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

Constituintes voláteis de Mentha pulegium L. e Plectranthus amboinicus (Lour.) Spreng Volatile constituents of Mentha pulegium L. and Plectranthus amboinicus (Lour.) Spreng

Nesse trabalho foi investigado a composição química de óleos essenciais de duas plantas medicinais cultivadas em Ilhéus, Brasil, Plectranthus amboinicus (Lour.) Spreng. (hortelã-grosso) e Mentha pulegium L. (poejo). Os óleos essenciais foram extraídos das folhas frescas por hidrodestilação e foram analisados por CG/FID e CG-EM, na primavera e no inverno. P. amboinicus forneceu, tanto na primavera como no inverno, 0,10% de óleo sendo timol o componente majoritário. M. pulegium forneceu na primavera 0,20% de óleo e no inverno 0,09%. Os componentes majoritários dos óleos foram pulegona e trans-cariofileno; borneol, mentol e piperitona foram identificados em menores quantidades. No inverno foram observados maiores quantidades de mentol e isomentol. Acetatos de neoisomentila, de mentila e de isometila foram observados somente no inverno. Esse trabalho contribui para o conhecimento das espécies vegetais cultivadas na região do sul da Bahia<br>This work investigated the chemical composition of the essential oils of two medicinal plants grown in Ilhéus Municipality, Bahia State, Brazil: Plectranthus amboinicus (Lour.) Spreng (Mexican mint) and Mentha pulegium L. (pennyroyal). The essential oils were extracted from fresh leaves by hydrodistillation and analyzed by GC-FID and GC-MS, in the spring and in the winter. In both seasons, P. amboinicus yielded 0.10% oil and had thymol as major component. M. pulegium yielded 0.20% and 0.09% oil in the spring and winter, respectively. The major components were pulegone and trans-caryophyllene, whereas borneol, menthol and piperitone were identified at small quantities. Higher menthol and isomenthol levels were detected in the winter. In addition, neoisomenthyl, menthyl and isomenthyl acetates were only observed in the winter. This work contributes to the knowledge of plant species grown in southern Bahi