Quantum mechanics on non commutative spaces and squeezed states: a functional approach

We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and the commutators in these theories generically leads to a harmonic oscillator whose positions and momenta mean values are not strictly equal to the ones predicted by classical mechanics. This raises the question of the nature of quasi classical states in these models. We propose an extension based on a variational principle. The action considered is the sum of the absolute values of the expressions associated to the non trivial Heisenberg uncertainty relations. We first verify that our proposal works in the usual theory i.e we recover the known Gaussian functions. Besides them, we find other states which can be expressed as products of Gaussians with specific hyper geometrics. We illustrate our construction in two models defined on a four dimensional phase space: a model endowed with a minimal length uncertainty and the non commutative plane. Our proposal leads to second order partial differential equations. We find analytical solutions in specific cases. We briefly discuss how our proposal may be applied to the fuzzy sphere and analyze its shortcomings.Comment: 15 pages revtex. The title has been modified,the paper shortened and misprints have been corrected. Version to appear in JHE

(Non)commutative isotropization in Bianchi I with Barotropic perfect fluid and Λ\Lambda Cosmological

We present the classical solutions to the Einstein field equations derived using the WKB-like and Hamilton procedures. The investigation is carried out in the commutative and noncommutative scenario for the Bianchi type I cosmological model coupled to barotropic perfect fluid and $\lambda$ Cosmological for two different gauges. Noncommutativity is achieved by modifying the symplectic structure considering that all minisuperspace variables $\rm q^i$ does not commute and by a deformation between all the minisuperspace variables. In the gauge N=1, it is possible to obtain that the anisotropic parameter $\rm \beta_{\pm nc}$ tend to a constant curvature for large period of time considering different values in the noncommutative parameters $\theta$ and cosmological term. However, this behavior give the idea that is necessary introduce other class of matter in the models, for to have a real isotropization in the model, such as dark energy or dark matter.Comment: 15 pages, 1 figur

Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry.Comment: 25 pages, JHEP3 style; minor changes; Published in JHE

Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology

Using the ADM formalism in the minisuperspace, we obtain the commutative and noncommutative exact classical solutions and exact wave function to the Wheeler-DeWitt equation with an arbitrary factor ordering, for the anisotropic Bianchi type I cosmological model, coupled to a scalar field, cosmological term and barotropic perfect fluid. We introduce noncommutative scale factors, considering that all minisuperspace variables $\rm q^i$ do not commute, so the symplectic structure was modified. In the classical regime, it is shown that the anisotropic parameter $\rm \beta_{\pm nc}$ and the field $\phi$, for some value in the $\lambda_{eff}$ cosmological term and noncommutative $\theta$ parameter, present a dynamical isotropization up to a critical cosmic time $t_{c}$; after this time, the effects of isotropization in the noncommutative minisuperspace seems to disappear. In the quantum regimen, the probability density presents a new structure that corresponds to the value of the noncommutativity parameter.Comment: 17 pages, 6 figures, Acepted in IJT

Strings, T-duality breaking, and nonlocality without the shortest distance

T-duality of string theory suggests nonlocality manifested as the shortest possible distance. As an alternative, we suggest a nonlocal formulation of string theory that breaks T-duality at the fundamental level and does not require the shortest possible distance. Instead, the string has an objective shape in spacetime at all length scales, but different parts of the string interact in a nonlocal Bohmian manner.Comment: 7 pages, revised, to appear in Eur. Phys. J.

Nutrição mineral de hortaliças: XXXII. marcha de absorção dos nutrientes pelo tomateiro (Lycopersicon esculentum Mill,) destinado ao processamento industrial

