Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the external curvature of the constraint manifold, the (Riemannian) curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is an example of geometric phase, closely related to that originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the external curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.Comment: 27 pages with 1 figure, submitted to Phys. Rev.

Curvature induced toroidal bound states

Curvature induced bound state (E < 0) eigenvalues and eigenfunctions for a particle constrained to move on the surface of a torus are calculated. A limit on the number of bound states a torus with minor radius a and major radius R can support is obtained. A condition for mapping constrained particle wave functions on the torus into free particle wave functions is established.Comment: 6 pages, no figures, Late

An effective mass theorem for the bidimensional electron gas in a strong magnetic field

We study the limiting behavior of a singularly perturbed Schr\"odinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane $(x,y)$ and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr\"odinger equations in the plane $(x,y)$, coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator

A Quantum-mechanical Approach for Constrained Macromolecular Chains

Many approaches to three-dimensional constrained macromolecular chains at thermal equilibrium, at about room temperatures, are based upon constrained Classical Hamiltonian Dynamics (cCHDa). Quantum-mechanical approaches (QMa) have also been treated by different researchers for decades. QMa address a fundamental issue (constraints versus the uncertainty principle) and are versatile: they also yield classical descriptions (which may not coincide with those from cCHDa, although they may agree for certain relevant quantities). Open issues include whether QMa have enough practical consequences which differ from and/or improve those from cCHDa. We shall treat cCHDa briefly and deal with QMa, by outlining old approaches and focusing on recent ones.Comment: Expands review published in The European Physical Journal (Special Topics) Vol. 200, pp. 225-258 (2011

Plantas medicinais em feiras e mercados públicos do Distrito Florestal Sustentável da BR-163, estado do Pará, Brasil Medicinal plants at fairs and public markets of the Sustainable Forest District of BR-163, Pará state, Brazil

As plantas medicinais constituem um grupo de produtos florestais não-madeireiros apontado como de grande potencial no Distrito Florestal Sustentável da BR-163. Visando compreender a cadeia produtiva de plantas medicinais oriundas do extrativismo, comercializadas em entrepostos, feiras e mercados públicos de municípios desta área, foram realizadas entrevistas semi-estruturadas com 20 vendedores de plantas medicinais. Foi estimada a riqueza de espécies a partir do estimador Bootstrap e analisada a similaridade entre os municípios estudados, através do Índice de Sørensen. Identificaram-se 46 etnoespécies de plantas medicinais, pertencentes a 42 gêneros e 21 famílias, sendo Fabaceae, Anacardiaceae e Bignoniaceae as famílias mais representativas. A riqueza esperada foi de 50 etnoespécies, sendo que coletas adicionais acrescentariam pelo menos quatro itens à lista geral de riqueza. Com relação à similaridade, Santarém, Itaituba e Altamira compartilham um maior número de espécies, sendo que Santarém mostra-se como centro diversificado de produtos medicinais, com maior número de ocorrências exclusivas (14). As feiras e mercados públicos, por serem um elo importante desse sistema de distribuição, devem ser incluídos nas ações governamentais sobre políticas públicas para a saúde.<br>Medicinal plants are non-timber forest products with great potential in the Sustainable Forest District of BR-163. In order to understand the productive chain from extractive medicinal plants marketed at emporiums, fairs and public markets of districts of this area, semi-structured interviews with 20 vendors of medicinal plants were carried out. Species richness was estimated by Bootstrap and similarity among the districts studied was analyzed by Sørensen's Index. 46 medicinal plants belonging to 42 genera and 21 botanical families were identified. Fabaceae, Anacardiaceae and Bignoniaceae were the most representative botanical families. The expected richness for the sample was 50 species and additional collecting would increase by at least four items the general list of richness. Santarém, Itaituba and Altamira share a larger number of species and the first is shown to be a diversified center of medicinal products, presenting the largest number of exclusive occurrences (14). The fairs and public markets are an important link of this distribution system, and should be included in government actions concerning public policies for health

Produtos alternativos na proteção da videira contra o míldio Alternative products for the protection of vine against downy mildew

O objetivo deste trabalho foi avaliar a eficiência de produtos alternativos na proteção da videira (Vitis vinifera) contra o míldio (Plasmopara viticola), bem como determinar a influência desses produtos na qualidade dos frutos da cultivar Merlot. Para o controle da doença, foram utilizados produtos à base de extratos vegetais, manano-oligossacarídeos fosforilados, fosfitos e acibenzolar-S-metil, além de fungicidas tradicionais. A intensidade do míldio em folhas e cachos, a produtividade, o número total de cachos por parcela, o peso médio do cacho e baga e as características analíticas do mosto foram avaliados nas safras de 2007/2008 e 2008/2009. Os fosfitos proporcionaram proteção contra o míldio da videira, com produtividade semelhante à do tratamento com fungicidas tradicionais. Os tratamentos baseados em manano-oligossacarídeos fosforilados, acibenzolar-S-metil e extratos vegetais não apresentaram controle eficiente do míldio. Os produtos alternativos testados não influenciam a qualidade analítica dos frutos, mas proporcionam, em geral, peso médio de cachos e de bagas menor que o do tratamento com fungicidas.<br>The objective of this work was to evaluate the efficiency of alternative products for the protection of vine (Vitis vinifera) against downy mildew (Plasmopara viticola), and to determine the influence of these products on the quality of Merlot cultivar grapes. Products based on plant extracts, phosphorylated mannanoligosaccharides, phosphites and acibenzolar-S-methyl, besides traditional fungicides, were used for the disease control. The intensity of downy mildew on leaves and bunches, productivity, total number of bunches per plot, average weight of bunch and berry and analytical characteristics of grapes were assessed during the 2007/2008 and 2008/2009 seasons. Phosphites provided protection against downy mildew, and the yield was similar that of to the treatment with traditional fungicides. Treatments based on phosphorylated mannanoligosaccharides, acibenzolar-S-methyl and plant extracts showed no effective control of downy mildew. The alternative products tested do not influence the analytical quality of the grapes, but generally provide lower average weight of bunches and berries than the treatment with fungicides