ShantanuT01/DACTYL-Pretraining huggingface dataset:
We provide a detailed analysis of a realization of chiral gapless edge modes in the framework of the Hofstadter model of interacting electrons. In a transverse homogeneous magnetic field and a rational magnetic flux through an unit cell the fermion spectrum splits into topological subbands with well-defined Chern numbers, contains gapless edge modes in the gaps. It is shown that the behavior of gapless edge modes is described within the framework of the Kitaev chain where the tunneling of Majorana fermions is determined by effective hopping of Majorana fermions between chains. The proposed approach makes it possible to study the fermion spectrum in the case of an irrational flux, to calculate the Hall conductance of subbands that form a fine structure of the spectrum. In the case of a rational flux and a strong on-site Hubbard interaction $U$, $ U >4 \Delta $ ($ \Delta $ is a gap), the topological state of the system, which is determined by the corresponding Chern number and chiral gapless edge modes, collapses. When the magnitude of the on-site Hubbard interaction changes, at the point $ U = 4 \Delta $ a topological phase transition is realized, i.e., there are changes in the Chern numbers of two subbands due to their degeneration.
A collider, where particles are injected to a beam splitter from opposite sides, has been used for identifying quantum statistics of identical particles. The collision leads to bunching of the particles for bosons and antibunching for fermions. In recent experiments, a collider was applied to a fractional quantum Hall regime hosting Abelian anyons. The observed negative cross correlation of electrical currents cannot be understood with fermionic antibunching. Here we predict, based on a conformal field theory and non-perturbative treatment of non-equilibrium anyon injection, that the collider provides a tool for direct observation of the braiding statistics of various Abelian and non-Abelian anyons. Its dominant process is not direct collision between injected anyons, contrary to common expectation, but braiding between injected anyons and an anyon excited at the collider. The dependence of the resulting negative cross correlation on the injection currents distinguishes non-Abelian SU(2)$_k$ anyons, Ising anyons, and Abelian Laughlin anyons.
A relativistic wave equation for bound states of two fermions with arbitrary masses which are exposed to a magnetic field is derived from quantum electrodynamics. The interaction kernels are based upon the generalized invariant M-matrices for inter-fermion and fermion-field interactions. As an application we calculate the energy corrections in a weak homogeneous B field to obtain the Zeeman splitting of the hyperfine structure and g-factors in the lowest order (i.e. to alpha^4). Lande g-factors are presented for several of the first excited states of hydrogen, muonium, and muonic-hydrogen.
We identify a close relation between stable distributions and the limiting homomorphisms central to the theory of regular variation. In so doing some simplifications are achieved in the direct analysis of these laws in Pitman and Pitman (2016); stable distributions are themselves linked to homomorphy.
The ability to engineer the quantum state of traveling optical fields is a central requirement for quantum information science and technology, including quantum communication, computing and metrology. In this video article, we describe the reliable generation of non-Gaussian states, including single-photon states and coherent state superpositions, using a conditional preparation method operated on the non-classical light emitted by optical parametric oscillators. Type-I and type-II phase-matched OPOs operated below threshold, i.e. single-mode or two-mode squeezed vacuum sources, are considered and common procedures, such as the required frequency filtering or the high-efficiency quantum state characterization by homodyning, are detailed. The reported method enables a high fidelity with the targeted state and the generation of the state in a well-controlled spatiotemporal mode, a crucial feature for their use in subsequent protocols.
The symmetry energy coefficients of dilute clusterized nuclear matter are evaluated in the $S$-matrix framework. Employing a few different definitions commonly used in the literature for uniform nuclear matter, it is seen that the different definitions lead to perceptibly different results for the symmetry coefficients for dilute nuclear matter. They are found to be higher compared to those obtained for uniform matter in the low density domain. The calculated results are in reasonable consonance with those extracted recently from experimental data.
This article adapts the results of arXiv:1305.6557 to the ultrametric setting. This is a re-edition of the Chapter V of author thesis.
Transient reflectivity (TR) measured at laser photon energy 1.51 eV from the indirectly intersurface coupled topological insulator Bi2-xMnxSe3 films (12 nm thick) revealed a strong dependence of the rise-time and initial decay-time constants on photoexcited carrier density and Mn content. In undoped samples (x = 0), these time constants are exclusively governed by electron-electron and electron-phonon scattering, respectively, whereas in films with x = 0.013 - 0.27 ultrafast carrier dynamics are completely controlled by photoexcited electron trapping by ionized Mn2+ acceptors and their dimers. The shortest decay-time (~0.75 ps) measured for the film with x = 0.27 suggests a great potential of Mn-doped Bi2Se3 films for applications in high-speed optoelectronic devices. Using Raman spectroscopy exploiting similar laser photon energy (1.58 eV), we demonstrate that due to indirect intersurface coupling in the films, the photoexcited electron trapping in the bulk enhances the electron-phonon interaction strength in Dirac surface states.
We study generalized Fibonacci sequences $F_{n+1}=PF_n-QF_{n-1}$ with initial values $F_0=0$ and $F_1=1$. Let $P,Q$ be nonzero integers such that $P^2-4Q$ is not a perfect square. We show that if $Q=\pm 1$ then the sequence $\{F_n\}_{n=0}^\infty$ misses a congruence class modulo every prime large enough. On the other hand, if $Q \neq \pm 1$, we prove that (under GRH) the sequence $\{F_n\}_{n=0}^\infty$ hits every congruence class modulo infinitely many primes.
Conjectures involving infinite families of restricted partition congruences can be difficult to verify for a number of individual cases, even with a computer. We demonstrate how the machinery of Radu's algorithm may be modified and employed to efficiently check a very large number of cases of such conjectures. This allows substantial evidence to be collected for a given conjecture, before a complete proof is attempted.
We present extensive photometric and spectroscopic observations of PTF1 J071912.13+485834.0, an outbursting AM CVn system discovered by the Palomar Transient Factory (PTF). AM CVn systems are stellar binaries with some of the smallest separations known and orbital periods ranging from 5 to 65 minutes. They are believed to be composed of a white dwarf accretor and a (semi)-degenerate He-rich donor and are considered to be the helium equivalents of Cataclysmic Variables. We have spectroscopically and photometrically identified an orbital period of 26.77 \pm 0.02 minutes for PTF1 J071912.13+485834.0 and found a super-outburst recurrence time of greater than 65 days along with the presence of "normal" outbursts - rarely seen in AM CVn systems but well known in super-outbursting Cataclysmic Variables. We present a long-term light curve over two super-cycles as well as high cadence photometry of both outburst and quiescent stages, both of which show clear variability. We also compare both the outburst and quiescent spectra of PTF1 J071912.13+485834.0 to other known AM CVn systems, and use the quiescent phase-resolved spectroscopy to determine the origin of the photometric variability. Finally, we draw parallels between the different subclasses of SU UMa-type Cataclysmic Variables and outbursting AM CVn systems. We conclude by predicting that the Palomar Transient Factory may more than double the number of outbursting AM CVn systems known, which would greatly increase our understanding of AM CVn systems.
The properties of red clump giants in the central regions of the Galactic bulge are investigated in the photometric $Z$ and $Y$ bands of the infrared VVV (VISTA/ESO) survey and the [3.6],[4.5], [5.8] and [8.0] bands of the GLIMPSE (Spitzer/IRAC) Galactic plane survey. The absolute magnitudes for objects of this class have been determined in these bands for the first time: $M_{Z}= -0.20\pm0.04$ and $M_{Y}=-0.470\pm0.045$, $M_{[3.6]}= -1.70\pm0.03$, $M_{[4.5]}= -1.60\pm0.03$, $M_{[5.8]}= -1.67\pm0.03$ and $M_{[8.0]}= -1.70\pm0.03$. A comparison of the measured magnitudes with the predictions of theoretical models for the spectra of the objects under study has demonstrated good mutual agreement and has allowed some important constraints to be obtained for the properties of bulge red clump giants. In particular, a comparison with evolutionary tracks has shown that we are dealing predominantly with the high-metallicity subgroup of bulge red clump giants. Their metallicity is slightly higher than has been thought previously, $[M/H]\simeq0.40$ (${\bf Z} \simeq 0.038$) with an error of $[M/H]\simeq 0.1$ dex, while the effective temperature is $4250\pm150$ K. Stars with an age of 9-10 Gyr are shown to dominate among the red clump giants, although some number of younger objects with an age of $\sim8$ can also be present. In addition, the distances to several Galactic bulge regions have been measured, as D = 8200-8500 pc, and the extinction law in these directions is shown to differ noticeably from the standard one.
We introduce a pairing on local intersection cohomology groups of variations of pure Hodge structure, which we call the asymptotic height pairing. Our original application of this pairing was to answer a question on the Ceresa cycle posed by R. Hain and D. Reed. (This question has since been answered independently by Hain.) Here we apply the pairing to show that a certain analytic line bundle, called the biextension line bundle, defined in terms of normal functions, always extends to any smooth partial compactification of the base. We show that the the pairing on intersection cohomology governs the extension of the natural metric on this line bundle studied by Hain and Reed (as well as, more recently, by several other authors). We also prove a positivity property of the asypmtotic height pairing, which generalize results of a recent preprint of J. Burgos Gill, D. Holmes and R. de Jong, along with a continuity property of the pairing in the normal function case. Moreover, we show that the asymptotic height pairing arises in a natural way from certain Mumford-Grothendieck biextensions associated to normal functions.
