Quantum effect induced reverse kinetic molecular sieving in microporous materials

We report kinetic molecular sieving of hydrogen and deuterium in zeolite rho at low temperatures, using atomistic molecular dynamics simulations incorporating quantum effects via the Feynman-Hibbs approach. We find that diffusivities of confined molecules decrease when quantum effects are considered, in contrast with bulk fluids which show an increase. Indeed, at low temperatures, a reverse kinetic sieving effect is demonstrated in which the heavier isotope, deuterium, diffuses faster than hydrogen. At 65 K, the flux selectivity is as high as 46, indicating a good potential for isotope separation.

Quantum effects on adsorption and diffusion of hydrogen and deuterium in microporous materials

Monte Carlo and molecular dynamics simulations and neutron scattering experiments are used to study the adsorption and diffusion of hydrogen and deuterium in zeolite Rho in the temperature range of 30-150 K. In the molecular simulations, quantum effects are incorporated via the Feynman-Hibbs variational approach. We suggest a new set of potential parameters for hydrogen, which can be used when Feynman-Hibbs variational approach is used for quantum corrections. The dynamic properties obtained from molecular dynamics simulations are in excellent agreement with the experimental results and show significant quantum effects on the transport at very low temperature. The molecular dynamics simulation results show that the quantum effect is very sensitive to pore dimensions and under suitable conditions can lead to a reverse kinetic molecular sieving with deuterium diffusing faster than hydrogen.

Studies on Wilson loops, correlators and localization in supersymmetric quantum field theories

In this thesis we study at perturbative level correlation functions of Wilson loops (and local operators) and their relations to localization, integrability and other quantities of interest as the cusp anomalous dimension and the Bremsstrahlung function. First of all we consider a general class of 1/8 BPS Wilson loops and chiral primaries in N=4 Super Yang-Mills theory. We perform explicit two-loop computations, for some particular but still rather general configuration, that confirm the elegant results expected from localization procedure. We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, when interacting diagrams do not cancel and contribute non-trivially to the final answer. We also discuss the near BPS expansion of the generalized cusp anomalous dimension with L units of R-charge. Integrability provides an exact solution, obtained by solving a general TBA equation in the appropriate limit: we propose here an alternative method based on supersymmetric localization. The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour. Also these observables localize on a two-dimensional gauge theory on S^2, opening the possibility of exact calculations. As a test of our proposal, we reproduce the leading Luscher correction at weak coupling to the generalized cusp anomalous dimension. This result is also checked against a genuine Feynman diagram approach in N=4 super Yang-Mills theory. Finally we study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U(N) and U(M) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentation structure for the related Wilson loops.

Non-planar double-box, massive and massless pentabox Feynman integrals in the negative-dimensional approach

The negative-dimensional integration method is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and the scalar pentabox in two cases, where six virtual particles have the same mass, and in the case all of them are massless. Our results are given in terms of hypergeometric functions of Mandelstam variables and also for arbitrary exponents of propagators and dimension D.

Massless and massive one-loop three-point functions in negative dimensional approach

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of the external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time is D. Our approach reproduces the known results; it produces other solutions as yet unknown in the literature as well. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories.

Semiclassical approach to black hole absorption of electromagnetic radiation emitted by a rotating charge

We consider an electric charge, minimally coupled to the Maxwell field, rotating around a Schwarzschild black hole. We investigate how much of the radiation emitted from the swirling charge is absorbed by the black hole and show that most of the photons escape to infinity. For this purpose we use the Gupta-Bleuler quantization of the electromagnetic field in the modified Feynman gauge developed in the context of quantum field theory in Schwarzschild spacetime. We obtain that the two photon polarizations contribute quite differently to the emitted power. In addition, we discuss the accurateness of the results obtained in a full general relativistic approach in comparison with the ones obtained when the electric charge is assumed to be orbiting a massive object due to a Newtonian force.

