ShantanuT01/DACTYL-Pretraining huggingface dataset:
The purpose of this thesis is to explore the properties of multiple coincident M2- and M5-branes. We begin with a review of the BLG and ABJM models of multiple M2-branes and our focus will be on their formulation in terms of 3-algebras. We then examine the coupling of multiple M2-branes to the background 3-form and 6-form gauge fields of eleven-dimensional supergravity. In particular we show in detail how a natural generalisation of the Myers flux-terms, along with the resulting curvature of the background metric, leads to mass terms in the effective field theory. Working to lowest nontrivial order in fermions, we demonstrate the supersymmetric invariance of the four-derivative order corrected Lagrangian of the Euclidean BLG theory and determine the theory's higher derivative corrected supersymmetry transformations. The supersymmetry algebra is also shown to close on the scalar and gauge fields. We also consider periodic arrays of M2-branes in the ABJM model in the spirit of a circle compactification to D2-branes in type IIA string theory. The result is a curious formulation of three-dimensional maximally supersymmetric Yang-Mills theory. Upon further T-duality on a transverse torus we obtain a non-manifest-Lorentz-invariant description of five-dimensional maximally supersymmetric Yang-Mills which can be viewed as an M-theory description of M5-branes on $\mathbb{T}^3$. After reviewing work to describe multiple M5-branes using 3-algebras we show how the resulting novel system of equations reduces to one-dimensional motion on instanton moduli space. Quantisation leads to the previous light-cone proposal of the (2,0) theory, generalised to include a potential that arises on the Coulomb branch as well as couplings to background gauge and self-dual 2-form fields.
We prove a general transfer theorem for multivariate random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and sufficient conditions for the convergence of randomly indexed random sequences. Special attention is paid to the case where the elements of the basic double array are formed as statistics constructed from samples with random sizes. Under rather natural conditions we prove the theorem on convergence of the distributions of such statistics to normal variance-mean mixtures.
We discuss some aspects of the recently discovered BPS black ring solutions in terms of the AdS/CFT correspondence. In the type IIB frame in which the black ring carries the charges of the D1-D5-P system, we propose a microscopic description of the rings in the orbifold CFT governing this system. In our proposal, the CFT effectively splits into two parts: one part captures the supertube-like properties of the ring, and the other captures the entropy. We can also understand the black ring entropy by relating the geometry near the ring to BPS black holes in four dimensions, although this latter approach does not directly lead to an identification of black rings in terms of the D1-D5-P CFT.
There exists a well-known hook-length formula for calculating the dimensions of 2D Young diagrams. Unfortunately, the analogous formula for 3D case is unknown. We introduce an approach for calculating the estimations of dimensions of three-dimensional Young diagrams also known as plane partitions. The most difficult part of this task is the calculation of co-transition probabilities for a central Markov process. We propose an algorithm for approximate calculation of these probabilities. It generates numerous random paths to a given diagram. In case the generated paths are uniformly distributed, the proportion of paths passing through a certain branch gives us an approximate value of the co-transition probability. As our numerical experiments show, the random generator based on the randomized variant of the Sch\"{u}tzenberger transformation allows to obtain accurate values of co-transition probabilities. Also a method to construct 3D Young diagrams with large dimensions is proposed.
Vibronic spectra of molecules are typically described within the Franck-Condon model. Here, we show that highly resolved vibronic spectra of large organic molecules on a single layer of MoS$_{2}$ on Au(111) show spatial variations in their intensities, which cannot be captured within this picture. We explain that vibrationally mediated perturbations of the molecular wave functions need to be included into the Franck-Condon model. Our simple model calculations reproduce the experimental spectra at arbitrary position of the STM tip over the molecule in great detail.
We perform multi-dimensional radiative transfer simulations to compute spectra for a hydrodynamical simulation of a line-driven accretion disk wind from an active galactic nucleus. The synthetic spectra confirm expectations from parameterized models that a disk wind can imprint a wide variety of spectroscopic signatures including narrow absorption lines, broad emission lines and a Compton hump. The formation of these features is complex with contributions originating from many of the different structures present in the hydrodynamical simulation. In particular, spectral features are shaped both by gas in a successfully launched outflow and in complex flows where material is lifted out of the disk plane but ultimately falls back. We also confirm that the strong Fe Kalpha line can develop a weak, red-skewed line wing as a result of Compton scattering in the outflow. In addition, we demonstrate that X-ray radiation scattered and reprocessed in the flow has a pivotal part in both the spectrum formation and determining the ionization conditions in the wind. We find that scattered radiation is rather effective in ionizing gas which is shielded from direct irradiation from the central source. This effect likely makes the successful launching of a massive disk wind somewhat more challenging and should be considered in future wind simulations.
