Probing the interaction between Rydberg-dressed atoms through interference

We study the dynamics of an atomic Bose-Einstein condensate in an optical lattice in which the electronic groundstate of each atom is weakly coupled to a highly excited Rydberg state by a far off-resonant laser. This dressing induces a switchable effective soft-core interaction between groundstate atoms which, in the lattice, gives rise to on-site as well as long-range interaction terms. Upon switching on the dressing laser the Bose-Einstein condensate undergoes a nontrivial collapse and revival dynamics which can be observed in the interference pattern that is created after a release of the atoms from the optical lattice. This interference signal strongly depends on the strength and the duration of the dressing laser pulse and can be used to probe and characterize the effective interaction between Rydberg-dressed atoms.Comment: 7 pages, 4 figure

Molecular Phylogeny and Taxonomy of Lepidoptera with Special Reference to Influence of Wolbachia Infection in the Genus Polytremis

This chapter provides a case of genus Polytremis Mabille, 1904 (Lepidoptera: Hesperiidae), to explain the molecular phylogeny and taxonomy of Lepidoptera and the influence of Wolbachia infection. Earlier studies of Lepidoptera were focused mainly on the morphological classification, population distribution, and identification of new species. As the supplementary to morphological research, analysis of DNA has been widely used in the phylogenetic studies of Lepidoptera. The study provides a conservative estimate that the Wolbachia infection rate in Polytremis nascens Leech (1893) is 31%, and no significant difference in the prevalence is found between the sexes. The Wolbachia infection mainly prevails in populations of P. nascens in southern China, which influence the diversity of mtDNA in P. nascens by a Wolbachia-induced sweep. The Wolbachia infection rate in Polytremis fukia Evans (1940) is 47% and shows a weak association existed between mitochondrial DNA haplotypes and wFuk1 infection status

Asymptotic Theory of General Multivariate GARCH Models

Generalized autoregressive conditional heteroscedasticity (GARCH) models are widely used in financial markets. Parameters of GARCH models are usually estimated by the quasi-maximum likelihood estimator (QMLE). In recent years, economic theory often implies equilibrium between the levels of time series, which makes the application of multivariate models a necessity. Unfortunately the asymptotic theory of the multivariate GARCH models is far from coherent since many algorithms on the univariate case do not extend to multivariate models naturally. This thesis studies the asymptotic theory of the QMLE under mild conditions. We give some counterexamples for the parameter identifiability result in Jeantheau [1998] and provide a better necessary and sufficient condition. We prove the ergodicity of the conditional variance process on an application of theorems by Meyn and Tweedie [2009]. Under those conditions, the consistency and asymptotic normality of the QMLE can be proved by the standard compactness argument and Taylor expansion of the score function. We also give numeric example on verifying the assumptions and the scaling issue when estimating GARCH parameters in S+ FinMetrics