ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider spin correlations in the one dimensional half filled repulsive Hubbard model. For very large values of the on-site repulsion U the spin correlations are dominated by virtual hopping processes of electrons and are described in terms of a spin-1/2 Heisenberg chain. As U is decreased real hopping processes of electrons become important and eventually dominate the spin response. We discuss the evolution of the dynamical structure factor as a function of U. We comment on the relevance of our results for inelastic neutron scattering experiments on quasi-1D materials.
This talk reports on work aimed at improving our understanding of charged states in gauge theories.Emphasis is placed on different ways of implementingthe gauge invariance of physical states. QED perturbative calculations are used to stress that gauge invariance is not enough: only a subset of such states have a direct physical significance. In QCD a non-perturbative obstruction means that quarks and gluons cannot form physical states and as such these particles are not truely observables. This sets a fundamental limit on the constituent quark model.
To date more than half a dozen X-ray dim isolated neutron stars are known. Their X-ray spectra are characterized by soft blackbody-like emission (kT about 50-120 eV) without indication for harder, non-thermal components. These stars apparently show no radio emission and no association with supernova remnants. Four of them exhibit pulsations in their X-ray flux with periods in the range of 8.39 s to 22.7 s. Similar pulse periods were found from AXPs, maybe suggesting evolutionary connections. In this talk I will review the recent observational results from X-ray dim isolated neutron obtained by the major X-ray observatories XMM-Newton and Chandra. Spectral and temporal characteristics, inferred luminosities and magnetic field strengths will be compared with those of AXPs.
Thermodynamics, the branch of physics concerned with the description of macroscopic bodies, heat exchange and the conversion of different forms of energy is based on four laws: the zeroth law, which states that bodies in thermal contact reach a state of thermal equilibrium, the first law, which postulates the energy conservation and establishes the way in which different forms of energy transform into each-other, the second law, which states that the entropy increases or stays constant in time in any isolated system, and, finally, the third law (or Nernst postulate), which states that the entropy of any system approaches a constant minimum when temperature approaches 0 K. One of the direct consequences of the third law is that the specific heat of any system converges to zero when its temperature decreases to zero Kelvins. Here we show that the third law is violated in a wide class of fermionic systems, by calculating the specific heat and showing that it diverges to infinity when the absolute zero temperature is approached. Until now, no exception to these four laws is know in physics. These findings ask for the revision of one of the most fundamental laws of nature.
An electron spin resonance (ESR) study of the heavy fermion compound YbRh2Si2 for fields up to ~ 8 T reveals a strongly anisotropic signal below the single ion Kondo temperature T_K ~ 25 K. A remarkable similarity between the T-dependence of the ESR parameters and that of the specific heat and the 29Si nuclear magnetic resonance data gives evidence that the ESR response is given by heavy fermions which are formed below T_K and that ESR properties are determined by their field dependent mass and lifetime. The signal anisotropy, otherwise typical for Yb{3+} ions, suggests that, owing to a strong hybridization with conduction electrons at T < T_K, the magnetic anisotropy of the 4f states is absorbed in the ESR of heavy quasiparticles. Tuning the Kondo effect on the 4f states with magnetic fields ~ 2 - 8 T and temperature 2 - 25 K yields a gradual change of the ESR g-factor and linewidth which reflects the evolution of the Kondo state in this Kondo lattice system.
Application of deconvolution algorithms to astronomical images is often limited by variations in PSF structure over the domain of the images. One major difficulty is that Fourier methods can no longer be used for fast convolutions over the entire images. However, if the PSF is modeled as a sum of orthogonal functions that are individually constant in form over the images, but whose relative amplitudes encode the PSF spatial variability, then separation of variables again allows global image operations to be used. This approach is readily adapted to the Lucy-Richardson deconvolution algorithm. Use of the Karhunen-Loeve transform allows for a particularly compact orthogonal expansion of the PSF. These techniques are demonstrated on the deconvolution of Gemini/Hokupa'a adaptive optics images of the galactic center.