We analyze the influence of the Fermi surface (FS) shape on magnetotransport properties, particularly on the Hall effect in the MnAs compound. It has been observed in MnAs films evidence of opposite conduction polarities for different crystal direction (goniopolarity) and a strong dependence of the carrier type with applied magnetic field. In order to understand this behaviour, we developed a model based on the semiclassical equations along with Boltzmann transport theory that takes into account both, the applied magnetic field and the FS shape. The FS of the MnAs compound is obtained by means of density functional theory (DFT), showing a clear dominance of the hyperboloid shape. Our study, corroborate that this specific topology of the FS gives rise to a goniopolar behaviour in the Hall transport. This theoretical results are supported by magnetotransport measurements on MnAs thin layers epitaxially grown on GaAs(001) and GaAs(111), where both configurations allow us to explore the transport characteristics for two different crystal directions of the MnAs.
In a six dimensional brane world model with multiple $S_1/Z_2$ warping, two of the 4-branes at the boundaries have coordinate dependent brane tensions in order to implement the orbifolded boundary conditions consistently. Such brane tension is shown to be equivalent to a scalar field distribution on the brane [1]. We show that in such a scenario a masslesss left chiral fermion on the 4-brane localizes naturally on the standard model 3-brane located at one edge of the compact manifold while the massless right chiral fermion wave function as well as the wave functions for the massive fermion modes peak away from this brane. This offers a mechanism of obtaining massless chiral fermion with only one of its chiral component present in our brane.
Mixed iodine-bromine perovskites used in solar cells undergo below a critical temperature an intrinsic demixing into phases with different iodine-bromine compositions. In addition, under illumination they show nucleation of an iodine-rich phase. We predict from thermodynamic considerations that in mixed iodine-bromine perovskites like MAPb(I$_{1-x}$Br$_x$)$_3$ the interplay of these effects can lead to coexistence of a bromine-rich, iodine-rich, and nearly iodine-pure nucleated phase. This three-phase coexistence occurs in a region in the composition-temperature phase diagram near the critical point for intrinsic demixing. We investigate the hysteresis in the evolution of this coexistence when temperature or illumination intensity are cycled. Depending on the particular way the coexistence is established, nearly iodine-pure nuclei should form either in the iodine-rich phase only or both in the bromine-rich and iodine-rich phases. Experimental verification of this fundamentally novel type of light-tunable three-phase coexistence should be possible by a combination of absorption and photoluminescence experiments.
Spectral and timing properties of accretion flows on a black hole depend on their density and temperature distributions, which in turn come from the underlying dynamics. Thus, an accurate description of the flow which includes hydrodynamics and radiative transfer is a must to interpret the observational results. In the case of non-rotating black holes, Pseudo-Newtonian description of surrounding space-time enables one to make a significant progress in predicting spectral and timing properties. This formalism is lacking for spinning black holes. In this paper, we show that there exists an exact form of 'natural' potential derivable from the general relativistic (GR) radial momentum equation. Use of this potential in an otherwise Newtonian set of equations allows to describe transonic flows very accurately as is evidenced by comparing with solutions obtained from the full GR framework. We study the properties of the critical points and the centrifugal pressure supported shocks in the parameter space spanned by the specific energy and the angular momentum, and compare with the results of GR hydrodynamics. We show that this potential can safely be used for the entire range of Kerr parameter $-1<a<1$ for modeling of observational results around spinning black holes. We assume the flow to be inviscid. Thus, it is non-dissipative with constant energy and angular momentum. These assumptions are valid very close to the black hole as the infall timescale is much shorter as compared to the viscous timescale.
A path integral formulation of the Bianchi I models containing a massless scalar field in loop quantum cosmology is constructed. Following the strategy used in the homogenous and isotropic case, the calculation is extended to the simplest non-isotropic models according to the $\bar{\mu}$ and $\bar{\mu}^{\prime}$ scheme. It is proved from the path integral angle that the quantum dynamic lacks the full invariance with respect to fiducial cell scaling in the $\bar{\mu}$ scheme, but it does not in the $\bar{\mu}^{\prime}$ scheme. The investigation affirms the equivalence of the canonical approach and the path integral approach in loop quantum cosmology.
We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil lattice and the geometric Picard number.
The damping of single-particle degrees of freedom in strongly correlated two-dimensional Fermi systems is analyzed. Suppression of the scattering amplitude due to the damping effects is shown to play a key role in preserving the validity of the Landau-Migdal quasiparticle picture in a region of a phase transition, associated with the divergence of the quasiparticle effective mass. The results of the analysis are applied to elucidate the behavior of the conductivity $\sigma(T)$ of the two-dimensional dilute electron gas in the density region where it undergoes a metal-insulator transition.
