Exactly-solvable problems for two-dimensional excitons

Several problems in mathematical physics relating to excitons in two dimensions are considered. First, a fascinating numerical result from a theoretical treatment of screened excitons stimulates a re-evaluation of the familiar two-dimensional hydrogen atom. Formulating the latter problem in momentum space leads to a new integral relation in terms of special functions, and fresh insights into the dynamical symmetry of the system are also obtained. A discussion of an alternative potential to model screened excitons is given, and the variable phase method is used to compare bound-state energies and scattering phase shifts for this potential with those obtained using the two-dimensional analogue of the Yukawa potential. The second problem relates to excitons in a quantising magnetic field in the fractional quantum Hall regime. An exciton against the background of an incompressible quantum liquid is modelled as a few-particle neutral composite consisting of a positively-charged hole and several quasielectrons with fractional negative charge. A complete set of exciton basis functions is derived, and these functions are classified using a result from the theory of partitions. Some exact results are obtained for this complex few-particle problem.Comment: 66 pages, 9 figure

The two-dimensional hydrogen atom revisited

The bound state energy eigenvalues for the two-dimensional Kepler problem are found to be degenerate. This "accidental" degeneracy is due to the existence of a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector. Reformulating the problem in momentum space leads to an integral form of the Schroedinger equation. This equation is solved by projecting the two-dimensional momentum space onto the surface of a three-dimensional sphere. The eigenfunctions are then expanded in terms of spherical harmonics, and this leads to an integral relation in terms of special functions which has not previously been tabulated. The dynamical symmetry of the problem is also considered, and it is shown that the two components of the Runge-Lenz vector in real space correspond to the generators of infinitesimal rotations about the respective coordinate axes in momentum space.Comment: 10 pages, no figures, RevTex

Thermodynamic calculations of oxygen self-diffusion in mixed-oxide nuclear fuels

Molecular dynamics calculations are used to provide a self-consistent prediction of the elastic, thermal expansion and oxygen self-diffusion properties of mixed oxide nuclear fuels at arbitrary compositions.</p

Superlattice properties of carbon nanotubes in a transverse electric field

Electron motion in a (n,1) carbon nanotube is shown to correspond to a de Broglie wave propagating along a helical line on the nanotube wall. This helical motion leads to periodicity of the electron potential energy in the presence of an electric field normal to the nanotube axis. The period of this potential is proportional to the nanotube radius and is greater than the interatomic distance in the nanotube. As a result, the behavior of an electron in a (n,1) nanotube subject to a transverse electric field is similar to that in a semiconductor superlattice. In particular, Bragg scattering of electrons from the long-range periodic potential results in the opening of gaps in the energy spectrum of the nanotube. Modification of the bandstructure is shown to be significant for experimentally attainable electric fields, which raises the possibility of applying this effect to novel nanoelectronic devices.Comment: 7 pages, 3 figure

Addendum: “The two-dimensional hydrogen atom revisited” [J. Math. Phys. 43, 4681 (2002)]

Copyright © 2003 American Institute of Physic

Effects of precompetition state anxiety interventions on performance time and accuracy among amateur soccer players: Revisiting the matching hypothesis

In this study, we tested the matching ypothesis, which contends that administration of a cognitive or somatic anxiety intervention should be matched to a participant's dominant anxiety response. Sixty-one male soccer players (mean age 31.6 years, s=6.3) were assigned to one of four groups based on their responses to the Competitive State Anxiety Inventory-2, which was modified to include a directional scale. Interventions were randomly administered in a counterbalanced order 10 min before each performance trial on a soccer skill test. The dominantly cognitive anxious group (n=17), the dominantly somatic anxious group (n=17), and the non-anxious control intervention group (n=14) completed a baseline performance trial. The second and third trials were completed with random administration of brief cognitive and somatic interventions. The non-anxious control group (n=13) completed three trials with no intervention. A mixed-model, GroupTreatment multivariate analysis of variance indicated significant (P0.05), or performance time or accuracy (P>0.05). The present findings do not provide support for the matching hypothesis for state anxiety intensity and direction, or for performance

Manejo da soja em terras baixas para alta produtividade.

As áreas de terras baixas do Rio Grande do Sul abrangem cerca de 4 milhões de hectares aptos à agricultura, onde predomina o cultivo do arroz irrigado no verão. A introdução da soja em rotação ao arroz nessas áreas tem aumentado nos últimos anos. Inicialmente, a rotação de culturas visou, fundamentalmente, o controle de plantas daninhas e de outras pragas prejudiciais ao arroz.bitstream/item/218062/1/CIRCULAR-207.pdfODS

Comportamento ecofisiológico de cultivares de arroz sobre Sulcocamalhão Residual em Terras Baixas de Clima Temperado.

O arroz é uma planta semiaquática, cultivada usualmente em monocultura em ambiente inundado. O sistema de sulco-camalhão foi idealizado para permitir o cultivo de espécies de sequeiro em terras baixas, viabilizando a rotação de culturas com o arroz. Após a colheita da espécie de sequeiro, normalmente o produtor retorna com o arroz, tendo custos associados ao desmonte dos camalhões antes da semeadura. Embora não seja a condição mais favorável ao arroz, a semeadura pode ocorrer sobre os camalhões residuais. Com o objetivo de averiguar a habilidade das plantas de arroz em retirar água do solo e em manter níveis adequados de clorofila nas folhas, quando semeadas sobre sulco-camalhão residual do cultivo anterior, foi instalado um experimento em condições de campo, na Embrapa Clima Temperado, com as cultivares BRS Pampa, BRS Pampeira e Guri. Os tratamentos consistiram na interação entre os seguintes fatores: (i) posição da planta na lavoura (início, centro e final); e (ii) posição da planta no perfil do sulco-camalhão (topo, base). Utilizou-se o método da amostragem aleatória com n = 15, e os dados foram analisados por estatística descritiva. Não foram observadas tensões de água no xilema maiores do que 530 kPa. BRS Pampeira apresentou melhor desempenho que as demais nesse quesito. Foi alcançado teor de clorofila total em torno de 42 ICF para BRS Pampa. O valor de referência (45 ICF de clorofila total) foi ultrapassado somente por BRS Pampa para plantas estabelecidas na base do camalhão, mais próximas à entrada de água. Os efeitos de tratamento sobre o teor de clorofila foram discretos.ODS