Stochastic electron heating in the laser and quasi-static electric and magnetic fields

The dynamics of relativistic electrons in the intense laser radiation and quasi-static electromagnetic fields both along and across to the laser propagating direction are studied in the 3/2 dimensional Hamiltonian framework. It is shown that the unperturbed oscillations of the relativistic electron in these electric fields could exhibit a long tail of harmonics which makes an onset of stochastic electron motion be a primary candidate for electron heating. The Poincar\'e mappings describing the electron motions in the laser and electric fields only are derived from which the criterions for instability are obtained. It follows that for both transverse and longitudinal electric fields, there exist upper limits of the stochastic electron energy depending on the laser intensity and electric field strength. Specifically, these maximum stochastic energies are enhanced by a strong laser intensity but weak electric field. Such stochastic heating would be reduced by the superluminal phase velocity in both cases. The impacts of the magnetic fields on the electron dynamics are different for these two cases and discussed qualitatively. These analytic results are confirmed by the numerical simulations of solving the 3/2D Hamiltonian equations directly

RKKY Interaction in Graphene from Lattice Green's Function

We study the exchange interaction $J$ between two magnetic impurities in graphene (the RKKY interaction) by directly computing the lattice Green's function for the tight-binding band structure for the honeycomb lattice. The method allows us to compute $J$ numerically for much larger distances than can be handled by finite-lattice calculations as well as for small distances. % avoids the use of a cutoff function often invoked in the literature to curtail the diverging contributions from the linear bands and yields results that are valid for all distances. In addition, we rederive the analytical long-distance behavior of $J$ for linearly dispersive bands and find corrections to the oscillatory factor that were previously missed in the literature. The main features of the RKKY interaction in graphene are that unlike the $J \propto (2k_FR)^{-2} \sin (2k_FR)$ behavior of an ordinary 2D metal in the long-distance limit, $J$ in graphene falls off as $1/R^3$, shows the $1 + \cos ((K-K').R)$-type oscillations with additional phase factors depending on the direction, and exhibits a ferromagnetic interaction for moments on the same sublattice and an antiferromagnetic interaction for moments on the opposite sublattices as required by particle-hole symmetry. The computed $J$ with the full band structure agrees with our analytical results in the long-distance limit including the oscillatory factors with the additional phases.Comment: 8 pages, 11 figure

The Picard group of the loop space of the Riemann sphere

The loop space of the Riemann sphere consisting of all C^k or Sobolev W^{k,p} maps from the circle S^1 to the sphere is an infinite dimensional complex manifold. We compute the Picard group of holomorphic line bundles on this loop space as an infinite dimensional complex Lie group with Lie algebra the first Dolbeault group. The group of Mobius transformations G and its loop group LG act on this loop space. We prove that an element of the Picard group is LG-fixed if it is G-fixed; thus completely answer the question by Millson and Zombro about G-equivariant projective embedding of the loop space of the Riemann sphere.Comment: International Journal of Mathematic

Linkages between Shanghai and Hong Kong stock indices

This paper examines the dynamics of the linkages between Shang- hai and Hong Kong stock indices. While the volatility linkage is anal- ysed by a multivariate GARCH framework, the linkage of returns is examined using a copula approach. Eight different copula functions are applied in this study including two time-varying copulas which capture the time varying process of the linkage. The results show sig- nificant tail dependence of the returns in the two markets.

On the Impact of Entity Linking in Microblog Real-Time Filtering

Microblogging is a model of content sharing in which the temporal locality of posts with respect to important events, either of foreseeable or unforeseeable nature, makes applica- tions of real-time filtering of great practical interest. We propose the use of Entity Linking (EL) in order to improve the retrieval effectiveness, by enriching the representation of microblog posts and filtering queries. EL is the process of recognizing in an unstructured text the mention of relevant entities described in a knowledge base. EL of short pieces of text is a difficult task, but it is also a scenario in which the information EL adds to the text can have a substantial impact on the retrieval process. We implement a start-of-the-art filtering method, based on the best systems from the TREC Microblog track realtime adhoc retrieval and filtering tasks , and extend it with a Wikipedia-based EL method. Results show that the use of EL significantly improves over non-EL based versions of the filtering methods.Comment: 6 pages, 1 figure, 1 table. SAC 2015, Salamanca, Spain - April 13 - 17, 201

Analytic continuation of single-particle resonance energy and wave function in relativistic mean field theory

Single-particle resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory. Taking the neutron resonant state $\nu 1g_{9/2}$ in $^{60}$Ca as an example, we examine the analyticity of the eigenvalue and eigenfunction for the Dirac equation with respect to the coupling constant by means of a \pade approximant of the second kind. The RMF-ACCC approach is then applied to $^{122}$Zr and, for the first time, this approach is employed to investigate both the energies, widths and wave functions for $l\ne 0$ resonant states close to the continuum threshold. Predictions are also compared with corresponding results obtained from the scattering phase shift method.Comment: 19 pages, 9 figure

Study of Proton Magic Even-Even Isotopes and Giant Halos of Ca Isotopes with Relativistic Continuum Hartree-Bogoliubov Theory

We study the proton magic O, Ca, Ni, Zr, Sn, and Pb isotope chains from the proton drip line to the neutron drip line with the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Particulary, we study in detail the properties of even-even Ca isotopes due to the appearance of giant halos in neutron rich Ca nuclei near the neutron drip line. The RCHB theory is able to reproduce the experimental binding energies $E_b$ and two neutron separation energies $S_{2n}$ very well. The predicted neutron drip line nuclei are $^{28}$O, $^{72}$Ca, $^{98}$Ni, $^{136}$Zr, $^{176}$Sn, and $^{266}$Pb, respectively. Halo and giant halo properties predicted in Ca isotopes with $A>60$ are investigated in detail from the analysis of two neutron separation energies, nucleon density distributions, single particle energy levels, the occupation probabilities of energy levels including continuum states. The spin-orbit splitting and the diffuseness of nuclear potential in these Ca isotopes are studied also. Furthermore, we study the neighboring lighter isotopes in the drip line Ca region and find some possibility of giant halo nuclei in the Ne-Na-Mg drip line nuclei.Comment: 45 pages, 20 figure

Distributed Deep Learning for Question Answering

This paper is an empirical study of the distributed deep learning for question answering subtasks: answer selection and question classification. Comparison studies of SGD, MSGD, ADADELTA, ADAGRAD, ADAM/ADAMAX, RMSPROP, DOWNPOUR and EASGD/EAMSGD algorithms have been presented. Experimental results show that the distributed framework based on the message passing interface can accelerate the convergence speed at a sublinear scale. This paper demonstrates the importance of distributed training. For example, with 48 workers, a 24x speedup is achievable for the answer selection task and running time is decreased from 138.2 hours to 5.81 hours, which will increase the productivity significantly.Comment: This paper will appear in the Proceeding of The 25th ACM International Conference on Information and Knowledge Management (CIKM 2016), Indianapolis, US