Statistical Properties of Interacting Bose Gases in Quasi-2D Harmonic Traps

The analytical probability distribution of the quasi-2D (and purely 2D) ideal and interacting Bose gas are investigated by using a canonical ensemble approach. Using the analytical probability distribution of the condensate, the statistical properties such as the mean occupation number and particle number fluctuations of the condensate are calculated. Researches show that there is a continuous crossover of the statistical properties from a quasi-2D to a purely 2D ideal or interacting gases. Different from the case of a 3D Bose gas, the interaction between atoms changes in a deep way the nature of the particle number fluctuations.Comment: RevTex, 10pages, 4 figures, E-mail: [email protected]

Anomaly Inflow and Membranes in QCD Vacuum

We study the membrane-like structure of topological charge density and its fluctuations in the QCD vacuum. Quark zero modes are localized on the membranes and the resultant gauge anomaly is cancelled by the gauge variation of a Chern-Simons type effective action in the bulk via the anomaly inflow mechanism. The coupling between brane fluctuations, described by the rotations of its normal vector, and the Chern-Simons current provides the needed anomaly inflow to the membrane. This coupling is also related to the axial U(1) anomaly which can induce brane punctures, and consequently quark-antiquark annihilation across the brane. As the Chern-Simons current has a long-range character, together with membranes it might lead to a solution to the confinement problem.Comment: 8 pages, no figure, Xth Conference on Quark Confinement and the Hadron Spectru

Providing a formal linkage between MDG and HOL based on a verified MDG system.

Formal verification techniques can be classified into two categories: deductive theorem proving and symbolic state enumeration. Each method has complementary advantages and disadvantages. In general, theorem provers are high reliability systems. They can be applied to the expressive formalisms that are capable of modelling complex designs such as processors. However, theorem provers use a glass-box approach. To complete a verification, it is necessary to understand the internal structure in detail. The learning curve is very steep and modeling and verifying a system is very time-consuming. In contrast, symbolic state enumeration tools use a black-box approach. When verifying a design, the user does not need to understand its internal structure. Their advantages are their speed and ease of use. But they can only be used to prove relatively simple designs and the system security is much lower than the theorem proving system. Many hybrid tools have been developed to reap the benefits of both theorem proving Systems and symbolic state enumeration Systems. Normally, the verification results from one system are translated to another system. In other words, there is a linkage between the two Systems. However, how can we ensure that this linkage can be trusted? How can we ensure the verification system itself is correct? The contribution of this thesis is that we have produced a methodology which can provide a formal linkage between a symbolic state enumeration system and a theorem proving system based on a verified symbolic state enumeration system. The methodology has been partly realized in two simplified versions of the MDG system (a symbolic state enumeration system) and the HOL system (a theorem proving system) which involves the following three steps. First, we have verified aspects of correctness of two simplified versions of the MDG system. We have made certain that the semantics of a program is preserved in those of its translated form. Secondly, we have provided a formal linkage between the MDG system and the HOL system based on importing theorems. The MDG verification results can be formally imported into HOL to form the HOL theorems. Thirdly, we have combined the translator correctness theorems with the importing theorems. This combination allows the low level MDG verification results to be imported into HOL in terms of the semantics of a high level language (MDG-HDL). We have also summarized a general method which is used to prove the existential theorem for the specification and implementation of the design. The feasibility of this approach has been demonstrated in a case study: the verification of the correctness and usability theorems of a vending machine

A Tri-band-notched UWB Antenna with Low Mutual Coupling between the Band-notched Structures

A compact printed U-shape ultra-wideband (UWB) antenna with triple band-notched characteristics is presented. The proposed antenna, with compact size of 24×33 mm2, yields an impedance bandwidth of 2.8-12GHz for VSWR<2, except the notched bands. The notched bands are realized by introducing two different types of slots. Two C-shape half-wavelength slots are etched on the radiating patch to obtain two notched bands in 3.3-3.7GHz for WiMAX and 7.25-7.75GHz for downlink of X-band satellite communication systems. In order to minimize the mutual coupling between the band-notched structures, the middle notched band in 5-6GHz for WLAN is achieved by using a U-slot defected ground structure. The parametric study is carried out to understand the mutual coupling. Surface current distributions and equivalent circuit are used to illustrate the notched mechanism. The performance of this antenna both by simulation and by experiment indicates that the proposed antenna is suitable and a good candidate for UWB applications

The generalized KP hierarchy

We propose one possible generalization of the KP hierarchy, which possesses multi bi--hamiltonian structures, and can be viewed as several KP hierarchies coupled together.Comment: 12