ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the spin-half Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square-lattice at one end, a set of decoupled spin-chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations and varying dimensionality. There is a large region of the usual 2-sublattice Ne\'el phase, a 3-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wavevector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical.
We analyze the ground state properties of the two-dimensional quantum antiferromagnet with a S=1/2 Kondo impurity. Perturbation theory around the strong Kondo coupling limit is developed and the results compared with studies, based on exact diagonalization of small clusters. We find that at intermediate coupling the impurity is partially screened and the magnetization locally suppressed. A local singlet between the impurity and the host spin is formed asymptotically.
In this paper we compute the multiple cover Gromov-Witten integrals (analog of the Aspinwall-Morrison formula) for the unramified compactification of the moduli space of stable maps to an embedded $\PO$ in a Calabi-Yau threefold $X$ with the normal bundle $\mathcal{O}_{\PO}(-1) \bigoplus \mathcal{O}_{\PO}(-1)$.
In 1960 R\'enyi in his Michigan State University lectures asked for the number of random queries necessary to recover a hidden bijective labeling of $n$ distinct objects. In each query one selects a random subset of labels and asks, which objects have these labels? We consider here an asymmetric version of the problem in which in every query an object is chosen with probability $p > 1/2$ and we ignore "inconclusive" queries. We study the number of queries needed to recover the labeling in its entirety ($H_n$), before at least one element is recovered ($F_n$), and to recover a randomly chosen element $(D_n)$. This problem exhibits several remarkable behaviors: $D_n$ converges in probability but not almost surely, $H_n$ and $F_n$ exhibit phase transitions with respect to $p$ in the second term. We prove that for $p>1/2$ with high probability (whp) we need $H_n=\log_{1/p} n +\frac 12 \log_{p/(1-p)}\log n +o(\log \log n) $ queries to recover the entire bijection. This should be compared to its symmetric ($p=1/2$) counterpart established by Pittel and Rubin, who proved that in this case one requires $H_n=\log_{2} n +\sqrt{2 \log_{2} n} +o(\sqrt{\log n}) $ queries. As a bonus, our analysis implies novel results for random PATRICIA tries, as the problem is probabilistically equivalent to that of the height, fillup level, and typical depth of a PATRICIA trie built from $n$ independent binary sequences generated by a biased($p$) memoryless source.
Despite the success of deep neural networks on facial action unit (AU) detection, better performance depends on a large number of training images with accurate AU annotations. However, labeling AU is time-consuming, expensive, and error-prone. Considering AU detection and facial expression recognition (FER) are two highly correlated tasks, and facial expression (FE) is relatively easy to annotate, we consider learning AU detection and FER in a multi-task manner. However, the performance of the AU detection task cannot be always enhanced due to the negative transfer in the multi-task scenario. To alleviate this issue, we propose a Meta Auxiliary Learning method (MAL) that automatically selects highly related FE samples by learning adaptative weights for the training FE samples in a meta learning manner. The learned sample weights alleviate the negative transfer from two aspects: 1) balance the loss of each task automatically, and 2) suppress the weights of FE samples that have large uncertainties. Experimental results on several popular AU datasets demonstrate MAL consistently improves the AU detection performance compared with the state-of-the-art multi-task and auxiliary learning methods. MAL automatically estimates adaptive weights for the auxiliary FE samples according to their semantic relevance with the primary AU detection task.
A spectroscopic analysis of the DBA (or DAB) white dwarf KUV 02196+2816 is presented. The observed hydrogen and helium line profiles are shown to be incompatible with model spectra calculated under the assumption of a homogeneous hydrogen and helium chemical composition. In contrast, an excellent fit to the optical spectrum of KUV 02196+2816 can be achieved if the object is interpreted as an unresolved double degenerate composed of a hydrogen-line DA star and a helium-line DB star. The atmospheric parameters obtained from the best fit are Teff=27,170 K and log g=8.09 for the DA star, Teff=36,340 K and log g=8.09 for the DB star, which implies that the total mass of the system (M~1.4 Msol) is very close to the Chandrasekhar limit. Moreover, the effective temperature of the DB stars lies well within the so-called DB gap where very few bright DB stars are found. The implications of this discovery with respect to the DAB and DBA spectral classes and to the evolution of double degenerate binaries are discussed.
