ShantanuT01/DACTYL-Pretraining huggingface dataset:
We derive the effective action for a one dimensional electron island formed between a double barrier in a single channel quantum wire including the electron spin. Current and energy addition terms corresponding to charge and spin are identified. The influence of the range and the strength of the electron interaction and other system parameters on the charge and spin addition energies, and on the excitation spectra of the modes confined within the island is studied. We find by comparison with experiment that spin excitations in addition to non-zero range of the interaction and inhomogeneity effects are important for understanding the electron transport through one dimensional quantum islands in cleaved-edge-overgrowth systems.
We construct a global counterpart to the notion of affine modification due to Kaliman and Zaidenberg. This leads to a simple explicit description of the structure of birational affine morphisms between arbitrary quasi-projective varieties.
We study the optional projection of a standard Brownian motion on the natural filtration of certain kinds of observation processes. The observation process, $Y$, is defined as a solution of a stochastic differential equation such that it reveals some (possibly noisy) information about the signs of the Brownian motion when $Y$ hits 0. As such, the associated optional projections are related to Az\'ema's martingales which are obtained by projecting the Brownian motion onto the filtration generated by observing its signs.
We study the multiplicity and concentration of complex valued solutions for a fractional magnetic Schr\"odinger equation involving a scalar continuous electric potential satisfying a local condition and a continuous nonlinearity with subcritical growth. The main results are obtained by applying a penalization technique, generalized Nehari manifold method and Ljusternik-Schnirelman theory. We also prove a Kato's inequality for the fractional magnetic Laplacian which we believe to be useful in the study of other fractional magnetic problems.
We apply magnetohydrodynamic (MHD) modeling to the radio galaxy Hercules A for investigating the jet-driven shock, jet/lobe transition, wiggling, and magnetic field distribution associated with this source. The model consists of magnetic tower jets in a galaxy cluster environment, which has been discussed in a series of our papers. The profile of underlying ambient gas plays an important role in jet-lobe morphology. The balance between the magnetic pressure generated by axial current and the ambient gas pressure can determine the lobe radius. The jet body is confined jointly by the external pressure and gravity inside the cluster core radius R_c, while outside R_c it expands radially to form fat lobes in a steeply decreasing ambient thermal pressure gradient. The current-carrying jets are responsible for generating a strong, tightly wound helical magnetic field. This magnetic configuration will be unstable against the current-driven kink mode and it visibly grows beyond R_c where a separation between the jet forward and return currents occurs. The reversed pinch profile of global magnetic field associated with the jet and lobes produces projected B-vector distributions aligned with the jet flow and the lobe edge. AGN-driven shock powered by the expanding magnetic tower jet surrounds the jet/lobe structure and heats the ambient ICM. The lobes expand subsonically; no obvious hot spots are produced at the heads of lobes. Several key features in our MHD modeling may be qualitatively supported by the observations of Hercules A.
We present the first fully quantum mechanical calculation of photon radiation accompanying charged particle decay from a barrier resonance. The soft-photon limit agrees with the classical results, but differences appear at next-to-leading-order. Under the conditions of alpha-decay of heavy nuclei, the main contribution to the photon emission stems from Coulomb acceleration and may be computed analytically. We find only a small contribution from the tunneling wave function under the barrier.
The empirical shock arrival (ESA) model was developed based on quadrature data from Helios (in-situ) and P-78 (remote-sensing) to predict the Sun-Earth travel time of coronal mass ejections (CMEs) [Gopalswamy et al. 2005a]. The ESA model requires earthward CME speed as input, which is not directly measurable from coronagraphs along the Sun-Earth line. The Solar Terrestrial Relations Observatory (STEREO) and the Solar and Heliospheric Observatory (SOHO) were in quadrature during 2010 - 2012, so the speeds of Earth-directed CMEs were observed with minimal projection effects. We identified a set of 20 full halo CMEs in the field of view of SOHO that were also observed in quadrature by STEREO. We used the earthward speed from STEREO measurements as input to the ESA model and compared the resulting travel times with the observed ones from L1 monitors. We find that the model predicts the CME travel time within about 7.3 hours, which is similar to the predictions by the ENLIL model. We also find that CME-CME and CME-coronal hole interaction can lead to large deviations from model predictions.
