31,821 research outputs found
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 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 ) exerted
on the system, while the other corresponds to the coupling constant between the
subsystems (characterized by ). 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 ), whereas the subsystem's cycle is of quantum Otto in another Brayton
cycle (characterized by ). 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 , 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.
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