The ability of a classifier to recognize unknown inputs is important for many classification-based systems. We discuss the problem of simultaneous classification and novelty detection, i.e. determining whether an input is from the known set of classes and from which specific class, or from an unknown domain and does not belong to any of the known classes. We propose a method based on the Generative Adversarial Networks (GAN) framework. We show that a multi-class discriminator trained with a generator that generates samples from a mixture of nominal and novel data distributions is the optimal novelty detector. We approximate that generator with a mixture generator trained with the Feature Matching loss and empirically show that the proposed method outperforms conventional methods for novelty detection. Our findings demonstrate a simple, yet powerful new application of the GAN framework for the task of novelty detection.
Single atoms can be considered as basic objects for electron microscopy to test the microscope performance and basic concepts for modeling of image contrast. In this work high-resolution transmission electron microscopy was applied to image single platinum atoms in an aberration-corrected transmission electron microscope. The atoms are deposited on a self-assembled monolayer substrate which induces only negligible contrast. Single-atom contrast simulations were performed on the basis of Weickenmeier-Kohl and Doyle-Turner scattering factors. Experimental and simulated intensities are in full agreement on an absolute scale.
We establish a weighted pointwise Jacobian determinant inequality on corank 1 Carnot groups related to optimal mass transportation akin to the work of Cordero-Erausquin, McCann and Schmuckenschl\"ager. In this setting, the presence of abnormal geodesics does not allow the application of the general sub-Riemannian optimal mass transportation theory developed by Figalli and Rifford and we need to work with a weaker notion of Jacobian determinant. Nevertheless, our result achieves a transition between Euclidean and sub-Riemannian structures, corresponding to the mass transportation along abnormal and strictly normal geodesics, respectively. The weights appearing in our expression are distortion coefficients that reflect the delicate sub-Riemannian structure of our space. As applications, entropy, Brunn-Minkowski and Borell-Brascamp-Lieb inequalities are established on Carnot groups.
The Unitary Correlation Operator Method (UCOM) is applied to realistic potentials. The effects of tensor correlations are investigated. The resulting phase shift equivalent correlated interactions are used in the no-core shell model for light nuclei and for mean-field calculations in the Fermionic Molecular Dynamics model for nuclei up to mass A=48.
We prove a variant of the central limit theorem (CLT) for a sequence of i.i.d. random variables $\xi_j$, perturbed by a stochastic sequence of linear transformations $A_j$, representing the model uncertainty. The limit, corresponding to a "worst" sequence $A_j$, is expressed in terms of the viscosity solution of the $G$-heat equation. In the context of the CLT under sublinear expectations this nonlinear parabolic equation appeared previously in the papers of S.Peng. Our proof is based on the technique of half-relaxed limits from the theory of approximation schemes for fully nonlinear partial differential equations.
Double-level quantum systems are good candidates for revealing coherent quantum transport properties. Here, we consider quantum interference effects due to the formation of a two-level system (TLS) coupled to the edge channel of a zigzag Phosphorene nanoribbon (ZPNR). Using the tight-binding approach, we first demonstrate the formation of a TLS in bulk Phosphorene sheet due to the existence of two nearby vacancy impurities. Then, we show that such a TLS can couple to the quasi-one-dimensional continuum of the edge states in a ZPNR which results in the the appearance of two-dip Fano-type line shapes. To this end, we generalize the Lippmann-Schwinger approach to study the scattering of edge electrons in a ZPNR by two coupled impurity defects. We obtain an analytical expression of the transmission coefficient which shows that the positions and widths of the anti-resonances can be controlled by changing the intervacancy distance as well as their distance from the edge of the ribbon. This work constitutes a clear example of the multiple Fano resonances in mesoscopic transport.
