23,982 research outputs found
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
Chiral quark dynamics and topological charge: The role of the Ramond-Ramond U(1) Gauge Field in Holographic QCD
The Witten-Sakai-Sugimoto construction of holographic QCD in terms of D4
color branes and D8 flavor branes in type IIA string theory is used to
investigate the role of topological charge in the chiral dynamics of quarks in
QCD. The QCD theta term arises from a compactified 5-dimensional Chern-Simons
term on the D4 branes. This term couples the QCD topological charge to the
Ramond-Ramond gauge field of IIA string theory. The nonzero topological
susceptibility of pure-glue QCD can be attributed to the presence of D6 branes,
which constitute magnetic sources of the RR gauge field. The topological charge
of QCD is required, by an anomaly inflow argument, to coincide in space-time
with the intersection of the D6 branes and the D4 color branes. This clarifies
the relation between D6 branes and the coherent, codimension-one topological
charge membranes observed in QCD Monte Carlo calculations. Using
open-string/closed-string duality, we interpret a quark loop (represented by a
D4-D8 open string loop) in terms of closed-string exchange between color and
flavor branes. The role of the RR gauge field in quark-antiquark annihilation
processes is discussed. RR exchange in the s-channel generates a 4-quark
contact term which produces an mass insertion and provides an
explanation for the observed spin-parity structure of the OZI rule. The form of the anomaly emerges naturally. RR exchange in
the t-channel of the scattering amplitude produces a Nambu-Jona
Lasinio interaction which may provide a mechanism for spontaneous breaking of
.Comment: 20 pages, 7 figure
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
Anomaly Inflow and Membrane Dynamics in the QCD Vacuum
Large and holographic arguments, as well as Monte Carlo results,
suggest that the topological structure of the QCD vacuum is dominated by
codimension-one membranes which appear as thin dipole layers of topological
charge. Such membranes arise naturally as branes in the holographic
formulation of QCD based on IIA string theory. The polarizability of these
membranes leads to a vacuum energy , providing the origin of
nonzero topological susceptibility. Here we show that the axial U(1) anomaly
can be formulated as anomaly inflow on the brane surfaces. A 4D gauge
transformation at the brane surface separates into a 3D gauge transformation of
components within the brane and the transformation of the transverse component.
The in-brane gauge transformation induces currents of an effective Chern-Simons
theory on the brane surface, while the transformation of the transverse
component describes the transverse motion of the brane and is related to the
Ramond-Ramond closed string field in the holographic formulation of QCD. The
relation between the surface currents and the transverse motion of the brane is
dictated by the descent equations of Yang-Mills theory.Comment: 22 pages, 3 figure
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