We propose parameterization procedures of the scattering amplitude f_{1+}^{3}(s)) with a view to extracting the pole parameters from data in the elastic region of {\pi}N scattering. This is achieved by considering the analyticity properties of partial wave amplitudes directly and writing dispersion relations for the amplitude explicitly.
We classify all possible implementations of an abelian symmetry in the two-Higgs-doublet model with fermions. We identify those symmetries which are consistent with non-vanishing quark masses and a CKM matrix which is not block-diagonal. Our analysis takes us from a plethora of possibilities down to 246 relevant cases, requiring only 34 distinct matrix forms. We show that applying Z_n with n \geq 4 to the scalar sector leads to a continuous U(1) symmetry in the whole Lagrangian. Finally, we address the possibilities of spontaneous CP violation and of natural suppression of the flavour changing neutral currents. We explain why our work is relevant even for non-abelian symmetries.
Many combinatorial sequences (for example, the Catalan and Motzkin numbers) may be expressed as the constant term of $P(x)^k Q(x)$, for some Laurent polynomials $P(x)$ and $Q(x)$ in the variable $x$ with integer coefficients. Denoting such a sequence by $a_k$, we obtain a general formula that determines the congruence class, modulo $p$, of the indefinite sum $\sum_{k=0}^{rp -1} a_k$, for {\it any} prime $p$, and any positive integer $r$, as a linear combination of sequences that satisfy linear recurrence (alias difference) equations with constant coefficients. This enables us (or rather, our computers) to automatically discover and prove congruence theorems for such partial sums. Moreover, we show that in many cases, the set of the residues is finite, regardless of the prime $p$.
Long gamma-ray bursts (GRBs) with a plateau phase in their X-ray afterglows obeys a three-dimensional (3D) relation (Dainotti et al. 2016), between the rest-frame time at the end of the plateau, Ta, its corresponding X-ray luminosity, La, and the peak luminosity in the prompt emission, Lpeak, an extension of the two-dimensional Dainotti relation. This 3D relation identifies a GRB fundamental plane whose existence we here confirm. We extend the original analysis with X-ray data untill July 2016 gathering 183 Swift GRBs with afterglow plateaus and known redshifts. We compare several GRB categories, such as shorts with extended emission, SEE, X-ray Flashes, GRBs associated with SNe, a sample of only long-duration GRBs (132), selected from the total sample by excluding GRBs of the previous categories, and the gold sample, composed by GRBs with light curves with good data coverage and relatively flat plateaus. The relation planes for each of these categories are not statistically different from the gold fundamental plane, with the exception of the SEE, which are hence identified as a physically distinct class of objects. The gold fundamental plane has an intrinsic scatter smaller than any plane derived from the other sample categories. Thus, the distance of any particular GRB category from this plane becomes a key parameter. Additionally, we tested this 3D relations by using GRBs observed at high energy, namely the peak luminosity values derived by the Fermi-Gamma Ray Burst Monitor (GBM). The 3D relation is also confirmed for GRBs observed by the GBM, thus showing its independence from the energy range. Furthermore, we computed the several category planes with T*a as a dependent parameter obtaining for each category smaller intrinsic scatters (reaching a reduction of $24\%$ for the long GRBs). The fundamental plane is independent from several prompt and afterglow parameters.