Consider a real matrix $\Theta$ consisting of rows $(\theta_{i,1},\ldots,\theta_{i,n})$, for $1\leq i\leq m$. The problem of making the system linear forms $x_{1}\theta_{i,1}+\cdots+x_{n}\theta_{i,n}-y_{i}$ for integers $x_{j},y_{i}$ small naturally induces an ordinary and a uniform exponent of approximation, denoted by $w(\Theta)$ and $\widehat{w}(\Theta)$ respectively. For $m=1$, a sharp lower bound for the ratio $w(\Theta)/\widehat{w}(\Theta)$ was recently established by Marnat and Moshchevitin. We give a short, new proof of this result upon a hypothesis on the best approximation integer vectors associated to $\Theta$. Our conditional result extends to general $m>1$ (but may not be optimal in this case). Moreover, our hypothesis is always satisfied in particular for $m=1, n=2$ and thereby unconditionally confirms a previous observation of Jarn\'ik. We formulate our results in the more general context of approximation of subspaces of Euclidean spaces by lattices. We further establish criteria upon which a given number $\ell$ of consecutive best approximation vectors are linearly independent. Our method is based on Siegel's Lemma.
This document contains supplementary material for the main articles in our Random Cayley Graphs project.   We prove refined results about simple random walks on the integers and on the cycle. We are primarily interested in the entropy of these random walks at certain times and how this entropy changes when the time changes slightly. Additionally, we prove some large deviation and exit time estimates.   We prove some results on the size of discrete lattice balls and how this size changes when the radius changes slightly. We do this in a general $L_q$ norm, with $q \in [1,\infty]$.   We also prove some other technical results deferred from the main papers.   We hope that some of the results, particularly the simple random walk estimates, will be useful in their own right for other researchers.
The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are estimated by extrapolating our data to the infinite cluster size limit, which are in good accordance with recent simulation results. Within the cluster mean-field approximation scheme, the PCPD and the DPCPD share the same mean-field critical behavior. The application of the coherent anomaly method, however, shows that the two models develop different coherent anomalies, which lead to different true critical scaling. The values of the critical exponents for the particle density, the pair density, the correlation length, and the relaxation time are fairly well estimated for the DPCPD. These results support and complement our recent simulation results for the DPCPD.
Observations have shown that a model with a positive cosmological constant is more appropriate to describe our universe. The aim of this manuscript is to study the gravitational fields in de Sitter space-time. To achieve this goal, de Sitter metric is written in Bondi Sachs form and the Einstein equations are solved for this form of the metric in presence of $\Lambda$. On the other hand, a null tetrad is defined for the de Sitter metric and its form in Bondi gauge is obtained by using the general transformation. Then a new result for the Bondi news in de Sitter background is obtained, using the coordinate independent notion of Bondi news which was first presented by Penrose in 1963.
The spectral function, measured in $A(e,e'p)$ reactions, is distorted by the final-state interaction of the struck proton with the residual nucleus. This causes a broadening of the observed transverse-momentum distribution which is large even in the $d(e,e'p)$ reaction. We discuss the effects of this $p_{\perp}$-broadening on the nuclear transparency measured in the recent NE18 experiment. Within conventional Glauber theory we can describe the measurements. Transparency effects are thus small in agreement with our earlier predictions.
We present a study of the equilibration process of nonequilibrium systems by means of molecular dynamics simulation technique. The nonequilibrium conditions are achieved in systems by defining velocity components of the constituent atoms randomly. The calculated Shannon en- tropy from the probability distribution of the kinetic energy among the atoms at different instants during the process of equilibration shows oscillation as the system relaxes towards equilibrium. Fourier transformations of these oscillating Shannon entropies reveal the existance of Debye frequency of the concerned system. From these studies it was concluded that the signature of the equilibration process of dynamical systems is the time invariance of Shannon entropy.
We present the second results of an ensemble and systematic survey of oscillation mode variability in compact pulsators observed with the original {\sl Kepler} mission. Two types of flux calibrations, raw and corrected, collected on two hot B subdwarf stars, KIC\,2438324 and KIC\,11179657, are thoroughly examined with the goal to evaluate the difference of patterns when oscillation modes modulate in amplitude (AM) and frequency (FM). We concentrate on AMs and FMs occurring in seven multiplet components in each star as representative frequencies. The analysis shows that FM measurements are independent of the flux calibration we choose. However, if flux contamination by nearby stars is large, AMs may be significantly different between raw and corrected flux. In addition, AMs suffer, to some extent, from systematic modulation pattern which is most likely induced by instrumental effects {and} differs from one star to another. Our results indicate that stars with no contamination are better candidates to quantitatively compare modulation patterns with theory and should be given a higher priority for such studies, since light contamination will destroy real amplitude modulation patterns.
The exact Green function is constructed for a quantum system, with known Green function, which is decorated by two delta function impurities.It is shown that when two such impurities coincide they behave as a single singular potential with combined amplitude. The results are extended to N impurities.