A study of meson-baryon systems with total strangeness -1 is made within a framework based on the chiral and hidden local symmetries. These systems consist of octet baryons, pseudoscalar and vector mesons. The pseudoscalar meson-baryon (PB) dynamics has been earlier found determinant for the existence of some strangeness -1 resonances, for example, $\Lambda(1405)$, $\Lambda(1670)$, etc. The motivation of the present work is to study the effect of coupling the closed vector meson-baryon (VB) channels to these resonances. To do this, we obtain the $PB \rightarrow PB$ and $VB \rightarrow VB$ amplitudes from the t-channel diagrams and the $PB \leftrightarrow VB$ amplitudes are calculated using the Kroll-Ruddermann term where, considering the vector meson dominance phenomena, the photon is replaced by a vector meson. The calculations done within this formalism reveal a very strong coupling of the VB channels to the $\Lambda(1405)$ and $\Lambda(1670)$. In the isospin 1 case, we find an evidence for a double pole structure of the $\Sigma (1480)$ which, like the isospin 0 resonances, is also found to couple strongly to the VB channels. The strong coupling of these low-lying resonances to the VB channels can have important implications on certain reactions producing them.
Consider a random real tree whose leaf set, or boundary, is endowed with a finite mass measure. Each element of the tree is further given a type, or allele, inherited from the most recent atom of a random point measure (infinitely-many-allele model) on the skeleton of the tree. The partition of the boundary into distinct alleles is the so-called allelic partition.   In this paper, we are interested in the infinite trees generated by supercritical, possibly time-inhomogeneous, binary branching processes, and in their boundary, which is the set of particles `co-existing at infinity'. We prove that any such tree can be mapped to a random, compact ultrametric tree called coalescent point process, endowed with a `uniform' measure on its boundary which is the limit as $t\to\infty$ of the properly rescaled counting measure of the population at time $t$.   We prove that the clonal (i.e., carrying the same allele as the root) part of the boundary is a regenerative set that we characterize. We then study the allelic partition of the boundary through the measures of its blocks. We also study the dynamics of the clonal subtree, which is a Markovian increasing tree process as mutations are removed.
The recombination model as a model for hadronization from a quark-gluon plasma has been recently revived since it has advantages in explaining several important features of the final state produced in heavy-ion collisions at RHIC, such as the constituent quark number scaling of the elliptic coefficient versus the transverse energy of identified hadrons, the bending shape of the $p_T$ spectrum of hadrons near 5 GeV/c, and the measured large value of baryon to meson ratio(of the order of unity) in the same $p_T$ range. We have developed a dynamic simulation model of heavy-ion collisions in which a quark-gluon plasma, starting from a certain initial condition, evolves hydrodynamically until it reaches the phase boundary, and then hadronizes by valence quark recombination. Rescattering after hadronization is described by UrQMD. We discuss some details of the model and report first, preliminary results.
Neutrinos are neutral, spin-$\frac{1}{2}$ particles which undergo only weak interactions. The experimentally observed phenomenon of neutrino oscillation establishes the fact that neutrinos are massive and there is mixing between different neutrino flavours. This constitutes the first unambiguous hint towards the physics Beyond Standard Model (BSM). In the BSM theories, the neutrino mass terms in the Lagrangian lead to the non-diagonal neutrino mass matrix in the flavour basis which depends on neutrino mass and mixing parameters. Thus knowledge of the neutrino oscillation parameters and understanding the underlying symmetries of the neutrino mass matrix are very important as they can give an insight to the new physics beyond Standard Model. Therefore the measurement of different oscillation parameters and studying the structure of the neutrino mass matrix are some of the main goals in neutrino physics at present. In this thesis we have studied the potential of present/future neutrino oscillation experiments and synergy between them to determine the unknown parameters in the neutrino sector in the light of current experimental results. We have also studied the phenomenological consequences of texture zeros in the neutrino mass matrices in the presence of a sterile neutrino.
