Estatística não-extensiva aplicada ao cálculo do calor específico eletrônico em estruturas quasiperiódicas

Systems whose spectra are fractals or multifractals have received a lot of attention in recent years. The complete understanding of the behavior of many physical properties of these systems is still far from being complete because of the complexity of such systems. Thus, new applications and new methods of study of their spectra have been proposed and consequently a light has been thrown on their properties, enabling a better understanding of these systems. We present in this work initially the basic and necessary theoretical framework regarding the calculation of energy spectrum of elementary excitations in some systems, especially in quasiperiodic ones. Later we show, by using the Schr¨odinger equation in tight-binding approximation, the results for the specific heat of electrons within the statistical mechanics of Boltzmann-Gibbs for one-dimensional quasiperiodic systems, growth by following the Fibonacci and Double Period rules. Structures of this type have already been exploited enough, however the use of non-extensive statistical mechanics proposed by Constantino Tsallis is well suited to systems that have a fractal profile, and therefore our main objective was to apply it to the calculation of thermodynamical quantities, by extending a little more the understanding of the properties of these systems. Accordingly, we calculate, analytical and numerically, the generalized specific heat of electrons in one-dimensional quasiperiodic systems (quasicrystals) generated by the Fibonacci and Double Period sequences. The electronic spectra were obtained by solving the Schr¨odinger equation in the tight-binding approach. Numerical results are presented for the two types of systems with different values of the parameter of nonextensivity q

Formação de caudas maxwellianas no Contexto da rotação estelar

In this Thesis, we analyzed the formation of maxwellian tails of the distributions of the rotational velocity in the context of the out of equilibrium Boltzmann Gibbs statistical mechanics. We start from a unified model for the angular momentum loss rate which made possible the construction of a general theory for the rotational decay in the which, finally, through the compilation between standard Maxwellian and the relation of rotational decay, we defined the (_, _) Maxwellian distributions. The results reveal that the out of equilibrium Boltzmann Gibbs statistics supplies us results as good as the one of the Tsallis and Kaniadakis generalized statistics, besides allowing fittings controlled by physical properties extracted of the own theory of stellar rotation. In addition, our results point out that these generalized statistics converge to the one of Boltzmann Gibbs when we inserted, in your respective functions of distributions, a rotational velocity defined as a distribution

Estudo de sistemas complexos com interações de longo alcance : percolação, redes e tráfego

In this thesis we investigate physical problems which present a high degree of complexity using tools and models of Statistical Mechanics. We give a special attention to systems with long-range interactions, such as one-dimensional long-range bondpercolation, complex networks without metric and vehicular traffic. The flux in linear chain (percolation) with bond between first neighbor only happens if pc = 1, but when we consider long-range interactions , the situation is completely different, i.e., the transitions between the percolating phase and non-percolating phase happens for pc < 1. This kind of transition happens even when the system is diluted ( dilution of sites ). Some of these effects are investigated in this work, for example, the extensivity of the system, the relation between critical properties and the dilution, etc. In particular we show that the dilution does not change the universality of the system. In another work, we analyze the implications of using a power law quality distribution for vertices in the growth dynamics of a network studied by Bianconi and Barabási. It incorporates in the preferential attachment the different ability (fitness) of the nodes to compete for links. Finally, we study the vehicular traffic on road networks when it is submitted to an increasing flux of cars. In this way, we develop two models which enable the analysis of the total flux on each road as well as the flux leaving the system and the behavior of the total number of congested roads

Conceitos e técnicas da mecânica estatística e termodinâmica aplicados ao estudo dos grafos aleatórios

This dissertation briefly presents the random graphs and the main quantities calculated from them. At the same time, basic thermodynamics quantities such as energy and temperature are associated with some of their characteristics. Approaches commonly used in Statistical Mechanics are employed and rules that describe a time evolution for the graphs are proposed in order to study their ergodicity and a possible thermal equilibrium between them

Aplicações da q-Álgebra em física da matéria condensada

We address the generalization of thermodynamic quantity q-deformed by q-algebra that describes a general algebra for bosons and fermions . The motivation for our study stems from an interest to strengthen our initial ideas, and a possible experimental application. On our journey, we met a generalization of the recently proposed formalism of the q-calculus, which is the application of a generalized sequence described by two parameters deformation positive real independent and q1 and q2, known for Fibonacci oscillators . We apply the wellknown problem of Landau diamagnetism immersed in a space D-dimensional, which still generates good discussions by its nature, and dependence with the number of dimensions D, enables us future extend its application to systems extra-dimensional, such as Modern Cosmology, Particle Physics and String Theory. We compare our results with some experimentally obtained performing major equity. We also use the formalism of the oscillators to Einstein and Debye solid, strengthening the interpretation of the q-deformation acting as a factor of disturbance or impurity in a given system, modifying the properties of the same. Our results show that the insertion of two parameters of disorder, allowed a wider range of adjustment , i.e., enabling change only the desired property, e.g., the thermal conductivity of a same element without the waste essence