Monochromatic opacities from the Opacity Project (OP) (Seaton et al.) have been augmented by hitherto missing inner-shell contributions (Badnell & Seaton). OP Rosseland-mean opacities are compared with results from OPAL (Iglesias & Rogers) for the elements H, He, C, O, S and Fe. Overall, there is good agreement between OP and OPAL Rosseland-mean opacities for the 6-elements, but there are some differences. In particular, recent work (Bahcall et al.) has shown that helioseismology measurements give a very accurate value for the depth of the solar convection zone and that solar models give agreement with that value only if opacities there are about 7% larger than OPAL values. For the 6-element mix, here, we obtain Rosseland-mean opacities to be larger than OPAL by 5%.
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition appears. In this paper we study the intermediately subcritical case, which constitutes the borderline within this phase transition. We study the asymptotic behavior of the survival probability. Next the size of the population and the shape of the random environment conditioned on non-extinction is examined. Finally we show that conditioned on non-extinction periods of small and large population sizes alternate. This kind of 'bottleneck' behavior appears under the annealed approach only in the intermediately subcritical case.
We consider (2+1)-dimensional (N, M)-extended higher-spin anti-de Sitter supergravity and study its asymptotic symmetries. The theory is described by the Chern-Simons action based on a real, infinite-dimensional higher-spin superalgebra. We specify consistent boundary conditions on the higher-spin super-gauge connection corresponding to asymptotically anti-de Sitter spacetimes. We then determine the residual gauge transformations that preserve these asymptotic conditions and compute their Poisson bracket algebra. We find that the asymptotic symmetry is enhanced from the higher-spin superalgebra to some (N,M)-extended super-W(infinity) nonlinear superalgebra. The latter has the same classical central charge as pure Einstein gravity. Special attention is paid to the (1,1)-case. Truncation to the bosonic sector yields the previously found W(infinity) algebra, while truncation to the underlying finite-dimensional superalgebra reproduces the N-extended superconformal algebra (in its nonlinear version for N>2). We discuss string theory realization of these higher-spin anti-de Sitter supergravity theories as well as relations to previous treatments of super-W(infinity) in the literature.
We study the pointwise regularity properties of the L\'evy fields introduced by T. Mori; these fields are the most natural generalization of L\'evy processes to the multivariate setting. We determine their spectrum of singularities, and we show that their H\"older singularity sets satisfy a large intersection property in the sense of K. Falconer.
X-ray luminous clusters of galaxies at z~1 are emerging as major cosmological probes and are fundamental tools to study the cosmic large-scale structure and environmental effects of galaxy evolution at large look-back times. We present details of the newly-discovered galaxy cluster XMMU J0104.4-0630 at z=0.947 and a probable associated system in the LSS environment. The clusters were found in a systematic study for high-redshift systems using deep archival XMM-Newton data for the serendipitous detection and the X-ray analysis, complemented by optical/NIR imaging observations and spectroscopy of the main cluster. We find a well-evolved, intermediate luminosity cluster with Lx=(6.4+-1.3)x10^43 erg/s (0.5-2.0 keV) and strong central 1.4 GHz radio emission. The cluster galaxy population exhibits a pronounced transition toward bluer colors at cluster-centric distances of 1-2 core radii, consistent with an age difference of 1-2 Gyr for a single burst solar metallicity model. The second, less evolved X-ray cluster at a projected distance of 6.4 arcmin (~3 Mpc) and a concordant red-sequence color likely forms a cluster-cluster bridge with the main target as part of its surrounding large-scale structure at z~0.95.
It is likely that the LHC will observe a color- and charge-neutral scalar whose decays are consistent with those of the Standard Model (SM) Higgs boson. The Higgs interpretation of such a discovery is not the only possibility. For example, electroweak symmetry breaking (EWSB) could be triggered by a spontaneously broken, nearly conformal sector. The spectrum of states at the electroweak scale would then contain a narrow scalar resonance, the pseudo-Goldstone boson of conformal symmetry breaking, with Higgs-like properties. If the conformal sector is strongly coupled, this pseudo-dilaton may be the only new state accessible at high energy colliders. We discuss the prospects for distinguishing this mode from a minimal Higgs boson at the LHC and ILC. The main discriminants between the two scenarios are (1) cubic self-interactions and (2) a potential enhancement of couplings to massless SM gauge bosons. A particularly interesting situation arises when the scale f of conformal symmetry breaking is approximately the electroweak scale v~246 GeV. Although in this case the LHC may not be able to tell apart a pseudo-dilaton from the Higgs boson, the self-interactions differ in a way that depends only on the scaling dimension of certain operators in the conformal sector. This opens the possibility of using dilaton pair production at future colliders as a probe of EWSB induced by nearly conformal new physics.