We shortly review recent successes in applying Bose-Einstein interferometry in heavy ion collisions and the proceed to some model calculations for 3-dimensional Bose-Einstein correlation functions in electron-positron collisions at the Z0 pole.
We consider the Gelfand problem on a planar domain. Under some conditions on the potential, we provide the first examples of multiplicity for blowing-up solutions at a given point in the domain. The argument is based on a refined Lyapunov-Schmidt reduction and the computation of the degree of a finite-dimensional map.
The results of VLBI total intensity (I) and linear polarization (P) observations at 6cm are presented for ten radio bright BL Lacertae objects. These images complete first-epoch polarization observations for the 1-Jy sample of northern BL Lacertae objects defined by Kuhr and Schmidt. Estimates of superluminal speeds are presented for several sources, bringing the total number of sources in the sample for which such estimates are available to 16. Second epoch observations currently being reduced should yield speed estimates for VLBI features in essentially all the sources in the sample. The jet magnetic fields of these BL Lacertae objects are usually transverse to the local jet direction, but a sizeable minority (about 30%) have VLBI jet components with longitudinal magnetic fields. This may suggest that the conditions in the VLBI jets of BL Lacertae objects are favorable for the formation of relativistic shocks; alternatively, it may be that the toroidal component of the intrinsic jet magnetic field is characteristically dominant in these sources.
Nitrogen is one of the most abundant metals in the interstellar medium (ISM), and thus it constitutes an excellent test to study a variety of astrophysical environments, ranging from nova to active galactic nuclei. We present a detailed analysis of the gaseous component of the N K~edge using high-resolution {\it XMM-Newton} spectra of 12 Galactic and 40 extragalactic sources. For each source, we have estimated column densities for {\rm N}~{\sc i}, {\rm N}~{\sc ii}, {\rm N}~{\sc iii}, {\rm N}~{\sc v}, {\rm N}~{\sc vi} and {\rm N}~{\sc vii} ionic species, which trace the cold, warm and hot phases of the local Galactic interstellar medium. We have found that the cold-warm component column densities decrease with the Galactic latitude while the hot component does not. Moreover, the cold column density distribution is in good agreement with UV measurements. This is the first detailed analysis of the nitrogen K-edge absorption due to ISM using high-resolution X-ray spectra.
An investigation of the N\'eel Long Range Order (NLRO) in the ground state of antiferromagnetic Heisenberg spin system on the two-dimensional, uniform, bipartite lattice consisting of squares, hexagons and dodecagons is presented. Basing on the analysis of the order parameter and the long-distance correlation function the NLRO is shown to occur in this system. Exact diagonalization and variational (Resonating Valence Bond) methods are applied.
Two-point correlation functions of cosmic microwave background polarization provide a physically independent probe of the surprising suppression of correlations in the cosmic microwave background temperature anisotropies at large angular scales. We investigate correlation functions constructed from both the Q and U Stokes parameters and from the E and B polarization components. The dominant contribution to these correlation functions comes from local physical effects at the last scattering surface or from the epoch of reionization at high redshift, so all should be suppressed if the temperature suppression is due to an underlying lack of correlations in the cosmological metric perturbations larger than a given scale. We evaluate the correlation functions for the standard $\Lambda$CDM cosmology constrained by the observed temperature correlation function, and compute statistics characterizing their suppression on large angular scales. Future full-sky polarization maps with minimal systematic errors on large angular scales will provide strong tests of whether the observed temperature correlation function is a statistical fluke or reflects a fundamental shortcoming of the standard cosmological model.
