Non-Hermitian Hamiltonians in Field Theory

This thesis is centred around the role of non-Hermitian Hamiltonians in Physics both at the quantum and classical levels. In our investigations of two-level models we demonstrate [1] the phenomenon of fast transitions developed in the PT -symmetric quantum brachistochrone problem may in fact be attributed to the non-Hermiticity of evolution operator used, rather than to its invariance under PT operation. Transition probabilities are calculated for Hamiltonians which explicitly violate PT -symmetry. When it comes to Hilbert spaces of infinite dimension, starting with non-Hermitian Hamiltonians expressed as linear and quadratic combinations of the generators of the su(1; 1) Lie algebra, we construct [2] Hermitian partners in the same similarity class. Alongside, metrics with respect to which the original Hamiltonians are Hermitian are also constructed, allowing to assign meaning to a large class of non-Hermitian Hamiltonians possessing real spectra. The finding of exact results to establish the physical acceptability of other non-Hermitian models may be pursued by other means, especially if the system of interest cannot be expressed in terms of Lie algebraic elements. We also employ [3] a representation of the canonical commutation relations for position and momentum operators in terms of real-valued functions and a noncommutative product rule of differential form. Besides exact solutions, we also compute in a perturbative fashion metrics and isospectral partners for systems of physical interest. Classically, our efforts were concentrated on integrable models presenting PT - symmetry. Because the latter can also establish the reality of energies in classical systems described by Hamiltonian functions, we search for new families of nonlinear differential equations for which the presence of hidden symmetries allows one to assemble exact solutions. We use [4] the Painleve test to check whether deformations of integrable systems preserve integrability. Moreover we compare [5] integrable deformed models, which are thus likely to possess soliton solutions, to a broader class of systems presenting compacton solutions. Finally we study [6] the pole structure of certain real valued nonlinear integrable systems and establish that they behave as interacting particles whose motion can be extended to the complex plane in a PT -symmetric way

Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

Experimental Fowler-Nordheim plots taken from orthodoxly behaving carbon nanotube (CNT) field electron emitters are known to be linear. This shows that, for such emitters, there exists a characteristic field enhancement factor (FEF) that is constant for a range of applied voltages and applied macroscopic fields $F_\text{M}$. A constant FEF of this kind can be evaluated for classical CNT emitter models by finite-element and other methods, but (apparently contrary to experiment) several past quantum-mechanical (QM) CNT calculations find FEF-values that vary with $F_\text{M}$. A common feature of most such calculations is that they focus only on deriving the CNT real-charge distributions. Here we report on calculations that use density functional theory (DFT) to derive real-charge distributions, and then use these to generate the related induced-charge distributions and related fields and FEFs. We have analysed three carbon nanostructures involving CNT-like nanoprotrusions of various lengths, and have also simulated geometrically equivalent classical emitter models, using finite-element methods. We find that when the DFT-generated local induced FEFs (LIFEFs) are used, the resulting values are effectively independent of macroscopic field, and behave in the same qualitative manner as the classical FEF-values. Further, there is fair to good quantitative agreement between a characteristic FEF determined classically and the equivalent characteristic LIFEF generated via DFT approaches. Although many issues of detail remain to be explored, this appears to be a significant step forwards in linking classical and QM theories of CNT electrostatics. It also shows clearly that, for ideal CNTs, the known experimental constancy of the FEF value for a range of macroscopic fields can also be found in appropriately developed QM theory.Comment: A slightly revised version has been published - citation below - under a title different from that originally used. The new title is: "Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

On the Integrability and Chaos of an N=2 Maxwell-Chern-Simons-Higgs Mechanical Model

We apply different integrability analysis procedures to a reduced (spatially homogeneous) mechanical system derived from an off-shell non-minimally coupled N=2 Maxwell-Chern-Simons-Higgs model that presents BPS topological vortex excitations, numerically obtained with an ansatz adopted in a special - critical coupling - parametric regime. As a counterpart of the regularity associated to the static soliton-like solution, we investigate the possibility of chaotic dynamics in the evolution of the spatially homogeneous reduced system, descendant from the full N=2 model under consideration. The originally rich content of symmetries and interactions, N=2 susy and non-minimal coupling, singles out the proposed model as an interesting framework for the investigation of the role played by (super-)symmetries and parametric domains in the triggering/control of chaotic behavior in gauge systems. After writing down effective Lagrangian and Hamiltonian functions, and establishing the corresponding canonical Hamilton equations, we apply global integrability Noether point symmetries and Painleveproperty criteria to both the general and the critical coupling regimes. As a non-integrable character is detected by the pair of analytical criteria applied, we perform suitable numerical simulations, as we seek for chaotic patterns in the system evolution. Finally, we present some Comments on the results and perspectives for further investigations and forthcoming communications.Comment: 18 pages, 5 figure