We present the first study of pairing in nuclei including three-nucleon forces. We perform systematic calculations of the odd-even mass staggering generated using a microscopic pairing interaction at first order in chiral low-momentum interactions. Significant repulsive contributions from the leading chiral three-nucleon forces are found. Two- and three-nucleon interactions combined account for approximately 70% of the experimental pairing gaps, which leaves room for self-energy and induced interaction effects that are expected to be overall attractive in nuclei.
We present results from photometric and spectroscopic data obtained with SOAR and Gemini observatory facilities in the field of a recently discovered star cluster. The cluster, projected towards the Eastern side of the outer disc of the Large Magellanic Cloud (LMC), was originally placed nearly 10 kpc behind the LMC with an age and metallicity typical of the innermost LMC star cluster population. We assigned radial velocity (RV) memberships to stars observed spectroscopically, and derived the cluster age and distance from theoretical isochrone fitting to the cluster colour-magnitude diagram. The new object turned out to be a 0.9 Gyr old outer LMC disc cluster, which possibly reached the present position after being scattered from the innermost LMC regions where it might have been born. We arrived at this conclusion by examining the spatial distribution of LMC star clusters of similar age, by comparing the derived spectroscopic metallicity with that expected for an outside-in galaxy formation scenario, by considering the cluster internal dynamical stage as inferred from its derived structural parameters and by estimating the circular velocity of a disc that rotates with the corresponding star cluster radial velocity at the cluster's deprojected distance, which resulted to be nearly 60 per cent higher than that of most of the outer LMC disc clusters.
On 2018 Feb. 4.41, the All-Sky Automated Survey for SuperNovae (ASAS-SN) discovered ASASSN-18bt in the K2 Campaign 16 field. With a redshift of z=0.01098 and a peak apparent magnitude of B_{max}=14.31, ASASSN-18bt is the nearest and brightest SNe Ia yet observed by the Kepler spacecraft. Here we present the discovery of ASASSN-18bt, the K2 light curve, and pre-discovery data from ASAS-SN and the Asteroid Terrestrial-impact Last Alert System (ATLAS). The K2 early-time light curve has an unprecedented 30-minute cadence and photometric precision for an SN~Ia light curve, and it unambiguously shows a ~4 day nearly linear phase followed by a steeper rise. Thus, ASASSN-18bt joins a growing list of SNe Ia whose early light curves are not well described by a single power law. We show that a double-power-law model fits the data reasonably well, hinting that two physical processes must be responsible for the observed rise. However, we find that current models of the interaction with a non-degenerate companion predict an abrupt rise and cannot adequately explain the initial, slower linear phase. Instead, we find that existing, published models with shallow 56Ni are able to span the observed behavior and, with tuning, may be able to reproduce the ASASSN-18bt light curve. Regardless, more theoretical work is needed to satisfactorily model this and other early-time SNe~Ia light curves. Finally, we use Swift X-ray non-detections to constrain the presence of circumstellar material (CSM) at much larger distances and lower densities than possible with the optical light curve. For a constant density CSM these non-detections constrain rho<4.5 * 10^5 cm^-3 at a radius of 4 *10^15 cm from the progenitor star. Assuming a wind-like environment, we place mass-loss limits of Mdot< 8 * 10^-6 M_sun yr^-1 for v_w=100 km s^-1, ruling out some symbiotic progenitor systems.
We simultaneously present constraints on the stellar-to-halo mass relation for central and satellite galaxies through a weak lensing analysis of spectroscopically classified galaxies. Using overlapping data from the fourth data release of the Kilo-Degree Survey (KiDS), and the Galaxy And Mass Assembly survey (GAMA), we find that satellite galaxies are hosted by halo masses that are $0.53 \pm 0.39$ dex (68\% confidence, $3\sigma$ detection) smaller than those of central galaxies of the same stellar mass (for a stellar mass of $\log(M_{\star}/M_{\odot}) = 10.6$). This is consistent with galaxy formation models, whereby infalling satellite galaxies are preferentially stripped of their dark matter. We find consistent results with similar uncertainties when comparing constraints from a standard azimuthally averaged galaxy-galaxy lensing analysis and a two-dimensional likelihood analysis of the full shear field. As the latter approach is somewhat biased due to the lens incompleteness and as it does not provide any improvement to the precision when applied to actual data, we conclude that stacked tangential shear measurements are best-suited for studies of the galaxy-halo connection.
The calculation of the quartic mass terms at order \alpha_s^3 to the hadronic R ratio is described. It is based on the operator product expansion for the quark current correlator, combined with an application of the renormalization group equation.
We give a bound for the order of the local monodromy of a compatible system of l-adic representations, which is independent of l. For the etale cohomology of a variety, the bound depends only on some numerical invariants of varieties.