Negative dimensional approach for scalar two-loop three-point and three-loop two-point integrals

The well-known D-dimensional Feynman integrals were shown, by Halliday and Ricotta, to be capable of undergoing analytic continuation into the domain of negative values for the dimension of space-time. Furthermore, this could be identified with Grassmannian integration in positive dimensions. From this possibility follows the concept of negative-dimensional integration for loop integrals in field theories. Using this technique, we evaluate three two-loop three-point scalar integrals, with five and six massless propagators, with specific external kinematic configurations (two legs on-shell), and four three-loop two-point scalar integrals. These results are given for arbitrary exponents of propagators and dimension, in Euclidean space, and the particular cases compared to results published in the literature.

A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL

It is a well known result that the Feynman's path integral (FPI) approach to quantum mechanics is equivalent to Schrodinger's equation when we use as integration measure the Wiener-Lebesgue measure. This results in little practical applicability due to the great algebraic complexibity involved, and the fact is that almost all applications of (FPI) - ''practical calculations'' - are done using a Riemann measure. In this paper we present an expansion to all orders in time of FPI in a quest for a representation of the latter solely in terms of differentiable trajetories and Riemann measure. We show that this expansion agrees with a similar expansion obtained from Schrodinger's equation only up to first order in a Riemann integral context, although by chance both expansions referred to above agree for the free. particle and harmonic oscillator cases. Our results permit, from the mathematical point of view, to estimate the many errors done in ''practical'' calculations of the FPI appearing in the literature and, from the physical point of view, our results supports the stochastic approach to the problem.

Feynman integrals with tensorial structure in the negative dimensional integration scheme

The negative-dimensional integration method (NDIM) is revealing itself as a very useful technique for computing massless and/or massive Feynman integrals, covariant and noncovanant alike. Up until now however, the illustrative calculations done using such method have been mostly covariant scalar integrals/without numerator factors. We show here how those integrals with tensorial structures also can be handled straightforwardly and easily. However, contrary to the absence of significant features in the usual approach, here the NDIM also allows us to come across surprising unsuspected bonuses. Toward this end, we present two alternative ways of working out the integrals and illustrate them by taking the easiest Feynman integrals in this category that emerge in the computation of a standard one-loop self-energy diagram. One of the novel and heretofore unsuspected bonuses is that there are degeneracies in the way one can express the final result for the referred Feynman integral.

The Epstein-Glaser causal approach to the light-front QED(4). I: Free theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Coordenadas vestidas: formulação segundo a interpretação de Dirac-Feynman para a mecânica quântica e aplicações em CQED

Pós-graduação em Física - IFT

The Feynman-Kac formula and applications to PDEs

The thesis presents a probabilistic approach to the theory of semigroups of operators, with particular attention to the Markov and Feller semigroups. The first goal of this work is the proof of the fundamental Feynman-Kac formula, which gives the solution of certain parabolic Cauchy problems, in terms of the expected value of the initial condition computed at the associated stochastic diffusion processes. The second target is the characterization of the principal eigenvalue of the generator of a semigroup with Markov transition probability function and of second order elliptic operators with real coefficients not necessarily self-adjoint. The thesis is divided into three chapters. In the first chapter we study the Brownian motion and some of its main properties, the stochastic processes, the stochastic integral and the Itô formula in order to finally arrive, in the last section, at the proof of the Feynman-Kac formula. The second chapter is devoted to the probabilistic approach to the semigroups theory and it is here that we introduce Markov and Feller semigroups. Special emphasis is given to the Feller semigroup associated with the Brownian motion. The third and last chapter is divided into two sections. In the first one we present the abstract characterization of the principal eigenvalue of the infinitesimal generator of a semigroup of operators acting on continuous functions over a compact metric space. In the second section this approach is used to study the principal eigenvalue of elliptic partial differential operators with real coefficients. At the end, in the appendix, we gather some of the technical results used in the thesis in more details. Appendix A is devoted to the Sion minimax theorem, while in appendix B we prove the Chernoff product formula for not necessarily self-adjoint operators.