In order to find out the concentration of macro and micronutrients, as well the total amounts of nutrients absorved by Roma VF, of the Santa Cruz group of tomato, plants were collected from field from 15 days up to 105 days and analysed for the nutrients. At the flowering period the leaves presented the following concentration on nutrients: 3.7% N; 0.5% P; 3.2% Ca; 0,9% Mg; 0,4% S; 72 ppm B; 15 ppm Cu; 434 ppm Fe; 375 ppm Mn; 0.1 ppm Mo and 148 ppm Zn. A production of 65 t/ha effective hasrvested content: 67.8 kg N; 8.9 kg P; 112.2 kg K; 7.7 kg Ca; 6.0 kg Mg; 3.1 kg S; 93 g B; 45 g Cu; 547 g Fe; 163 g Mn; 485 mg Mo; 321 g Zn.Reveste-se de grande importância o conhecimento da marcha de absorção de nutrientes pelas culturas, principalmente visando uma aplicação racional dos fertilizantes. Utilizou-se no presente experimento a cultivar Roma VF, de porte determinado, que tem tido grande aceitação tanto pelos tomaticultores como pelas industrias processadoras. As amostras para analise foram coletadas no período junho a outubro de 1977, em uma área experimental instalada num solo representativo da região oeste do Estado de São Paulo (Latossol Vermelho Amarelo), no município de Narandiba (DIRA de Presidente Prudente)· A cultura recebeu uma adubação de 85--300-100 kg/ha de NPK, sendo 1/3 do N aplicado juntamente com todo o P e K no plantio e os 2/3 restantes aplicados em cobertura aos 30 e 35 dias após a germinação. A área foi de 1,25 x 0,30 m (26,666 covas/ha), com culturais foram os normalmente recomendados para a cultura na região. As amostras (4 repetições) foram coletadas aos 15, 30, 45, 60, 75, 90 e 105 dias após a germinação. As plantas foram separadas em folhas cotiledonares, folhas, caule e frutos. Determinou-se o peso de matéria seca e analisou-se para N, P, K, Ca, Mg, S, B, Cu, Fe, Mo e Zn. Os resultados analíticos obtidos revelaram um crescimento lento ate aos 30 dias, após o que houve um crescimento acelerado, com o peso da materia seca praticamente dobrando a cada quinzena no período dos 45 aos 75 dias, atingindo o máximo aos 105 dias (5.706,61 kg/ha). Quanto ao crescimento dos frutos, expresso em peso de materia seca, houve um aumento de cerca de 20 vezes no intervalo dos 45 aos 75 dias, praticamente duplicando o peso no período dos 75 aos 90 dias e estabilizando-se aos 105 dias (2.708,6 kg/ha). Na época de floração, as folhas apresentavam, em função da materia seca, 3,7% N; 0,50% P; 4,44% K; 3,24% Ca; 0,99% Mg; 0,46% S; 72 ppm B; 15 ppm Cu; 434 ppm Fe; 375 ppm Mn; 0,18 ppm Mo; 148 ppm Zn. A produção efetiva de 65 ton/ha obtida na área experimental, contem as seguintes quantidades de nutrientes nos frutos: 67,8 g N; 8,9 g P; 112,2g K; 7,7 g Ca; 6,0 g Mg; 3,1 g S; 93 g B; 45 g Cu; 547 g Fe; 163 g Mn; 485 mg Mo

Removing the Big Bang Singularity: The role of the generalized uncertainty principle in quantum gravity

The possibility of avoiding the big bang singularity by means of a generalized uncertainty principle is investigated. In relation with this matter, the statistical mechanics of a free-particle system obeying the generalized uncertainty principle is studied and it is shown that the entropy of the system has a finite value in the infinite temperature limit. It is then argued that negative temperatures and negative pressures are possible in this system. Finally, it is shown that this model can remove the big bang singularity.Comment: 8 pages, Accepted for publication in Astrophysics & Space Scienc

Noncommutativity, generalized uncertainty principle and FRW cosmology

We consider the effects of noncommutativity and the generalized uncertainty principle on the FRW cosmology with a scalar field. We show that, the cosmological constant problem and removability of initial curvature singularity find natural solutions in this scenarios.Comment: 8 pages, to appear in IJT

Horizon Problem Remediation via Deformed Phase Space

We investigate the effects of a special kind of dynamical deformation between the momenta of the scalar field of the Brans-Dicke theory and the scale factor of the FRW metric. This special choice of deformation includes linearly a deformation parameter. We trace the deformation footprints in the cosmological equations of motion when the BD coupling parameter goes to infinity. One class of the solutions gives a constant scale factor in the late time that confirms the previous result obtained via another approach in the literature. This effect can be interpreted as a quantum gravity footprint in the coarse grained explanation. The another class of the solutions removes the big bang singularity, and the accelerating expansion region has an infinite temporal range which overcomes the horizon problem. After this epoch, there is a graceful exiting by which the universe enters in the radiation dominated era.Comment: 13 pages, 2 figures, to appear in GER

Noncommutative quantum mechanics and Bohm's ontological interpretation

We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale physics can have influence at large scales, something similar to the IR-UV mixing