Experimental Observation of Quantum Correlations in Modular Variables

We experimentally detect entanglement in modular position and momentum variables of photon pairs which have passed through $D$-slit apertures. We first employ an entanglement criteria recently proposed in [Phys. Rev. Lett. {\bf 106}, 210501 (2011)], using variances of the modular variables. We then propose an entanglement witness for modular variables based on the Shannon entropy, and test it experimentally. Finally, we derive criteria for Einstein-Podolsky-Rosen-Steering correlations using variances and entropy functions. In both cases, the entropic criteria are more successful at identifying quantum correlations in our data.Comment: 7 pages, 4 figures, comments welcom

Optical-force laws for guided light in linear media

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPEMIG - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE MINAS GERAISCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORThe mechanical response of transparent materials to optical forces is a topic that concerns a wide range of fields, from the manipulation of biological material by optical tweezers to the design of nano-optomechanical systems. However, the fundamental aspects of such forces have always been surrounded by controversies, and several different formulations have been proposed. In this paper, we propose a general stress tensor formalism to put all optical forces in a consistent presentation that allows us to study how different predictions emerge, and use the specific case of light propagating as a superposition of guided modes in lossless dielectric waveguides as a physical example. We use this formalism to calculate optical forces for straight and curved waveguide sections and all possible excitation configurations for a given set of coupled eigenmodes, and then compare the results for each of the known proposed optical-force laws in a framework that permits distinguishing where there will be differences between the force laws proposed. The general formalism also allows us to show that proper use of the divergence theorem is crucial to account for all force terms, many of which vanish if the procedure most commonly used is applied for situations other than eigenmodes in straight waveguides in vacuum. Finally, it is known that discrepancies in the predicted forces arise from the incompleteness of each stress tensor with respect to the total-energy-momentum tensor of the system. A better understanding of how different stress tensors predict very different forces for certain waveguide geometries should open a pathway to identifying how to properly assemble the full tensor, as well as for experimental tests to confirm the predictions.100117CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPEMIG - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE MINAS GERAISCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPEMIG - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE MINAS GERAISCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORSem informaçãoSem informaçãoSem informaçã

Uso de metodologia simples por análise de imagens para acompanhamento da proliferação de fungos em frutos fatiados.

bitstream/CNPDIA-2009-09/11851/1/BPD17_2006.pd

Produção de palha e forragem por espécies anuais e perenes em sucessão à soja.

O objetivo deste trabalho foi avaliar a produção de palha e de forragem por forrageiras anuais e perenes implantadas em sucessão à cultura da soja, e seus efeitos sobre a produtividade de grãos da cultura no próximo cultivo. O delineamento experimental utilizado foi o de blocos ao acaso, com parcelas subdivididas (crescimento livre e sob cortes sucessivos), com quatro repetições. Foram avaliadas oito forrageiras em dois municípios de Mato Grosso do Sul. A produção de palha e forragem foi avaliada em 2005 e 2006, nas espécies Urochloa ruziziensis; U. decumbens; U. brizantha cv. Marandu e Xaraés; Panicum maximum cv. Tanzânia e Mombaça, P. maximum x P. infestans cv. Massai; Pennisetum americanum cv. BRS 1501; e Sorghum bicolor cv. Santa Elisa. As forrageiras foram semeadas mecanicamente após a colheita da soja, em 1/4/2005 e 24/3/2006, em São Gabriel do Oeste, e em 20/3/2005 e 13/3/2006, em Dourados. Sorgo, U. brizantha cv. Xaraés e P. maximum cv. Tanzânia apresentaram características como elevada produtividade, alta qualidade da forragem e facilidade de controle, favoráveis para produção tanto de forragem quanto de palha. Urochloa ruziziensis e U. decumbens apresentaram melhor desempenho para a produção de palha. O cultivo das espécies forrageiras em sucessão à soja não afeta a produtividade da cultura.The objective of this work was to evaluate forage and straw production, of annual and perennial forage implanted in succession to soybean, and their effects on crop grain yield in the following season. The experimental design was in randomized blocks with four replicates, in a split-plot arrangement (free growth and successive cuts). Eight forages were evaluated in two municipalities of the state of Mato Grosso do Sul, Brazil. Straw and forage production was evaluated in 2005 and 2006, in the following species: Urochloa ruziziensis, U. decumbens; U. brizantha cv. Marandu and Xaraés; Panicum maximum cv. Tanzânia and Mombaça, P. maximum x P. infestans cv. Massai, Pennisetum americanum cv. BRS 1501, and Sorghum bicolor cv. Santa Elisa. Forages were planted mechanically, after the soybean crop harvest on 4/1/2005 and 3/24/2006, in São Gabriel do Oeste, and 3/20/2005 and 3/13/2006, in Dourados. Sorghum, U. brizantha cv. Xaraés and P. maximum cv. Tanzânia characteristics, such as high productivity, high forage quality and easiness in control, were favorable for production of both forage and straw. Urochloa ruziziensis and U. decumbens showed better performance for straw production. Forage cultivation in soybean succession does not affect crop yield