Inversely Unstable Solutions of Two-Dimensional Systems on Genus-p Surfaces and the Topology of Knotted Attractors

In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins, 2004] and give conditions under which these invariant sets are not homeomorphic to a circle individually, which implies the existence of chaotic behaviour. This is achieved by studying the appearance of inversely unstable solutions within each invariant set.Comment: 19 pages with 20 figures, AMS La-TeX, to be published in International Journal of Bifurcation and Chao

Singlet and triplet BCS pairs in a gas of two-species fermionic polar molecules

We investigate the BCS pairing in a mixture of fermionic polar molecules with two different hyperfine states. We derive a set of coupled gap equations and find that this system supports both spin-singlet and -triplet BCS pairs. We also calculate the critical temperatures and the angular dependence of order parameters. In addition, by tuning short-range interaction between inter-species molecules, the transition between singlet and triplet paired states may be realized.Comment: 5 pages, 4 figure

Making vortices in dipolar spinor condensates via rapid adiabatic passage

We propose to the create vortices in spin-1 condensates via magnetic dipole-dipole interaction. Starting with a polarized condensate prepared under large axial magnetic field, we show that by gradually inverting the field, population transfer among different spin states can be realized in a controlled manner. Under optimal condition, we generate a doubly quantized vortex state containing nearly all atoms in the condensate. The resulting vortex state is a direct manifestation of the dipole-dipole interaction and spin textures in spinor condensates. We also point out that the whole process can be qualitatively described by a simple rapid adiabatic passage model.Comment: 4 pages, 4 figure

Probing dipolar effects with condensate shape oscillation

We discuss the low energy shape oscillations of a magnetic trapped atomic condensate including the spin dipole interaction. When the nominal isotropic s-wave interaction strength becomes tunable through a Feshbach resonance (e.g. as for $^{85}$Rb atoms), anisotropic dipolar effects are shown to be detectable under current experimental conditions [E. A. Donley {\it et al.}, Nature {\bf 412}, 295 (2001)].Comment: revised version, submitte

The Effects of Halo Assembly Bias on Self-Calibration in Galaxy Cluster Surveys

Self-calibration techniques for analyzing galaxy cluster counts utilize the abundance and the clustering amplitude of dark matter halos. These properties simultaneously constrain cosmological parameters and the cluster observable-mass relation. It was recently discovered that the clustering amplitude of halos depends not only on the halo mass, but also on various secondary variables, such as the halo formation time and the concentration; these dependences are collectively termed assembly bias. Applying modified Fisher matrix formalism, we explore whether these secondary variables have a significant impact on the study of dark energy properties using the self-calibration technique in current (SDSS) and the near future (DES, SPT, and LSST) cluster surveys. The impact of the secondary dependence is determined by (1) the scatter in the observable-mass relation and (2) the correlation between observable and secondary variables. We find that for optical surveys, the secondary dependence does not significantly influence an SDSS-like survey; however, it may affect a DES-like survey (given the high scatter currently expected from optical clusters) and an LSST-like survey (even for low scatter values and low correlations). For an SZ survey such as SPT, the impact of secondary dependence is insignificant if the scatter is 20% or lower but can be enhanced by the potential high scatter values introduced by a highly correlated background. Accurate modeling of the assembly bias is necessary for cluster self-calibration in the era of precision cosmology.Comment: 13 pages, 5 figures, replaced to match published versio

Quantum Brayton cycle with coupled systems as working substance

We explore the quantum version of Brayton cycle with a composite system as the working substance. The actual Brayton cycle consists of two adiabatic and two isobaric processes. Two pressures can be defined in our isobaric process, one corresponds to the external magnetic field (characterized by $F_x$) exerted on the system, while the other corresponds to the coupling constant between the subsystems (characterized by $F_y$). As a consequence, we can define two types of quantum Brayton cycle for the composite system. We find that the subsystem experiences a quantum Brayton cycle in one quantum Brayton cycle (characterized by $F_x$), whereas the subsystem's cycle is of quantum Otto in another Brayton cycle (characterized by $F_y$). The efficiency for the composite system equals to that for the subsystem in both cases, but the work done by the total system are usually larger than the sum of work done by the two subsystems. The other interesting finding is that for the cycle characterized by $F_y$, the subsystem can be a refrigerator while the total system is a heat engine. The result in the paper can be generalized to a quantum Brayton cycle with a general coupled system as the working substance.Comment: 7 pages, 3 figures, accepted by Phys. Rev.