Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates

The Schr\"odinger Hamiltonian of a spin zero particle as well as the Pauli Hamiltonian with spin-orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate (OCC) are constructed. A new approach, based on the physical argument that upon squeezing the particle to the surface by a potential, then it is the physical gauge-covariant kinematical momentum operator (velocity operator) transverse to the surface that should be dropped from the Hamiltonian(s). In both cases,the resulting Hermitian gauge-invariant Hamiltonian on the surface is free from any reference to the component of the vector potential transverse to the surface, and the approach is completely gauge-independent. In particular, for the Pauli Hamiltonian these results are obtained exactly without any further assumptions or approximations. Explicit covariant plug-and-play formulae for the Schr\"odinger Hamiltonians on the surfaces of a cylinder, a sphere and a torus are derived.Comment: 7 pages, 1 figure, references adde

Hermitian spin-orbit Hamiltonians on a surface in orthogonal curvilinear coordinates: a new practical approach

The Hermitian Hamiltonian of a spin one-half particle with spin-orbit coupling (SOC) confined to a surface that is embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate (OCC) is constructed. A gauge field formalism, where the SOC is expressed as a non-Abelian $SU(2)$ gauge field is used. A new practical approach, based on the physical argument that upon confining the particle to the surface by a potential, then it is the physical Hermitian momentum operator transverse to the surface, rather than just the derivative with respect to the transverse coordinate that should be dropped from the Hamiltonian.Doing so, it is shown that the Hermitian Hamiltonian for SOC is obtained with the geometric potential and the geometric kinetic energy terms emerging naturally. The geometric potential is shown to represent a coupling between the transverse component of the gauge field and the mean curvature of the surface that replaces the coupling between the transverse momentum and the gauge field. The most general Hermitian Hamiltonian with linear SOC on a general surface embedded in any 3D OCC system is reported. Explicit plug-and-play formulae for this Hamiltonian on the surfaces of a cylinder, a sphere and a torus are given. The formalism is applied to the Rashba SOC in three dimensions (3D RSOC) and the explicit expressions for the surface Hamiltonians on these three geometries are worked out.Comment: 8 pages, 1 figur

Perturbative Chern-Simons Theory From The Penner Model

We show explicitly that the perturbative SU(N) Chern-Simons theory arises naturally from two Penner models, with opposite coupling constants. As a result computations in the perturbative Chern-Simons theory are carried out using the Penner model, and it turns out to be simpler and transparent. It is also shown that the connected correlators of the puncture operator in the Penner model, are related to the connected correlators of the operator that gives the Wilson loop operator in the conjugacy class.Comment: 7 Pages, Published Versio

Effect of Apple Juice on Whitening Teeth After Immersion in Coffee Solution in Vitro

The Background of this research because one of the extrinsic cause teeth discoloration is excessive coffee consumption. To cope teeth discoloration whitening teeth done either with chemicals or natural ingredients. Apples (Malus sylvestris Mill) is one of the fruits that contain Malic acid, substance that can whitening teeth. The General Objective is to determine the effect of giving apple juice (Malus sylvestris Mill) on a teeth that has been soaked in coffee solution on teeth whitening in vitro. Materials and Methods research is experimental laboratory use elements of the permanent maxillary premolar tooth from extraction indications orthodontic treatment, free of caries and hypoplasia as a sample of 12 pieces, divided into 2 groups. The first group as a control group with 100 ml distilled water immersion. The second group as the treatment group using apple juice immersion with 75% concentration. Samples of tooth element has immersed first in coffee solution during 2 weeks until discoloration then immersed according to the group for 2 weeks (3x@5minutes a day), then measured the color changes of tooth. The Result with Paired T-test showed significant effect on the group before treatment and after treatment (p <0.05). Independen T-test result showed significant difference between the control group immersed in 100 ml distilled water and treatment group, immersed in apple juice 75% concentration. Conclusion of the results showed that apple juice has the ability to whiten the tooth enamel surface that changes color because of immersion in coffee solution so it can return to the original color before discoloration

A Remark on the Renormalization Group Equation for the Penner Model

It is possible to extract values for critical couplings and gamma_string in matrix models by deriving a renormalization group equation for the variation of the of the free energy as the size N of the matrices in the theory is varied. In this paper we derive a ``renormalization group equation'' for the Penner model by direct differentiation of the partition function and show that it reproduces the correct values of the critical coupling and gamma_string and is consistent with the logarithmic corrections present for g=0,1.Comment: LaTeX, 5 pages, LPTHE-Orsay-94-5

Aplikasi Metode Multycriteria Decision Making (MCDM)dengan Teknik Pembobotan Dalam Mengidentifikasi Dan Mendesain Kawasan Konservasi Perairan Daerah Di Kabupaten Luwu Utara, Provinsi Sulawesi Selatan

The study, in 2012, has successfully formulated with the MCDM for each allocation of space in KKPD allotment (core areas, sustainable fisheries zone, used zone, and other zones). This weighting techniques need to be tested and be implemented in identifying and designing the KKPD in the study area. This study aims to identify and map the biophysical conditions and the potential of coastal and marine natural resources in marine conservation area candidate, North Luwu Regency; to identify the areas suitable for the KKPD based on weighting technique with the MCDM method; and to evaluate potential candidates for marine protected areas in the coastal region. This study used a survey method to perform in situ measurements of physico-chemical parameters, conducted a survey of coastal ecosystems using the transect method. The socio-economic data of coastal communities were collected using the questionnaire. The biophysical conditions and marine resources were analyzed using descriptive statistical methods. The results showed that the candidate region has a rich diversity of coastal ecosystems, but the ecosystem, particularly seagrass beds and coral reefs have been in damaged category. Only the mangrove ecosystem that was still in a good condition category with moderate-to-heavy levels of density. There were 6 species of seagrasses and 6 species of mangroves and 71 species of reef fish. It was discovered 2 regions corresponding to the allotment of the Core Zone, which is in the Region I and III with the total area of 654.22 hectares. For sustainable fisheries zone, Region II and IV would be the first choice with the total area of 620.27 hectares. The Used Zone was identified in the Region V with total area of 480.66 hectares. The total area of the region was equal to 1755.15 hectares. Marine protected areas of was suggested to the protection of coastal ecosystems including mangroves, seagrass beds, and coral reefs and its associated biota, especially the protection of local feeding ground of several species (sea turtles and dugongs)

Persepsi Wisatawan Tentang Destinasi Wisata Taman Marga Satwa dan Budaya Kinantan di Kota Bukittinggi

This research aimed to describe the perception of tourists about tourist destinations Wildlife Park and Kinantan's Culture in Bukittinggi terms of indicators attractions, accessibility, amenitas, human resources, image and price. The population is tourists visiting tourist destinations Wildlife Park and Kinantan's Culture in Bukittinggi numbered 53.853 peoples. Sampling technique using incidental sampling, are 100 peoples. Data was collected using a questionnaire and analyzed through descriptive analysis. The results showed that Perception of tourists about tourist destinations Wildlife Park and Kinantan's Culture in Bukittinggi in the category quite well (87%). While based on the indicators: 1) Tourist attractions in the category quite well (65%), 2) accessibility in the category quite well (44%), 3) Amenitas in the category quite well (60%), 4) human resources in the category quite well (49%), 5) image in the category quite well (50%), 6) Prices in the category quite well (67%)