We investigate the regularity of the free boundary for the Signorini problem in $\mathbb{R}^{n+1}$. It is known that regular points are $(n-1)$-dimensional and $C^\infty$. However, even for $C^\infty$ obstacles $\varphi$, the set of non-regular (or degenerate) points could be very large, e.g. with infinite $\mathcal{H}^{n-1}$ measure.   The only two assumptions under which a nice structure result for degenerate points has been established are: when $\varphi$ is analytic, and when $\Delta\varphi < 0$. However, even in these cases, the set of degenerate points is in general $(n-1)$-dimensional (as large as the set of regular points).   In this work, we show for the first time that, "usually", the set of degenerate points is small. Namely, we prove that, given any $C^\infty$ obstacle, for "almost every" solution the non-regular part of the free boundary is at most $(n-2)$-dimensional. This is the first result in this direction for the Signorini problem.   Furthermore, we prove analogous results for the obstacle problem for the fractional Laplacian $(-\Delta)^s$, and for the parabolic Signorini problem. In the parabolic Signorini problem, our main result establishes that the non-regular part of the free boundary is $(n-1-\alpha_\circ)$-dimensional for almost all times $t$, for some $\alpha_\circ > 0$.   Finally, we construct some new examples of free boundaries with degenerate points.
We present an extreme localization mechanism induced by a magnetic field for tight-binding electrons in two-dimensional structures. This spectacular phenomenon is investigated for a large class of tilings (periodic, quasiperiodic, or random). We are led to introduce the Aharonov-Bohm cages defined as the set of sites eventually visited by a wavepacket that can, for particular values of the magnetic flux, be bounded. We finally discuss the quantum dynamics which exhibits an original pulsating behaviour.
Mach's Principle says that a particle's inertia is due to some interaction of that particle with all the other masses in the universe. Here we explore the possibility of the gravitational interaction energy of the background quantum vacuum energy playing the role of a global Higg's field (described by a varying cosmological constant) entirely contributing to the local inertial masses of particles in the spirit of Mach's principle.
Twisted bilayer transition metal dichalcogenides have emerged as important model systems for the investigation of correlated electron physics because their interaction strength, carrier concentration, band structure, and inversion symmetry breaking are controllable by device fabrication, twist angle, and most importantly, gate voltage, which can be varied in situ. The low energy physics of some of these materials has been shown to be described by a "moir\'e Hubbard model" generalized from the usual Hubbard model by the addition of strong, tunable spin orbit coupling and inversion symmetry breaking. In this work, we use a Hartree-Fock approximation to reach a comprehensive understanding of the moir\'e Hubbard model on the mean field level. We determine the magnetic and metal-insulator phase diagrams, and assess the effects of spin orbit coupling, inversion symmetry breaking, and the tunable van Hove singularity. We also consider the spin and orbital effects of applied magnetic fields. This work provides guidance for experiments and sets the stage for beyond mean-field calculations.
In their Comment, Greer et al (i) put us in charge of a pretended wrong claim, which we never made in Phys.~Rev.~B {\bf 78}, 115315 (2008), where we criticized a method (DG)proposed by two of them, (ii) incorrectly claim that the DG method can reproduce the conductance quantum $g_0$, but (iii) to deduce $g_0$ for a toy model, they carry out calculations within the standard Landauer method, which has nothing to do with the DG's. We present results for their model obtained within the DG method, which demonstrate that the DG method fails as lamentably as in the examples we presented in our earlier work. We also analyze the physical reasons why the DG method fails.
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can be inferred from the spectrum, i.e. the multiset of the eigenvalues, of an operator associated to a hypergraph. It is expected that a small perturbation of a hypergraph, such as the removal of a few vertices or edges, does not lead to a major change of the eigenvalues. In particular, it is expected that the eigenvalues of the original hypergraph interlace the eigenvalues of the perturbed hypergraph. Here we work on hypergraphs where, in addition, each vertex--edge incidence is given a real number, and we prove interlacing results for the adjacency matrix, the Kirchoff Laplacian and the normalized Laplacian. Tightness of the inequalities is also shown.
In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients.
