Stochastic semiclassical equations for weakly inhomogeneous cosmologies

Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.

Stochastic semiclassical cosmological models

We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless nonconformal matter fields in the early Universe. To this end, we supplement the stress-energy tensor of these fields with a stochastic part, which is computed along the lines of the Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is therefore upgraded to a so-called Einstein-Langevin equation. We consider in some detail the conformal fluctuations of flat spacetime and the fluctuations of the scale factor in a simple cosmological model introduced by Hartle, which consists of a spatially flat isotropic cosmology driven by radiation and dust.

Stochastic semiclassical gravity

In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy fluctuations, can be formally derived from a functional method based on the influence functional of Feynman and Vernon. In the second part, we derive a number of results for background solutions of semiclassical gravity consisting of stationary and conformally stationary spacetimes and scalar fields in thermal equilibrium states. For these cases, fluctuation-dissipation relations are derived. We also show that particle creation is related to the vacuum stress-energy fluctuations and that it is enhanced by the presence of stochastic metric fluctuations.

A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

V0 production in p+A collisions at √s = 41.6 GeV

Inclusive doubly differential cross sections d 2 σ pA /dx F   dp T 2 as a function of Feynman-x (x F ) and transverse momentum (p T ) for the production of K S 0 , Λ and Λ¯ in proton-nucleus interactions at 920 GeV are presented. The measurements were performed by HERA-B in the negative x F range (−0.12

Angular distributions of leptons from J/ ψ's produced in 920 GeV fixed-target proton-nucleus collisions

A study of the angular distributions of leptons from decays of J/ψ"s produced in p-C and p-W collisions at s√=41.6~GeV has been performed in the J/ψ Feynman-x region −0.341 GeV/c a significant dependence on the reference frame is found: the polar anisotropy is more pronounced in the Collins-Soper frame and almost vanishes in the helicity frame, where, instead, a significant azimuthal anisotropy arises.

Finite-temperature T matrix in a real-time formalism

A generalized off-shell unitarity relation for the two-body scattering T matrix in a many-body medium at finite temperature is derived, through a consistent real-time perturbation expansion by means of Feynman diagrams. We comment on perturbation schemes at finite temperature in connection with an erroneous formulation of the Dyson equation in a paper recently published.

Consumo de cafeína por grávidas usuárias de uma Unidade Básica de Saúde no município do Rio de Janeiro

OBJETIVO: avaliar o consumo de cafeína em gestantes e sua associação com variáveis demográficas, socioeconômicas, reprodutivas e comportamentais e com o estado nutricional materno. MÉTODOS: trata-se de estudo do tipo transversal, realizado entre 2005 e 2007. A presente análise refere-se ao período entre a oitava e a 13ª semana gestacional, sendo realizada com 255 gestantes entre 18 e 40 anos, usuárias de uma Unidade Básica de Saúde no município do Rio de Janeiro, Rio de Janeiro. A variável "desfecho"foi o consumo de cafeína quantificado por meio de questionário de freqüência alimentar semiquantitativo, previamente validado, o qual continha uma lista de alimentos com 81 itens e oito opções de freqüência de consumo. A ingestão de cafeína foi quantificada a partir do consumo de: chocolate em pó/Nescau®, chocolate em barra ou bombom, refrigerante, café e mate. A análise estatística foi realizada por meio de modelo hierarquizado de regressão linear múltipla. RESULTADOS: a mediana e o consumo médio de cafeína foram, respectivamente, de 97,5 e 121,1 mg (desvio padrão, dp=128,4). Já o consumo elevado da substância (>300 mg/dia) foi observado em 8,3% das gestantes. No modelo multivariado, observou-se que mulheres cuja menarca ocorreu mais cedo (β=-0,15), com maior número de pessoas vivendo na casa (β=0,17) e que não faziam uso de medicamentos (β=-0,24) apresentaram maior tendência ao consumo elevado de cafeína e esta foi estatisticamente significativa (p<0,05). CONCLUSÕES: o consumo de cafeína pela maioria das gestantes foi inferior ao limite de 300 mg/dia preconizado em outros estudos. Observou-se tendência ao consumo elevado de cafeína nas gestantes cuja menarca ocorreu mais cedo, com maior número de pessoas vivendo na casa e que não faziam uso de medicamentos.

Fatores determinantes da incidência de macrossomia em um estudo com mães e filhos atendidos em uma Unidade Básica de Saúde no município do Rio de Janeiro

OBJETIVO: investigar fatores determinantes da incidência de macrossomia em um estudo com mães e filhos atendidos em uma Unidade Básica de Saúde no município do Rio de Janeiro. MÉTODOS: estudo de coorte prospectivo, com 195 pares de mães e filhos, em que a variável dependente foi a macrossomia (peso ao nascer >4.000 g, independente da idade gestacional ou de outras variáveis demográficas) e as independentes foram variáveis socioeconômicas, reprodutivas pregressas/do curso da gestação, bioquímicas, comportamentais e antropométricas. A análise estatística foi feita por meio de regressão logística múltipla. Foram estimados valores de risco relativo (RR) baseado na fórmula simples: RR = OR /(1 - I0) + (I0 versus OR), em que I0 é a incidência de macrossomia em não-expostos. RESULTADOS: a incidência de macrossomia foi de 6,7%, sendo os maiores valores encontrados em filhos de mulheres com idade >30 anos (12,8%), brancas (10,4%), com dois filhos ou mais (16,7%), que tenham tido recém-nascidos do sexo masculino (9,6%), com estatura >1,6 m (12,5%), com estado nutricional pré-gestacional de sobrepeso ou obesidade (13,6%) e ganho de peso gestacional excessivo (12,7%). O modelo final revelou que ter dois filhos ou mais (RR=3,7; IC95%=1,1-9,9) e ter tido recém-nascido do sexo masculino (RR=7,5; IC95%=1,0-37,6) foram as variáveis que permaneceram associadas à ocorrência de macrossomia. CONCLUSÕES: a incidência de macrossomia foi maior que a observada no Brasil como um todo, mas ainda é inferior à relatada em estudos de países desenvolvidos. Ter dois filhos ou mais e ter tido recém-nascido do sexo masculino foram fatores determinantes da ocorrência de macrossomia.

Kvanttimies : kirja-arvostelu

Kirjallisuusarvostelu

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Distribution asymptotique du nombre de diviseurs premiers distincts inférieurs ou égaux à m

Le sujet principal de ce mémoire est l'étude de la distribution asymptotique de la fonction f_m qui compte le nombre de diviseurs premiers distincts parmi les nombres premiers $p_1,...,p_m$. Au premier chapitre, nous présentons les sept résultats qui seront démontrés au chapitre 4. Parmi ceux-ci figurent l'analogue du théorème d'Erdos-Kac et un résultat sur les grandes déviations. Au second chapitre, nous définissons les espaces de probabilités qui serviront à calculer les probabilités asymptotiques des événements considérés, et éventuellement à calculer les densités qui leur correspondent. Le troisième chapitre est la partie centrale du mémoire. On y définit la promenade aléatoire qui, une fois normalisée, convergera vers le mouvement brownien. De là, découleront les résultats qui formeront la base des démonstrations de ceux chapitre 1.

Équations différentielles issues des vecteurs singuliers des représentations de l'algèbre de Virasoro

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal