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

L'exploitation des algues rouges Gelidium dans la région d’El-Jadida : aspects socio-économiques et perspectives

L’algue rouge Gelidium forme le long de la côte atlantique marocaine des champs relativement importants. La majeure partie des algues récoltée et fournie à l’industrie de transformation provient de la zone maritime d’El Jadida-Jorf Lasfar. L’évaluation de l’évolution de la production d’algues rouges Gelidium sesquipedale dans 16 stations de la région d’El-Jadida a été entreprise dans le but d’élucider sa variation spatio-temporelle durant deux années d’étude 2011 et 2012. Les résultats montrent une variation de la production entre les différentes stations durant les deux années d’étude. Les productions enregistrées en 2011 dans les deux stations Sidi Abed (3086 tonnes d’algues humides) et Moulay Abdellah (5276 tonnes d’algues humides) sont les plus importantes, par contre la station de Sidi Bouzid a reconnu une substitution de l’espèce étudiée par l’Halopithys incurvus. En 2012, la production enregistrée dans la station de Sidi Abed reste aux alentours de 3281 tonnes d’algues humides. Cependant, celle enregistrée dans Moulay Abdelleah a trop diminué (2632 tonnes d’algues humides). L’effort de pêche pratiqué dans les stations de la zone étudiée signifie le nombre de jours de la collecte des algues pendant seulement les campagnes autorisées pour la collecte des algues marines. Les  résultats obtenus montrent qu’il y a une corrélation entre l’évolution de la production (tonnes) et l’effort de pêche. Ceci signifié que l’effort pratiqué pour la collecte de G. sesquipedale influence négativement les champsd’algues présents dans la zone d’étude. La classe d'âge comprise entre 19–35 ans représente la part la plus importante des enquêtés, suivieensuite par la classe 35–51 et la classe des moins de 18 ans. Cela traduit le potentiel humain important dans la communauté qui intervient dans la collecte des algues rouges. La classe active est dominante. Enfin, on note qu’il y a une surexploitation des champs d’algues naturels par braconnage ou par le non respect des quantités déterminées par quota nationale.Mots-clés : algue rouge, Gelidium sesquipedale, production, exploitation, effort de pêche, surexploitation

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

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%)

Pemetaan Spasio-temporal Ikan-ikan Herbivora di Kepulauan Spermonde, Sulawesi Selatan [Spatio-temporal Mapping Of Herbivorous Fishes At Spermonde Islands, South Sulawesi]

Ikan herbivora di terumbu karang menjadi salah satu indikator tingkat kesehatan ekosistem. Pada terumbu karang yang sehat biasanya ditandai dengan kelimpahan ikan herbivora yang tinggi. Penelitian ini bertujuan untuk memetakan distribusi spasial dan temporal ikan herbivora dalam kaitannya dengan kondisi kesehatan karang. Pendataan jumlah jenis dan kepadatan ikan herbivora dengan metode transek sabuk dan pencacahan dengan teknik visual sensus, sedangkan penilaian kesehatan karang dengan metode transek kuadran. Data sebaran diplot dengan teknik pemetaan sedangkan data kepadatan dikelompokkan berdasarkan pulau dan dianalisis perbedaannya dengan analisis ragam. Hubungan antara kepadatan ikan herbivora dengan kesehatan karang dilakukan dengan menggunakan regresi sederhana. Hasil penelitian menunjukkan rata-rata kepadatan ikan herbivora periode April-Agustus dengan kisaran 0,014-0,532 ekor.m-2. Hasil analisis ragam menunjukkan bahwa ada perbedaan kepadatan ikan herbivora antarpulau. Hubungan antara kepadatan ikan herbivora dengan kondisi kesehatan karang berkorelasi positif dan nyat