We have studied quantum statistical properties in a zero-temperature two-species Bose{Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is found that the two condensates may periodically exhibit sub-Poissonian distribution. It is revealed that the correlation be t ween the two condensates can benonclassical, which means that there exists a violation of Cauchy{Schwartz inequality. The nonclassical e ect about the correlation be t ween the two condensates can berealized experimentally by properly preparing the total numbe rof atoms in the two condensates.

Classical general relativity takes place on a manifold with a metric of fixed, Lorentzian, signature. However, attempts to amalgamate general relativity with quantum theory frequently involve manifolds with metrics whose signatures are Lorentzian in some regions and Euclidean in others. (Indeed even more exotic possibilities are discussed frequently.) Most theoretical calculations rely on analyticity arguments to continue variables from the Euclidean to the Lorentzian regime and vice versa. This paper examines models of signature change. It looks at a single second-order quasi-linear partial differential equation on a fixed background, whose principal part is elliptic in one regime and hyperbolic in another, i.e. a mixed problem. It introduces some examples, explains heuristically the concept of a well-posed problem and then discusses the issues involved in constructing a robust numerical algorithm to solve wellposed problems. The paper includes a worked example illustrating the proposed techniques, and a discussion of the role of the potential curvature singularity on the transition hypersurface.