We present B-, V-, and I-band images, as well as an H alpha image, of And VI. This is the second newly identified dwarf spheroidal (dSph) companion to M31 found using a digital filtering technique applied to the second Palomar Sky Survey for which 1550 square degrees now have been surveyed. And VI was confirmed to be a nearby dSph galaxy when it resolved into stars easily with a short 4-m V-band exposure. Sub-arcsec images taken at the Kitt Peak WIYN 3.5-m telescope provided (I,V-I) and (V,B-V) color-magnitude diagrams that yield a distance of 775 +/- 35 kpc using the tip of the red giant branch method, and a mean metallicity of [Fe/H] = -1.58 +/- 0.20 with a dispersion of approximately 0.3 dex. And VI has a galactocentric distance of approximately 271 kpc and an absolute V magnitude of -11.3. All observed properties of And VI are consistent with its classification as a dSph companion to M31. Despite the recent identification of the And V, And VI, and Cas dwarfs, the Local Group luminosity function remains highly deficient in faint galaxies relative both to CDM simulations of its formation, and to the luminosity functions for richer clusters of galaxies.
The concurrent growth of supermassive black holes (SMBHs) and their host galaxies remains to be fully explored, especially at high redshift. While often understood as a consequence of self-regulation via AGN feedback, it can also be explained by alternative SMBH accretion models. Here, we expand on previous work by studying the growth of SMBHs with the help of a large suite of cosmological zoom-in simulations (MassiveFIRE) that are part of the Feedback in Realistic Environments (FIRE) project. The growth of SMBHs is modelled in post-processing with different black hole accretion models, placements, and merger treatments, and validated by comparing to on-the-fly calculations. Scaling relations predicted by the gravitational torque driven accretion (GTDA) model agree with observations at low redshift without the need for AGN feedback, in contrast to models in which the accretion rate depends strongly on SMBH mass. At high redshift, we find deviations from the local scaling relations in line with previous theoretical results. In particular, SMBHs are under-massive, presumably due to stellar feedback, but start to grow efficiently once their host galaxies reach $M_* \sim 10^{10} M_{\odot}$. We analyse and explain these findings in the context of a simple analytic model. Finally, we show that the predicted scaling relations depend sensitively on the SMBH location and the efficiency of SMBH merging, particularly in low-mass systems. These findings highlight the relevance of understanding the evolution of SMBH-galaxy scaling relations to predict the rate of gravitational wave signals from SMBH mergers across cosmic history.
There is discussion if traffic displays multiple phases (e.g. laminar, jammed, synchronized) or not. This paper presents evidence that a stochastic car following model, by changing one of its parameters, can be moved from showing two phases (laminar and jammed) to showing only one phase. Models with two phases show three states: two being homogeneous states corresponding to each phase, and a third state which consists of a mix between the two phases (phase coexistence).   Although the gas-liquid analogy to traffic models has been widely discussed, no traffic-related model ever displayed a completely understood stochastic version of that transition. Having a stochastic model is however important to understand the potentially probabilistic nature of the transition. Most importantly, if indeed 2-phase models describe certain aspects correctly, then this leads to predictions for breakdown probabilities. Alternatively, if 1-phase models describe these aspects better, then there is no breakdown.Interestingly, such 1-phase models can still allow for jam formation on small scales, which may give the impression of having a 2-phase dynamics.
We study invariant divisors on the total spaces of the homogeneous deformations of rational complexity-one T-varieties constructed by Ilten and Vollmert. In particular, we identify a natural subgroup of the Picard group for any general fiber of such a deformation, which is canonically isomorphic to the Picard group of the special fiber. This isomorphism preserves Euler characteristic, intersection numbers, and the canonical class.
Nearly a century after the discovery that we live in an expanding Universe, and two decades after the discovery of accelerating cosmic expansion, there remains no direct detection of this acceleration via redshift drift - a change in the cosmological expansion velocity versus time. Because cosmological redshift drift directly determines the Hubble parameter H(z), it is arguably the cleanest possible measurement of the expansion history, and has the potential to constrain dark energy models (e.g. Kim et al. 2015). The challenge is that the signal is small - the best observational constraint presently has an uncertainty several orders of magnitude larger than the expected signal (Darling 2012). Nonetheless, direct detection of redshift drift is becoming feasible, with upcoming facilities such as the ESO-ELT and SKA projecting possible detection within two to three decades. This timescale is uncomfortably long given the potential of this cosmological test. With dedicated experiments it should be possible to rapidly accelerate progress and detect redshift drift with only a five-year observational baseline. Such a facility would also be ideal for precision radial velocity measurements of exoplanets, which could be obtained as a byproduct of the ongoing calibration measurements for the experiment.