Electronic phase separation (EPS) originates from an incomplete transformation between electronic phases, causing the inhomogeneous spatial distribution of electronic properties. In the system of two-dimensional electron gas (2DEG), the EPS is usually identified based on a percolative metal-to-superconductor transition. Here, we report a metal-insulator transition (MIT) in KTaO3-based 2DEG with the width of conductive channel decreasing into micrometer scale. Hysteretic resistance-temperature relations are observed due to the competition between metallic and insulating phases, which is tunable by magnetic field. Such a size-dependent MIT effect is attributed to the coexistence and separation of metallic and insulating phases. Combining density functional theory calculation, we propose a theoretical model to simulate the dynamic process of the EPS using the percolation theory, demonstrating the mechanism of size-dependent MIT. Our work suggests a clear and simple 2DEG platform to achieve the spatial coexistence of metallic and insulating phases.
We investigate the properties of an abstract family of advection diffusion equations in the context of the fractional Laplacian. Two independent diffusion parameters enter the system, one via the constitutive law for the drift velocity and one as the prefactor of the fractional Laplacian. We obtain existence and convergence results in certain parameter regimes and limits. We study the long time behaviour of solutions to the general problem and prove the existence of a unique global attractor. We apply results to two particular active scalar equations arising in geophysical fluid dynamics, namely the surface quasigeostrophic equation and the magnetogeostrophic equation.
GRB 111209A, one of the longest Gamma-Ray Bursts (GRBs) ever observed, is linked to SN 2011kl, the most luminous GRB-Supernova (SN) detected so far, which shows evidence for being powered by a magnetar central engine. We place SN 2011kl into the context of large samples of SNe, addressing in more detail the question of whether it could be radioactively powered, and whether it represents an extreme version of a GRB-SN or an underluminous Superluminous SN (SLSN). We model SN 2011kl using SN 1998bw as a template and derive a bolometric light curve including near-infrared data. We compare the properties of SN 2011kl to literature results on stripped-envelope and superluminous supernovae. Comparison in the k,s context, i.e., comparing it to SN 1998bw templates in terms of luminosity and light-curve stretch, clearly shows SN 2011kl is the most luminous GRB-SN to date, and it is spectrally very dissimilar to other events, being significantly bluer/hotter. Although SN 2011kl does not reach the classical luminosity threshold of SLSNe and evolves faster than any of them, it resembles SLSNe more than the classical GRB-associated broad-lined Type Ic SNe in several aspects. GRB 111209A was a very energetic event, both at early (prompt emission) and at very late (SN) times. We have shown in a further publication that with the exception of the extreme duration, the GRB and afterglow parameters are in agreement with the known distributions for these parameters. SN 2011kl, on the other hand, is exceptional both in luminosity and spectral characteristics, indicating that GRB 111209A was likely not powered by a standard-model collapsar central engine, further supporting our earlier conclusions. Instead, it reveals the possibility of a direct link between GRBs and SLSNe.
In this paper, we present CLCC, a novel contrastive learning framework for color constancy. Contrastive learning has been applied for learning high-quality visual representations for image classification. One key aspect to yield useful representations for image classification is to design illuminant invariant augmentations. However, the illuminant invariant assumption conflicts with the nature of the color constancy task, which aims to estimate the illuminant given a raw image. Therefore, we construct effective contrastive pairs for learning better illuminant-dependent features via a novel raw-domain color augmentation. On the NUS-8 dataset, our method provides $17.5\%$ relative improvements over a strong baseline, reaching state-of-the-art performance without increasing model complexity. Furthermore, our method achieves competitive performance on the Gehler dataset with $3\times$ fewer parameters compared to top-ranking deep learning methods. More importantly, we show that our model is more robust to different scenes under close proximity of illuminants, significantly reducing $28.7\%$ worst-case error in data-sparse regions.