Ultrafunctions are a particular class of functions defined on a Non Archimedean field E. They have been introduced and studied in some previous works. In this paper we develop the notion of fine ultrafunctions which improves the older definitions in many crucial points. Some applications are given to show how ultrafunctions can be applied in studing Partial Differential Equations. In particular, it is possible to prove the existence of ultrafunction solutions to ill posed evolution poblems.
Let $(X, \omega_X)$ be a compact K\"ahler manifold such that the anticanonical bundle $-K_X$ is nef. We prove that the slopes of the Harder-Narasimhan filtration of the tangent bundle with respect to a polarization of the form $\omega_X^{n-1}$ are semi-positive. As an application, we give a characterization of rationally connected compact K\"ahler manifolds with nef anticanonical bundles. As another application, we give a simple proof of the surjectivity of the Albanese map.
This paper presents $N$-body and stochastic models that describe the motion of tracer particles in a potential that contains a large population of extended substructures. Fluctuations of the gravitational field induce a random walk of orbital velocities that is fully specified by drift and diffusion coefficients. In the impulse and local approximations the coefficients are computed analytically from the number density, mass, size and relative velocity of substructures without arbitrary cuts in forces or impact parameters. The resulting Coulomb logarithm attains a well-defined geometrical meaning, $\ln(\Lambda)=\ln (D/c)$, where $D/c$ is the ratio between the average separation and the individual size of substructures. Direct-force and Monte-Carlo $N$-body experiments show excellent agreement with the theory if substructures are sufficiently extended ($c/D\gtrsim 10^{-3}$) and not spatially overlapping ($c/D\lesssim 10^{-1}$). However, close encounters with point-like objects ($c/D\ll 10^{-3}$) induce a heavy-tailed, non-Gaussian distribution of high-energy impulses that cannot be described with Brownian statistics. In the point-mass limit ($c/D\approx 0$) the median Coulomb logarithm measured from $N$-body models deviates from the theoretical relation, converging towards a maximum value $\langle \ln(\Lambda)\rangle \approx 8.2$ independently of the mass and relative velocity of nearby substructures.
This paper shows the fastest way to force a win with rook and king against king on an m*n board. In the classical case, this gives a faster win than what Capablanca suggested in his book 'Chess Fundamentals'.
We propose and study methods for detecting the Unruh effect in a Bose-Einstein condensate. The Bogoliubov vacuum of a Bose-Einstein condensate is used here to simulate a scalar field-theory, and accelerated atom dots or optical lattices as means for detecting phonon radiation due to acceleration effects. We study Unruh's effect for linear acceleration and circular acceleration. In particular, we study the dispersive effects of the Bogoliubov spectrum on the ideal case of exact thermalization. Our results suggest that Unruh's acceleration radiation can be tested using current accessible experimental methods.
We measure the cross-correlation of Atacama Cosmology Telescope CMB lensing convergence maps with quasar maps made from the Sloan Digital Sky Survey DR8 SDSS-XDQSO photometric catalog. The CMB lensing-quasar cross-power spectrum is detected for the first time at a significance of 3.8 sigma, which directly confirms that the quasar distribution traces the mass distribution at high redshifts z>1. Our detection passes a number of null tests and systematic checks. Using this cross-power spectrum, we measure the amplitude of the linear quasar bias assuming a template for its redshift dependence, and find the amplitude to be consistent with an earlier measurement from clustering; at redshift z ~ 1.4, the peak of the distribution of quasars in our maps, our measurement corresponds to a bias of b = 2.5 +/- 0.6. With the signal-to-noise ratio on CMB lensing measurements likely to improve by an order of magnitude over the next few years, our results demonstrate the potential of CMB lensing cross-correlations to probe astrophysics at high redshifts.
The scattering of Dirac particles by symmetric potentials in one dimension is studied. A Levinson theorem is established. By this theorem, the number of bound states with even (odd) parity, $n_+$ ($n_-$), is related to the phase shifts $\eta_+(\pm E_k)$ [$\eta_-(\pm E_k)$] of scattering states with the same parity at zero momentum as follows: $$\eta_\pm(\mu)+\eta_\pm(-\mu)\pm{\pi\over 2}[\sin^2\eta_\pm(\mu) -\sin^2\eta_\pm(-\mu)]=n_\pm\pi.$$ The theorem is verified by several simple examples.