Clustering plays an important role in the structure of nuclei, especially for light nuclei in the $p$-shell. In nuclear cluster models these degrees of freedom are introduced explicitly. In the Resonating Group Method or in the Generator Coordinate Method the clusters are built from individual nucleons interacting via an effective nucleon-nucleon interaction; the total wave function is antisymmetrized. Fermionic Molecular Dynamics (FMD) goes beyond pure cluster models. It is a microscopic many-body approach using a Gaussian wave packet basis that includes the harmonic oscillator shell model and Brink-type cluster model wave functions as special cases. Clustering is not imposed but appears dynamically in the calculations. The importance of clustering for the understanding of bound states, resonances and scattering states is illustrated with examples discussing the charge radii of the Neon isotopes, the $^3$He($\alpha$,$\gamma$)$^7$Be capture reaction and the cluster states in the $^{12}$C continuum.
We study the large-scale topological and dynamical properties of real Internet maps at the autonomous system level, collected in a three years time interval. We find that the connectivity structure of the Internet presents average quantities and statistical distributions settled in a well-defined stationary state. The large-scale properties are characterized by a scale-free topology consistent with previous observations. Correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the Internet. The study of the Internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models. We compare the properties of growing network models with the present real Internet data analysis.
We study the geodesic equations in the space-time of neutral Brans-Dicke Dilaton black hole in three dimensions, BTZ black holes and the 2+1 black hole. We use the process of separation of the Hamilton-Jacobi equation to obtain the constants of motion. The whole analytical solution of the geodesic equations in the space-times of the intended black holes are shown completely. Moreover, the geodesic equations are solved in terms of Weierstrass elliptic functions. Furthermore, with use of the analytical solution and effective potential technique some trajectories around the black holes are classified. Meanwhile, by analytical solution, effective potential and considering the zeroes of underlying polynomials, some possible orbits are plotted. Finally, we compare our results with Cruz {\it et. al.} \cite{Cruz:1994ar} and we indicate the benefits of the analytical method which is applied in this paper.
This review covers the important advances in recent years in the physics of thin film ferroelectric oxides, the strongest emphasis being on those aspects particular to ferroelectrics in thin film form. We introduce the current state of development in the application of ferroelectric thin films for electronic devices and discuss the physics relevant for the performance and failure of these devices. Following this we cover the enormous progress that has been made in the first principles computational approach to understanding ferroelectrics. We then discuss in detail the important role that strain plays in determining the properties of epitaxial thin ferroelectric films. Finally, we look at the emerging possibilities for nanoscale ferroelectrics, with particular emphasis on ferroelectrics in non conventional nanoscale geometries.
Symmetric logarithmic derivative (SLD) is a key quantity to obtain quantum Fisher information (QFI) and to construct the corresponding optimal measurements. Here we develop a method to calculate the SLD and QFI via anti-commutators. This method is originated from the Lyapunov representation and would be very useful for cases that the anti-commutators among the state and its partial derivative exhibits periodic properties. As an application, we discuss a class of states, whose squares linearly depend on the states themselves, and give the corresponding analytical expressions of SLD and QFI. A noisy scenario of this class of states is also considered and discussed. Finally, we readily apply the method to the block-diagonal states and the multi-parameter estimation problems.
