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Empirical autocorrelation functions of returns of stochastic price processes show phenomena of correlation on small intervals of time, which decay to zero after a short time. The paper deals with the concept of weakly correlated random processes to describe a mathematical model which takes into account this behaviour of statistical data. Weakly correlated functions have been applied to model numerous problems of physics and engineering. The main idea is, that the values of the functions at two points are uncorrelated if the distance between the points exceeds a certain quantity epsilon > 0. In contrast to the white noise model, for distances smaller than epsilon a correlation between the values is permitted.

Empirical autocorrelation functions of returns of stochastic price processes show phenomena of correlation on small intervals of time, which decay to zero after a short time. The paper deals with the concept of weakly correlated random processes to describe a mathematical model which takes into account this behaviour of statistical data. Weakly correlated functions have been applied to model numerous problems of physics and engineering. The main idea is, that the values of the functions at two points are uncorrelated if the distance between the points exceeds a certain quantity epsilon > 0. In contrast to the white noise model, for distances smaller than epsilon a correlation between the values is permitted.

Orientador: Valdeci Pereira Mariano de Souza / Resumo: Neste trabalho de Mestrado foram explorados aspectos fundamentais da Fı́sica do Estado Sólido através de três frentes de pesquisa. A primeira e principal frente de pesquisa é referente ao estudo da chamada fase ferroelétrica de Mott-Hubbard nos condutores moleculares orgânicos quase-unidimensionais da famı́lia (TMTTF)2X, onde TMTTF é a molécula tetrametiltetratiafulvaleno e X é um contra-ânion monovalente. Tal investigação foi realizada através de experimentos de constante dielétrica e o denominado Positive Up Negative Down (PUND) a qual permite obter informações acerca da polarização elétrica intrı́nseca de um sistema ferroelétrico. Os resultados mostram a anisotropia para a constante dielétrica e a presença de polarização intrı́nseca abaixo de Tco . Uma segunda frente é relacionada às oscilações de cargas em sólidos onde foi investigado o quão suscetı́vel tais oscilações são à variações de volume. Esta análise foi realizada através do cálculo do parâmetro de Grüneisen fonônico para a frequência de plasma. Os cálculos realizados mostram que as oscilações de carga são fortemente influenciadas por variações de volume e, consequentemente de pressão. A última frente de estudo é relacionada ao solo da Amazônia conhecido como Terra Preta de Índio para o qual foram realizadas medidas de ressonância paramagnética eletrônica. Esta permitiu obter informações acerca de propriedades conectadas ao spin eletrônico do sistema. As medidas mostram um possı́vel ordenamento ferromagnético na T... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this Master thesis, fundamental aspects of Solid State Physics were explored through three research topics. The first and main research topic is the investigation of the so-called Mott-Hubbard ferroelectric phase in quasi-one-dimensional organic molecular conductors of the (TMTTF)2X family, where TMTTF is the tetramethyltetrathiafulvalene molecule and X is a monovalent counter-anion. This investigation was carried out through dielectric constant and the so-called Positive Up Negative Down (PUND) experiments, which enable to obtain physical information about the intrinsic electric polarization of a ferroelectric system. Our results reveled the anisotropy of the the dielectric constant and the presence of intrinsic electric polarization below Tco . The second topic is related to the charge oscillations in solids, the so-called plasma frequency, where it was investigated how susceptible such frequency is to volume variations. This analysis was performed by calculating the phononic Grüneisen parameter for the plasma frequency. The calculations reveled that the charge oscillations are strongly influenced by changes in volume and, consequently, of pressure. The last research topic is related to the Amazonian soil known as Terra Preta de Índio, for which electron spin resonance measurements were performed. This allowed to obtain information about properties connected to the electronic spin of the system. The measurements reveled a possible ferromagnetic ordering in TPI, which may... (Complete abstract click electronic access below) / Mestre

The search for alternate and renewable energy resources as well as the efficient use of energy and development of such systems that can help to save the energy consumption is needed because of exponential growth in world population, limited conventional fossil fuel resources, and to meet the increasing demand of clean and environment friendly substitutes. Hydrogen being the simplest, most abundant and clean energy carrier has the potential to fulfill some of these requirements provided the development of efficient, safe and durable systems for its production, storage and usage. Chemical hydrides, complex hydrides and nanomaterials, where the hydrogen is either chemically bonded to the metal ions or physiosorbed, are the possible means to overcome the difficulties associated with the storage and usage of hydrogen at favorable conditions. We have studied the structural and electronic properties of some of the chemical hydrides, complex hydrides and functionalized nanostructures to understand the kinetics and thermodynamics of these materials. Another active field relating to energy storage is rechargeable batteries. We have studied the detailed crystal and electronic structures of Li and Mg based cathode materials and calculated the average intercalation voltage of the corresponding batteries. We found that transition metal doped MgH2 nanocluster is a material to use efficiently not only in batteries but also in fuel-cell technologies. MAX phases can be used to develop the systems to save the energy consumption. We have chosen one compound from each of all known types of MAX phases and analyzed the structural, electronic, and mechanical properties using the hybrid functional. We suggest that the proper treatment of correlation effects is important for the correct description of Cr2AlC and Cr2GeC by the good choice of Hubbard 'U' in DFT+U method. Hydrogen is fascinating to physicists due to predicted possibility of metallization and high temperature superconductivity. On the basis of our ab initio molecular dynamics studies, we propose that the recent claim of conductive hydrogen by experiments might be explained by the diffusion of hydrogen at relevant pressure and temperature. In this thesis we also present the studies of phase change memory materials, oxides and amorphization of oxide materials, spintronics and sulfide materials.