We derive sharp lower bounds for L^p-functions on the n-dimensional unit hypercube in terms of their p-th marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the marginals. For square-integrable functions, the bounds have an explicit expression in terms of the second marginals moments.
An interface modification of LCMO-BTO superlattices was found to massively influence magnetic and magnetotransport properties. Moreover it determines the crystal structure of the manganite layers, changing it from orthorhombic (Pnma) for the conventional superlattice (cSL), to rhombohedral (R-3c) for the modified one (mSL). While the cSL shows extremely nonlinear ac transport, the mSL is an electrically homogeneous material. The observations go beyond an oversimplified picture of dead interface layers and evidence the importance of electronic correlations at perovskite interfaces.
We show that over any algebraically closed field of positive characteristic, there exists a smooth rational surface which violates Kawamata-Viehweg vanishing.
We construct two bijections of the symmetric group S_n onto itself that enable us to show that three new three-variable statistics are equidistributed with classical statistics involving the number of fixed points. The first one is equidistributed with the triplet (fix,des,maj), the last two with (fix,exc,maj), where "fix," "des," "exc" and "maj" denote the number of fixed points, the number of descents, the number of excedances and the major index, respectively.
Cloaking a source via anomalous localized resonance (ALR) was discovered by Milton and Nicorovici in \cite{MiltonNicorovici}. A general setting in which cloaking a source via ALR takes place is the settting of doubly complementary media. This was introduced and studied in \cite{Ng-CALR} for the quasistatic regime. In this paper, we study cloaking a source via ALR for doubly complementary media in the finite frequency regime as a natural continuation of \cite{Ng-CALR}. We establish the following results: 1) Cloaking a source via ALR appears if and only if the power blows up; 2) The power blows up if the source is ``placed" near the plasmonic structure; 3) The power remains bounded if the source is far away from the plasmonic structure. Concerning the analysis, we extend ideas from \cite{Ng-CALR} and add new insights on the problem which allows us to overcome difficulties related to the finite frequency regime and to obtain new information on the problem. In particular, we are able to characterize the behaviour of the fields far enough from the plasmonic shell as the loss goes to 0 for an {\bf arbitrary source} outside the core-shell structure in the doubly complementary media setting.
Recently, convolutional networks (convnets) have proven useful for predicting optical flow. Much of this success is predicated on the availability of large datasets that require expensive and involved data acquisition and laborious la- beling. To bypass these challenges, we propose an unsuper- vised approach (i.e., without leveraging groundtruth flow) to train a convnet end-to-end for predicting optical flow be- tween two images. We use a loss function that combines a data term that measures photometric constancy over time with a spatial term that models the expected variation of flow across the image. Together these losses form a proxy measure for losses based on the groundtruth flow. Empiri- cally, we show that a strong convnet baseline trained with the proposed unsupervised approach outperforms the same network trained with supervision on the KITTI dataset.
We report on numerical results from an independent formalism to describe the quasi-equilibrium structure of nonsynchronous binary neutron stars in general relativity. This is an important independent test of controversial numerical hydrodynamic simulations which suggested that nonsynchronous neutron stars in a close binary can experience compression and even collapse prior to the last stable circular orbit. We show that the interior density indeed increases as irrotational binary neutron stars approach their last orbits for particular values of the compaction ratio. The observed compression is however at a significantly reduced level.
We prove a result on the inversion of adjunction for log canonical pairs that generalizes Kawakita's result to log canonical centers of arbitrary codimension.
Our recent arXiv preprints have described the experimental evidence for the universal occurrence of short circuit photocurrents on illumination of solid state surfaces by strongly absorbed light. A likely mechanism has been proposed based on the photodesorption of surface ions to the surrounding atmosphere. Analyses have been made of observed oscilloscope tracings of short circuit photo voltages in terms of the linear rate theory in fair concomitance. Space charge effects having been left unaccounted for, we now propose an approach to them in the diffusion-free approximation.
In the present paper, as a continuation of our preceding paper [10], we study another kind of central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a viewpoint of discrete geometric analysis developed by Kotani and Sunada. We introduce a one-parameter family of random walks which interpolates between the original non-symmetric random walk and the symmetrized one. We first prove a semigroup CLT for the family of random walks by realizing the nilpotent covering graph into a nilpotent Lie group via discrete harmonic maps. The limiting diffusion semigroup is generated by the homogenized sub-Laplacian with a constant drift of the asymptotic direction on the nilpotent Lie group, which is equipped with the Albanese metric associated with the symmetrized random walk. We next prove a functional CLT (i.e., Donsker-type invariance principle) in a Holder space over the nilpotent Lie group by combining the semigroup CLT, standard martingale techniques, and a novel pathwise argument inspired by rough path theory. Applying the corrector method, we finally extend these CLTs to the case where the realizations are not necessarily harmonic.