Various topological excitations in the SO(4) gauge field in higher dimensions

Following the original analysis Of Zhang and Hu for the 4-dimensional generalization of Quantum Hall effect, there has been much work from different viewpoints on the higher dimensional condensed matter systems. In this paper, we discuss three kinds of topological excitations in the SO(4) gauge field of condensed matter systems in 4-dimension-the instantons and anti-instantons, the 't Hooft-Polyakov monopoles, and the 2-membranes. Using the phi-mapping topological theory, it is revealed that there are 4-, 3-, and 2-dimensional topological currents inhering in the SO (4) gauge field, and the above three kinds of excitations can be directly and explicitly derived from these three kinds of currents, respectively. Moreover, it is shown that the topological charges of these excitations are characterized by the Hopf indices and Brouwer degrees of phi-mapping. (c) 2005 Elsevier Inc. All rights reserved.

Multi-types of Skyrmions in SU(N) Quantum Hall System

The skyrmions in SU(N) quantum Hall (QH) system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU(N) QH system there can exist (N-1) types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the (N-1) Cartan subalgebra local bases, we obtain the (N-1) U(1) electromagnetic field tensors in the SU(N) gauge field of the QH system, and then derive (N-1) types of skyrmion structures from these U(1) sub-field tensors. Furthermore, in light of the phi-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.

Critical Temperature of a Trapped Bose Gas: Comparison of Theory and Experiment

We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature T-c of a harmonically confined Bose gas as reported in Gerbier , Phys. Rev. Lett. 92, 030405 (2004). The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment.

Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

Do predators aggregate in response to pest density in agroecosystems? Assessing within-field spatial patterns

1. The spatial heterogeneity of predator populations is an important component of ecological theories pertaining to predator-prey dynamics. Most studies within agricultural fields show spatial correlation (positive or negative) between mean predator numbers and prey abundance across a whole field over time but generally ignore the within-field spatial dimension. We used explicit spatial mapping to determine if generalist predators aggregated within a soybean field, the size of these aggregations and if predator aggregation was associated with pest aggregation, plant damage and predation rate. 2. The study was conducted at Gatton in the Lockyer Valley, 90 km west of Brisbane, Australia. Intensive sampling grids were used to investigate within-field spatial patterns. The first row of each grid was located in a lucerne field (10 m from interface) and the remaining rows were in an adjacent soybean field. At each point on the grid the abundance of foliage-dwelling and ground-dwelling pests and predators was measured, predation rates [using sentinel Helicoverpa armigera (Hubner) egg cards] and plant damage were estimated. Eight grids were sampled across two summer cropping seasons (2000/01, 2001/02). 3. Predators exhibited strong spatial patterning with regions of high and low abundance and activity within what are considered to be uniform soybean fields. Ground-dwelling and foliage-dwelling predators were often aggregated in patches approximately 40 m across. 4. Lycosidae (wolf spiders) displayed aggregation and were consistently more abundant within the lucerne, with a decreasing trap catch with distance from the lucrene/soybean interface. This trend was consistent between subsequent grids in a single field and between fields. 5. The large amount of spatial variability in within-field arthropod abundance (pests and predators) and activity (egg predation and plant damage) indicates that whole field averages were misleading. This result has serious implications for sampling of arthropod abundance and pest management decision-making based on scouting data. 6. There was a great deal of temporal change in the significant spatial patterns observed within a field at each sampling time point during a single season. Predator and pest aggregations observed in these fields were generally not stable for the entire season. 7. Predator aggregation did not correlate consistently with pest aggregation, plant damage or predation rate. Spatial patterns in predator abundance were not associated consistently with any single parameter measured. The most consistent positive association was between foliage-dwelling predators and pests (significant in four of seven grids). Inferring associations between predators and prey based on an intensive one-off sampling grid is difficult, due to the temporal variability in the abundance of each group. 8. Synthesis and applications. This study demonstrated that generalist predator populations are rarely distributed randomly and field edges and adjacent crops can have an influence on within-field predator abundance. This must be considered when estimating arthropod (pest and predator) abundance from a set of samples taken at random locations within a field.