibrations are thoroughly studied with the conclusion that deformations strongly inhibits their existence. These studies have been performed for a selection of nuclei: spherical, deformed and with different degree of collectivity.
The notion of geometric construction is introduced. This notion allows to compare incidence configurations in the algebraic and tropical plane. We provide an algorithm such that, given a tropical instance of a geometric construction, it computes sufficient conditions to have an algebraic counterpart related by tropicalization. We also provide sufficient conditions in a geometric construction to ensure that the algebraic counterpart always exists. Geometric constructions are applied to transfer classical theorems to the tropical framework, we provide a notion of incidence theorems and prove several tropical versions of classical theorems like converse Pascal, Fano plane or Cayley-Bacharach.
Random planar maps are considered in the physics literature as the discrete counterpart of random surfaces. It is conjectured that properly rescaled random planar maps, when conditioned to have a large number of faces, should converge to a limiting surface whose law does not depend, up to scaling factors, on details of the class of maps that are sampled. Previous works on the topic, starting with Chassaing and Schaeffer, have shown that the radius of a random quadrangulation with $n$ faces, that is, the maximal graph distance on such a quadrangulation to a fixed reference point, converges in distribution once rescaled by $n^{1/4}$ to the diameter of the Brownian snake, up to a scaling constant. Using a bijection due to Bouttier, Di Francesco and Guitter between bipartite planar maps and a family of labeled trees, we show the corresponding invariance principle for a class of random maps that follow a Boltzmann distribution putting weight $q_k$ on faces of degree $2k$: the radius of such maps, conditioned to have $n$ faces (or $n$ vertices) and under a criticality assumption, converges in distribution once rescaled by $n^{1/4}$ to a scaled version of the diameter of the Brownian snake. Convergence results for the so-called profile of maps are also provided. The convergence of rescaled bipartite maps to the Brownian map, in the sense introduced by Marckert and Mokkadem, is also shown. The proofs of these results rely on a new invariance principle for two-type spatial Galton--Watson trees.
In matter coupled $F(4)$ gauged supergravity in six dimensions, we study supersymmetric $AdS_6$ black holes with various horizon geometries. We find new $AdS_2\,\times\,\Sigma_{\mathfrak{g}_1}\times\Sigma_{\mathfrak{g}_2}$ horizons with $\mathfrak{g}_1>1$ and $\mathfrak{g}_2>1$, and present the black hole solution numerically. The full black hole is an interpolating geometry between the asymptotically $AdS_6$ boundary and the $AdS_2\,\times\,\Sigma_{\mathfrak{g}_1}\times\Sigma_{\mathfrak{g}_2}$ horizon. We also find black holes with horizons of K\"ahler four-cycles in Calabi-Yau fourfolds and Cayley four-cycles in $Spin(7)$ manifolds.
A universal approach to decoherence control combined with quantum estimation theory reveals a critical behavior, akin to a phase transition, of the information obtainable by a qubit probe concerning the memory time of environmental fluctuations. This criticality emerges only when the probe is subject to dynamical control. It gives rise to a sharp transition between two dynamical phases characterized by either a short or long memory time compared to the probing time. This phase-transition of the environmental information is a fundamental feature that facilitates the attainment of the highest estimation precision of the environment memory-time and the characterization of probe dynamics.