The Dynamics of the Bounds of Squared Concurrence

We study the dynamics of upper and lower bounds of squared concurrence.Our results are similar to that of Konard et al. and can help the estimation of high-dimension bipartite entanglement in experiments.Comment: 5 pages, 2 figures accepted by PR

The K\"ahler Potential of Abelian Higgs Vortices

We calculate the K\"ahler potential for the Samols metric on the moduli space of Abelian Higgs vortices on \mathbbm{R}^{2}, in two different ways. The first uses a scaling argument. The second is related to the Polyakov conjecture in Liouville field theory. The K\"ahler potential on the moduli space of vortices on \mathbbm{H}^{2} is also derived, and we are led to a geometrical reinterpretation of these vortices. Finally, we attempt to find the K\"ahler potential for vortices on \mathbbm{R}^{2} in a third way by relating the vortices to SU(2) Yang-Mills instantons on \mathbbm{R}^{2}\times S^{2}. This approach does not give the correct result, and we offer a possible explanation for this.Comment: 25 page

Bounds on Negativity of Superpositions

The entanglement quantified by negativity of pure bipartite superposed states is studied. We show that if the entanglement is quantified by the concurrence two pure states of high fidelity to one another still have nearly the same entanglement. Furthermore this conclusion can be guaranteed by our obtained inequality, and the concurrence is shown to be a continuous function even in infinite dimensions. The bounds on the negativity of superposed states in terms of those of the states being superposed are obtained. These bounds can find useful applications in estimating the amount of the entanglement of a given pure state.Comment: 5 page

A Naturally Minute Quantum Correction to the Cosmological Constant Descended from the Hierarchy

We demonstrate that an extremely small but positive quantum correction, or the Casimir energy, to the cosmological constant can arise from a massive bulk fermion field in the Randall-Sundrum model. Specifically, a cosmological constant doubly descended from the Planck-electroweak hierarchy and as minute as the observed dark energy scale can be naturally achieved without fine-tuning of the bulk fermion mass. To ensure the stabilization of the system, we discuss two stabilization mechanisms under this setup. It is found that the Goldberger-Wise mechanism can be successfully introduced in the presence of a massive bulk fermion, without spoiling the smallness of the quantum correction.Comment: 5 page

Particle Entanglement in Rotating Gases

In this paper, we investigate the particle entanglement in 2D weakly-interacting rotating Bose and Fermi gases. We find that both particle localization and vortex localization can be indicated by particle entanglement. We also use particle entanglement to show the occurrence of edge reconstruction of rotating fermions. The different properties of condensate phase and vortex liquid phase of bosons can be reflected by particle entanglement and in vortex liquid phase we construct a trial wave function in the viewpoint of entanglement to relate the ground state with quantum Hall state. Finally, the relation between particle entanglement and interaction strength is studied.Comment: 7 pages, 9 figure