We present a catalog of extended objects in the vicinity of M81 based a set of 24 Hubble Space Telescope Advanced Camera for Surveys (ACS) Wide Field Camera (WFC) F814W (I-band) images. We have found 233 good globular cluster candidates; 92 candidate HII regions, OB associations, or diffuse open clusters; 489 probable background galaxies; and 1719 unclassified objects. We have color data from ground-based g- and r-band MMT Megacam images for 79 galaxies, 125 globular cluster candidates, 7 HII regions, and 184 unclassified objects. The color-color diagram of globular cluster candidates shows that most fall into the range 0.25 < g-r < 1.25 and 0.5 < r-I < 1.25, similar to the color range of Milky Way globular clusters. Unclassified objects are often blue, suggesting that many of them are likely to be HII regions and open clusters, although a few galaxies and globular clusters may be among them.
Except for the Hermitian buildings $\mathcal{H}(4,q^2)$, up to a combination of duality, translation duality or Payne integration, every known finite building of type $\mathbb{B}_2$ satisfies a set of general synthetic properties, usually put together in the term "skew translation generalized quadrangle" (STGQ). In this series of papers, we classify finite skew translation generalized quadrangles. In the first installment of the series, as corollaries of the machinery we develop in the present paper, (a) we obtain the surprising result that any skew translation quadrangle of odd order $(s,s)$ is a symplectic quadrangle; (b) we determine all skew translation quadrangles with distinct elation groups (a problem posed by Payne in a less general setting); (c) we develop a structure theory for root-elations of skew translation quadrangles which will also be used in further parts, and which essentially tells us that a very general class of skew translation quadrangles admits the theoretical maximal number of root-elations for each member, and hence all members are "central" (the main property needed to control STGQs, as which will be shown throughout); (d) we solve the Main Parameter Conjecture for a class of STGQs containing the class of the previous item, and which conjecturally coincides with the class of all STGQs.
We present a combined study of Ni $K$-edge resonant x-ray scattering and density functional calculations to probe and distinguish electronically driven ordering and lattice distortions in nickelate heterostructures. We demonstrate that due to the low crystal symmetry, contributions from structural distortions can contribute significantly to the energy-dependent Bragg peak intensities of a bond-ordered NdNiO$_3$ reference film. For a LaNiO$_3$-LaAlO$_3$ superlattice that exhibits magnetic order, we establish a rigorous upper bound on the bond-order parameter. We thus conclusively confirm predictions of a dominant spin density wave order parameter in metallic nickelates with a quasi-two-dimensional electronic structure.
We compute and study two determinantal representations of the discriminant of a cubic quaternary form. The first representation is the Chow form of the $2$-uple embedding of $\mathbb{P}^3$ and is computed as the Pfaffian of the Chow form of a rank 2 Ulrich bundle on this Veronese variety. We then consider the determinantal representation described by Nanson. We investigate the geometric nature of cubic surfaces whose discriminant matrices satisfy certain rank conditions. As a special case of interest, we use certain minors of this matrix to suggest equations vanishing on the locus of $k$-nodal cubic surfaces.
The first stars are the key to the formation of primitive galaxies, early cosmological reionization and chemical enrichment, and the origin of supermassive black holes. Unfortunately, in spite of their extreme luminosities, individual Population III stars will likely remain beyond the reach of direct observation for decades to come. However, their properties could be revealed by their supernova explosions, which may soon be detected by a new generation of NIR observatories such as JWST and WFIRST. We present light curves and spectra for Pop III pair-instability supernovae calculated with the Los Alamos radiation hydrodynamics code RAGE. Our numerical simulations account for the interaction of the blast with realistic circumstellar envelopes, the opacity of the envelope, and Lyman absorption by the neutral IGM at high redshift, all of which are crucial to computing the NIR signatures of the first cosmic explosions. We find that JWST will detect pair-instability supernovae out to z > 30, WFIRST will detect them in all-sky surveys out to z ~ 15 - 20 and LSST and Pan-STARRS will find them at z ~ 7 - 8. The discovery of these ancient explosions will probe the first stellar populations and reveal the existence of primitive galaxies that might not otherwise have been detected.