Duality between quantum and classical dynamics for integrable billiards

We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be observed in physical experiments through the auto-correlation of the transmission coefficient of waves in quantum billiards. Exact classical trace formulas of the resolvent are derived for the rectangle, equilateral triangle, and circle billiards. We also establish a correspondence between the classical periodic orbit length spectrum and the quantum spectrum for integrable polygonal billiards.Comment: 12 pages, 4 figure

Decoherence of Semiclassical Wigner Functions

The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation for this equation. The semiclassical description of the Wigner function in terms of chords, each with its classically defined amplitude and phase, is thus inserted in the integrals, which leads to an explicit differential equation for the Wigner function. All the Lindblad operators are assumed to be represented by smooth phase space functions corresponding to classical variables. In the case that these are real, representing hermitian operators, the semiclassical Lindblad equation can be integrated. There results a simple extension of the unitary evolution of the semiclassical Wigner function, which does not affect the phase of each chord contribution, while dampening its amplitude. This decreases exponentially, as governed by the time integral of the square difference of the Lindblad functions along the classical trajectories of both tips of each chord. The decay of the amplitudes is shown to imply diffusion in energy for initial states that are nearly pure. Projecting the Wigner function onto an orthogonal position or momentum basis, the dampening of long chords emerges as the exponential decay of off-diagonal elements of the density matrix.Comment: 23 pg, 2 fi

Semiclassical Evolution of Dissipative Markovian Systems

A semiclassical approximation for an evolving density operator, driven by a "closed" hamiltonian operator and "open" markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra "open" term is added to the double Hamiltonian by the non-hermitian part of the Lindblad operators in the general case of dissipative markovian evolution. The particular case of generic hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighborhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further "small-chord" approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.Comment: 33 pages - accepted to J. Phys.

Singularities of equidistants and global centre symmetry sets of Lagrangian submanifolds

We define the Global Centre Symmetry set (GCS) of a smooth closed m-dimensional submanifold M of R^n, $n \leq 2m$, which is an affinely invariant generalization of the centre of a k-sphere in R^{k+1}. The GCS includes both the centre symmetry set defined by Janeczko and the Wigner caustic defined by Berry. We develop a new method for studying generic singularities of the GCS which is suited to the case when M is lagrangian in R^{2m} with canonical symplectic form. The definition of the GCS, which slightly generalizes one by Giblin and Zakalyukin, is based on the notion of affine equidistants, so, we first study singularities of affine equidistants of Lagrangian submanifolds, classifying all the stable ones. Then, we classify the affine-Lagrangian stable singularities of the GCS of Lagrangian submanifolds and show that, already for smooth closed convex curves in R^2, many singularities of the GCS which are affine stable are not affine-Lagrangian stable.Comment: 26 pages, 2 figure

Litter deposition in integrated agricultural systems in the Brazilian Cerrado.

In agro-ecosystems, litter is a major component, comprising material that is deposited in the soil by fauna and flora. Integrated crop-livestock systems (ICL) and crop-livestock-forest systems (ICLF) are expected to enhance the use of plant biological cycle. Therefore, this study aimed to characterize litter deposition in integrated systems at the Brazilian Savannah, the Cerrado in Mato Grosso do Sul State, Brazil

Importância econômica do controle de moscas-das-frutas para a comercialização da manga in natura.

Os polos de fruticultura irrigada da região nordeste do Brasil concentram a maior produção de manga. Destinada aos mercados interno e externo. No período de janeiro a dezembro de 2011 o país exportou 126.430,77 t. de manga com um valor de US$140.910,324 (BRASIL, 2012). Em 2010 o estado da Bahia possuía 28.058 ha de manga em produção, com um volume de 509.676 ton. e gerando uma receita de R$ 214.624.000,00 (IBGE, 2012)

Pair of Heavy-Exotic-Quarks at LHC

We study the production and signatures of heavy exotic quarks pairs at LHC in the framework of the vector singlet model (VSM), vector doublet model (VDM) and fermion-mirror-fermion (FMF) model. The pair production cross sections for the electroweak and strong sector are computed.Comment: 7 pages, 6 figures. accept at Int. Jour. of Mod. Phy

Teste alternativo para avaliação do potencial fisiológico de sementes de milho e feijão de porco.

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Produtividade de genótipos de feijão-caupi avaliados para produção de feijão-verde no Estado do Ceará.

O presente trabalho foi realizado com o objetivo de avaliar componentes de produção e produtividade de genótipos de feijão-caupi avaliados para feijão-verde. Foram utilizados dados de produtividade de grãos de 16 genótipos de feijão-caupi avaliados em Pentecoste - Ceará. A análise de variância univariada foi utilizada para a determinação da variabilidade e da resposta dos genótipos quanto à produtividade. Em seguida os valores médios de cada variável analisada para os diferentes genótipos foram agrupadas pelo teste de Scott-Knott. Foi observada resposta diferenciada dos genótipos para todos os caracteres avaliados, demonstrando presença de variabilidade genética. O genótipo BRS Tumucumaque apresentou a maior média de produtividade de grãos verdes e se destacou quanto aos componentes primários da produção em relação aos demais genótipos.CONAC 2012. Disponível em: http://www.conac2012.org/resumos/pdf/142b.pdf. Acesso em: 26 jul. 2013

Diversity of epigeous soil macrofauna in spring and summer in two cultivated pasture systems and in the Brazilian Cerrado.

The different management practices used in agricultural systems can directly and indirectly interfere in soil fauna diversity, being an important indicator of biological quality of the environment. A trial was established to evaluate epigeous soil macrofauna diversity in different environments and seasons