Rational algorithms for the decomposition of Feynman integrals via intersection theory

The decomposition of Feynman integrals into a basis of independent master integrals is an essential ingredient of high-precision theoretical predictions, that often represents a major bottleneck when processes with a high number of loops and legs are involved. In this thesis we present a new algorithm for the decomposition of Feynman integrals into master integrals with the formalism of intersection theory. Intersection theory is a novel approach that allows to decompose Feynman integrals into master integrals via projections, based on a scalar product between Feynman integrals called intersection number. We propose a new purely rational algorithm for the calculation of intersection numbers of differential $n-$forms that avoids the presence of algebraic extensions. We show how expansions around non-rational poles, which are a bottleneck of existing algorithms for intersection numbers, can be avoided by performing an expansion in series around a rational polynomial irreducible over $\mathbb{Q}$, that we refer to as $p(z)-$adic expansion. The algorithm we developed has been implemented and tested on several diagrams, both at one and two loops.

Phosphate Regulated Proteins Of Xanthomonas Citri Subsp. Citri: A Proteomic Approach.

Xanthomonas citri subsp. citri (X. citri) is the causative agent of the citrus canker, a disease that affects several citrus plants in Brazil and across the world. Although many studies have demonstrated the importance of genes for infection and pathogenesis in this bacterium, there are no data related to phosphate uptake and assimilation pathways. To identify the proteins that are involved in the phosphate response, we performed a proteomic analysis of X. citri extracts after growth in three culture media with different phosphate concentrations. Using mass spectrometry and bioinformatics analysis, we showed that X. citri conserved orthologous genes from Pho regulon in Escherichia coli, including the two-component system PhoR/PhoB, ATP binding cassette (ABC transporter) Pst for phosphate uptake, and the alkaline phosphatase PhoA. Analysis performed under phosphate starvation provided evidence of the relevance of the Pst system for phosphate uptake, as well as both periplasmic binding proteins, PhoX and PstS, which were formed in high abundance. The results from this study are the first evidence of the Pho regulon activation in X. citri and bring new insights for studies related to the bacterial metabolism and physiology. Biological significance Using proteomics and bioinformatics analysis we showed for the first time that the phytopathogenic bacterium X. citri conserves a set of proteins that belong to the Pho regulon, which are induced during phosphate starvation. The most relevant in terms of conservation and up-regulation were the periplasmic-binding proteins PstS and PhoX from the ABC transporter PstSBAC for phosphate, the two-component system composed by PhoR/PhoB and the alkaline phosphatase PhoA.

A New Extraction Approach To Correct The Effect Of Apparent Increase In The Secoiridoid Content After Filtration Of Virgin Olive Oil.

In the current study, a new approach has been developed for correcting the effect that moisture reduction after virgin olive oil (VOO) filtration exerts on the apparent increase of the secoiridoid content by using an internal standard during extraction. Firstly, two main Spanish varieties (Picual and Hojiblanca) were submitted to industrial filtration of VOOs. Afterwards, the moisture content was determined in unfiltered and filtered VOOs, and liquid-liquid extraction of phenolic compounds was performed using different internal standards. The resulting extracts were analyzed by HPLC-ESI-TOF/MS, in order to gain maximum information concerning the phenolic profiles of the samples under study. The reduction effect of filtration on the moisture content, phenolic alcohols, and flavones was confirmed at the industrial scale. Oleuropein was chosen as internal standard and, for the first time, the apparent increase of secoiridoids in filtered VOO was corrected, using a correction coefficient (Cc) calculated from the variation of internal standard area in filtered and unfiltered VOO during extraction. This approach gave the real concentration of secoiridoids in filtered VOO, and clarified the effect of the filtration step on the phenolic fraction. This finding is of great importance for future studies that seek to quantify phenolic compounds in VOOs.