Níveis críticos de fósforo para o estabelecimento de gramíneas forrageiras em Latossolo vermelho amarelo, Álico: II. Experimento de campo.

O objetivo do trabalho foi determinar os níveis criticos de (P) são solo pelos extratores de Mehlich I e Resina e na planta

Níveis criticos de fósforo para o estabelecimento de gramíneas forrageiras em Latossolo vermelho-amarelo, Álico: I: Ensaio em casa de vegetação.

Determinar níveis críticos de P no solo, avaliados pelos extratores de Mehlich I e Resina e na planta, para o estabelecimento das gramineas Brachiaria decumbens Stapf., Brachiaria brizantha Stapf. cv. Marandu e Panicum maximum Jacq., em Latossolo vermelho amarelo, Alico

Disponibilidade de fósforo pelos extratores de Mehlich 1 e resina em latossolo vermelho amarelo, álico cultivado com três gramíneas forrageiras.

Comparação dos extratores de mehlich 1 e resina na avaliação do P disponível em latossolo vermelho amarelo, alico cultivado com gramineas brachiaria decumbens

Comment on: Modular Theory and Geometry

In this note we comment on part of a recent article by B. Schroer and H.-W. Wiesbrock. Therein they calculate some new modular structure for the U(1)-current-algebra (Weyl-algebra). We point out that their findings are true in a more general setting. The split-property allows an extension to doubly-localized algebras.Comment: 13 pages, corrected versio

Effective quantum gravity observables and locally covariant QFT

Perturbative algebraic quantum field theory (pAQFT) is a mathematically rigorous framework that allows to construct models of quantum field theories on a general class of Lorentzian manifolds. Recently this idea has been applied also to perturbative quantum gravity, treated as an effective theory. The difficulty was to find the right notion of observables that would in an appropriate sense be diffeomorphism invariant. In this article I will outline a general framework that allows to quantize theories with local symmetries (this includes infinitesimal diffeomorphism transformations) with the use of the BV (Batalin-Vilkovisky) formalism. This approach has been successfully applied to effective quantum gravity in a recent paper by R. Brunetti, K. Fredenhagen and myself. In the same paper we also proved perturbative background independence of the quantized theory, which is going to be discussed in the present work as well.Comment: 16 pages, based on a plenary talk given at the 14th Marcel Grossmann Meeting in Rome (July 2015

A Way Out of the Quantum Trap

We review Event Enhanced Quantum Theory (EEQT). In Section 1 we address the question "Is Quantum Theory the Last Word". In particular we respond to some of recent challenging staments of H.P. Stapp. We also discuss a possible future of the quantum paradigm - see also Section 5. In Section 2 we give a short sketch of EEQT. Examples are given in Section 3. Section 3.3 discusses a completely new phenomenon - chaos and fractal-like phenomena caused by a simultaneous "measurement" of several non-commuting observables (we include picture of Barnsley's IFS on unit sphere of a Hilbert space). In Section 4 we answer "Frequently Asked Questions" concerning EEQT.Comment: Replacement. Corrected affiliation. Latex, one .jpg figure. To appear in Proc. Conf. Relativistic Quantum Measurements, Napoli 1998, Ed. F. Petruccion

Nonlinear Quantum Mechanics and Locality

It is shown that, in order to avoid unacceptable nonlocal effects, the free parameters of the general Doebner-Goldin equation have to be chosen such that this nonlinear Schr\"odinger equation becomes Galilean covariant.Comment: 10 pages, no figures, also available on http://www.pt.tu-clausthal.de/preprints/asi-tpa/012-97.htm

Vacuum Structures in Hamiltonian Light-Front Dynamics

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light-front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure.Comment: 16 pages, report \# ANL-PHY-7524-TH-93, (Latex

Entropy inequalities from reflection positivity

We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of the space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for the correlators are mapped into inequalities for the entropies. We write them using a real time version of reflection positivity, which can be generalized to general quantum systems. Using this generalization we can prove an infinite sequence of inequalities which are obeyed by the Renyi entropies of integer index. There is one independent inequality involving any number of different subsystems. In quantum field theory the inequalities acquire a simple geometrical form and are consistent with the integer index Renyi entropies being given by vacuum expectation values of twisting operators in the Euclidean formulation. Several possible generalizations and specific examples are analyzed.Comment: Significantly enlarged and corrected version. Counterexamples found for the most general form of the inequalities. V3: minor change

Nonlinear Schr\"odinger equation for a PT symmetric delta-functions double well

The time-independent nonlinear Schr\"odinger equation is solved for two attractive delta-function shaped potential wells where an imaginary loss term is added in one well, and a gain term of the same size but with opposite sign in the other. We show that for vanishing nonlinearity the model captures all the features known from studies of PT symmetric optical wave guides, e.g., the coalescence of modes in an exceptional point at a critical value of the loss/gain parameter, and the breaking of PT symmetry beyond. With the nonlinearity present, the equation is a model for a Bose-Einstein condensate with loss and gain in a double well potential. We find that the nonlinear Hamiltonian picks as stationary eigenstates exactly such solutions which render the nonlinear Hamiltonian itself PT symmetric, but observe coalescence and bifurcation scenarios different from those known from linear PT symmetric Hamiltonians.Comment: 16 pages, 9 figures, to be published in Journal of Physics