A relativistic distorted wave impulse approximation model for electron-induced one proton knockout reactions and a Green's function approach to inclusive scattering are developed. Results for (e,e'p) and (e,e') reactions are presented in various kinematical conditions and compared (when possible) with nonrelativistic calculations.
Previous measurements utilizing Maxwell relations to measure change in entropy, $S$, demonstrated remarkable accuracy of measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had the benefit of making the determination of entropy independent of measurement scaling, but at the cost of limiting the applicability of the approach to relatively simple systems. To measure entropy of more exotic mesoscopic systems, a new analysis technique can be employed; however, doing so requires precise knowledge of the measurement scaling. Here, we give details on the necessary improvements made to the original experimental approach and highlight some of the common challenges (along with strategies to overcome them) that other groups may face when attempting this type of measurement.
In this paper, we consider global solutions for the following nonlinear Schr\"odinger equation $iu_t+\Delta u+\lambda|u|^\alpha u=0,$ in $\R^N,$ with $\lambda\in\R$ and $0\le\alpha<\frac{4}{N-2}$ $(0\le\alpha<\infty$ if $N=1).$ We show that no nontrivial solution can decay faster than the solutions of the free Schr\"odinger equation, provided that $u(0)$ lies in the weighted Sobolev space $H^1(\R^N)\cap L^2(|x|^2;dx),$ in the energy space, namely $H^1(\R^N),$ or in $L^2(\R^N),$ according to the different cases.
EL CVn-type binaries contain an A-type dwarf star and a very low mass ($\sim 0.2M_\odot$) helium white dwarf precursor (pre-He WD). Recent surveys and observations have discovered dozens of them, and showed that some pre-He WDs have multi-periodic pulsations, opening up the possibility of using asteroseismology to study the interior structure of these stars. We have studied the formation of EL CVn-type binaries to understand the physics of their formation and give the properties and the space density of this population of stars in the Galaxy. We use a simple analysis to show that EL CVn binaries cannot be produced by rapid common envelope evolution because this process leads to merging of the components when a giant has such a low-mass core. We find that EL CVn-type binaries can be produced by long-term stable mass transfer between low-mass stars in close binary systems. We have comprehensively studied this formation channel and the characteristics of the resulting population of EL CVn-type binaries from more than 65,000 runs of binary evolution with primary star masses between 0.9 and $2.0M_\odot$ and assuming composition appropriate for Population I stars. The theoretical evolutionary tracks, mass ratios and the WD mass-period ($M_{\rm WD}-P$) relation are generally in agreement with observations. We conclude that many more EL CVn-type binaries remain to be discovered and that these binaries will be predominantly low-mass systems in old stellar populations.
In 1998, Leclerc and Zelevinsky introduced the notion of weakly separated collections of subsets of the ordered $n$-element set $[n]$ (using this notion to give a combinatorial characterization for quasi-commuting minors of a quantum matrix). They conjectured the purity of certain natural domains $D\subseteq 2^{[n]}$ (in particular, of the hypercube $2^{[n]}$ itself, and the hyper-simplex $\{X\subseteq[n]\colon |X|=m\}$ for $m$ fixed), where $D$ is called pure if all maximal weakly separated collections in $D$ have the same cardinality. These conjectures have been answered affirmatively.   In this paper, generalizing those earlier results, we reveal wider classes of pure domains in $2^{[n]}$. This is obtained as a consequence of our study of a novel geometric--combinatorial model for weakly separated set-systems, so-called \emph{combined (polygonal) tilings} on a zonogon, which yields a new insight in the area.
In this paper we give a very elementary proof that if A and B are subsets of {1,2,...,N}, each having at least 5N^{1 - (4(k-1))^{-1}} elements, then the sumset A+B has a k-term arithmetic progression.