Entropy accumulation near a quantum critical point was expected based on general scaling arguments, and has recently been explicitly observed. We explore this issue further in two canonical models for quantum criticality, with particular attention paid to the potential effects beyond hyperscaling. In the case of a one-dimensional transverse field Ising model, we derive the specific scaling form of the free energy. It follows from this scaling form that the singular temperature dependence at the critical field has a vanishing prefactor but the singular field dependence at zero temperature is realized. For the spin-density-wave model above its upper critical dimension, we show that the dangerously irrelevant quartic coupling comes into the free energy in a delicate way but in the end yields only subleading contributions beyond hyperscaling. We conclude that entropy accumulation near quantum critical point is a robust property of both models.
In 2017, Duminil-Copin et al. introduced the OSSS method to study properties of diverse percolation models. This document aims to introduce the reader to this new method. It contains a introduction to percolation theory, then concentrates on the case of Poisson-Boolean percolation. The majority of this document is dedicated to an detailed analysis of [DRT18]. This work is the result of an internship in Summer 2019 with Jean-Baptiste Gou\'er\'e at the University of Tours.
New Ekpyrotic Cosmology is an alternative scenario of the early universe which relies on a phase of slow contraction before the big bang. We calculate the 3-point and 4-point correlation functions of primordial density perturbations and find a generically large non-Gaussian signal, just below the current sensitivity level of CMB experiments. This is in contrast with slow-roll inflation, which predicts negligible non-Gaussianity. The model is also distinguishable from alternative inflationary scenarios that yield large non-Gaussianity, such as DBI inflation and the simplest curvaton-like models, through the shape dependence of the correlation functions. Non-Gaussianity therefore provides a distinguishing and testable prediction of New Ekpyrotic Cosmology.
The nature of most of the ~300 high-energy gamma-ray sources discovered by the EGRET instrument aboard the Gamma-ray Observatory (GRO) between 1991 and 1999 is one of the greatest enigmas in high-energy astrophysics. While about half of the extragalactic sources have been optically identified with Active Galactic Nuclei (AGN), only a meagre 10% of the galactic sources have a reliable identification. This low success rate has mainly to be ascribed to the local crowding of potential optical counterparts and to the large gamma-ray error boxes (of the order of one degree in radius) which prevented a straightforward optical identification. Indeed, a multi-wavelength identification strategy, based on a systematic coverage of the gamma-ray error boxes, has been the only do-able approach. The situation is now greatly improving thanks to the observations performed by the Fermi Gamma-ray Space Telescope which, thanks to the LAT instrument, provides a factor of 50 improvement in sensitivity and a factor of 10 improvement in positional accuracy. However, while the smaller error boxes will make the multi-wavelength follow-ups easier, the larger sensitivity will enormously increase the number of detected gamma-ray sources, requiring an even larger effort in the multi-wavelength follow-ups. This effort can not be obviously sustained by targeted observations only and it would greatly benefit from multi-wavelength data and advanced data products available world wide through the science data centres and interfaced by the Virtual Observatory (VO) tools. In this contribution, I outline the science case, the multi-wavelength observation synergies, and the requirements for both the the science data centres and the VO.
Starting with Green-Schwarz superstring action, we construct a type IIB matrix model. We fix the local $\kappa$ symmetry in the Killing spinor gauge and then perform the world-sheet duality transformation. A matrix model obtained from this gauge-fixed action is shown to be equivalent to the type IIB matrix model constructed by Ishibashi et al. Our construction does not make use of an analytic continuation of spinor variable. Moreover, it seems that our construction is applicable to that of more general type IIB matrix models in a curved background such as $AdS_5 \times S^5$.
The possibility is discussed to observe the sparticle decay modes of the heavy MSSM Higgs bosons at the Large Hadron Collider. We focus on the heavy neutral Higgses, and argue that their decay into neutralinos may access an interesting region in the MSSM parameter space up to masses around 450 GeV for low and intermediate values of tan beta. If neutralinos and sleptons are light enough, this channel - leading to a four lepton final state topology - can complement the reach of the SM channels.