Conditions for entanglement transformation between a class of multipartite pure states with generalized Schmidt decompositions

In this note we generalize Nielsen's marjoization criterion for the convertibility of bipartite pure states [Phys. Rev. Lett \textbf{83}, 436(1999)] to a special class of multipartite pure states which have generalized Schmidt decompositions.Comment: 3 pages (Revetex 4), no figures. A brief note on entanglement transformation. Comments are welcom

Nonlocal Dynamics of Passive Tracer Dispersion with Random Stopping

We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion equation with a memory term. We have shown the exponential decay of the passive tracer concentration, under suitable conditions for the velocity field and the probability distribution of random stopping time.Comment: 7 page

Topological Properties of Spatial Coherence Function

Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.Comment: 9 page

Dissipative Quasigeostrophic Dynamics under Random Forcing

The quasigeostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with dissipation under random forcing in bounded domains. We show that global unique solutions exist for appropriate initial data. Unlike the deterministic quasigeostrophic equation whose well-posedness is well-known, there seems no rigorous result on global existence and uniqueness of the randomly forced quasigeostrophic equation. Our work provides such a rigorous result on global existence and uniqueness, under very mild conditions.Comment: LaTeX, 15 page

Optimal time decay of the non cut-off Boltzmann equation in the whole space

In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space \threed_x with \DgE. We use the existence theory of global in time nearby Maxwellian solutions from \cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to determine the large time decay rates for the soft potential Boltzmann equation in the whole space, with or without the angular cut-off assumption \cite{MR677262,MR2847536}. For perturbative initial data, we prove that solutions converge to the global Maxwellian with the optimal large-time decay rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the L^2_\vel(L^r_x)-norm for any $2\leq r\leq \infty$.Comment: 31 pages, final version to appear in KR

Topology of Knotted Optical Vortices

Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the $\phi$-mapping topological current theory, we investigate the topology in the closed and knotted optical vortices. The topological inner structure of the optical vortices are obtained, and the linking of the knotted optical vortices is also given.Comment: 11 pages, no figures, accepted by Commun. Theor. Phys. (Beijing, P. R. China