Fundamentação cinética da estatística não gaussiana : efeitos em politrópicas

Considering a non-relativistic ideal gas, the standard foundations of kinetic theory are investigated in the context of non-gaussian statistical mechanics introduced by Kaniadakis. The new formalism is based on the generalization of the Boltzmann H-theorem and the deduction of Maxwells statistical distribution. The calculated power law distribution is parameterized through a parameter measuring the degree of non-gaussianity. In the limit = 0, the theory of gaussian Maxwell-Boltzmann distribution is recovered. Two physical applications of the non-gaussian effects have been considered. The first one, the -Doppler broadening of spectral lines from an excited gas is obtained from analytical expressions. The second one, a mathematical relationship between the entropic index and the stellar polytropic index is shown by using the thermodynamic formulation for self-gravitational systems

Termoestatística quântica: uma abordagem via estatísticas não-gaussianas

Considering a quantum gas, the foundations of standard thermostatistics are investigated in the context of non-Gaussian statistical mechanics introduced by Tsallis and Kaniadakis. The new formalism is based on the following generalizations: i) Maxwell- Boltzmann-Gibbs entropy and ii) deduction of H-theorem. Based on this investigation, we calculate a new entropy using a generalization of combinatorial analysis based on two different methods of counting. The basic ingredients used in the H-theorem were: a generalized quantum entropy and a generalization of collisional term of Boltzmann equation. The power law distributions are parameterized by parameters q;, measuring the degree of non-Gaussianity of quantum gas. In the limit q

Não-extensividade no contexto da atividade magnética solar: o problema da assimetria hemisférica

Solar activity indicators, each as sunspot numbers, sunspot area and flares, over the Sun’s photosphere are not considered to be symmetric between the northern and southern hemispheres of the Sun. This behavior is also known as the North-South Asymmetry of the different solar indices. Among the different conclusions obtained by several authors, we can point that the N-S asymmetry is a real and systematic phenomenon and is not due to random variability. In the present work, the probability distributions from the Marshall Space Flight Centre (MSFC) database are investigated using a statistical tool arises from well-known Non-Extensive Statistical Mechanics proposed by C. Tsallis in 1988. We present our results and discuss their physical implications with the help of theoretical model and observations. We obtained that there is a strong dependence between the nonextensive entropic parameter q and long-term solar variability presents in the sunspot area data. Among the most important results, we highlight that the asymmetry index q reveals the dominance of the North against the South. This behavior has been discussed and confirmed by several authors, but in no time they have given such behavior to a statistical model property. Thus, we conclude that this parameter can be considered as an effective measure for diagnosing long-term variations of solar dynamo. Finally, our dissertation opens a new approach for investigating time series in astrophysics from the perspective of non-extensivity.

Efeitos do freio magnético sobre a distribuição da rotação estelar

The pioneering work proposed by Skumanich (1972) has shown that the projected mean rotational velocity < v sini > for solar type stars follows a rotation law decreases with the time given by t −1/2 , where t is the stellar age. This relationship is consistent with the theories of the angular momentum loss through the ionized stellar wind, which in turn is coupled to the star through its magnetic field. Several authors (e.g.: Silva et al. 2013 and de Freitas et al. 2014) have analyzed the possible matches between the rotational decay and the profile of the velocity distribution. These authors came to a simple heuristic relationship, but did not build a direct path between the exponent of the rotational decay (j) and the exponent of the distribution of the rotational velocity (q). The whole theoretical scenario has been proposed using an efficient and strong statistical mechanics well known as non-extensive statistical mechanics. The present dissertation proposes effectively to close this issue by elaborating a theoretical way to modify the q-Maxwellians’ distributions into q-Maxwellians with physics links extracted from the theory of magnetic braking. In order to test our distributions we have used the GenevaCapenhagen Survey data with approximately 6000 F and G field stars limited by age. As a result, we obtained that the exponents of the decay law and distribution follow a similar relationship to that proposed by Silva et al. (2013).