Already in ancient Greece, the pre-Socratic philosophers thought that natural phenomena, although different, were homogeneous, of the same fundamental nature. In their theories can be found the search for a common reference point (arché) that puts order in the chaotic multiplicity of phenomena. After Albert Einstein’s theory of gravitation (General Relativity -GR-) was published in 1915, the search for a unified field theory that combines gravity with electromagnetism began to become serious. It seemed plausible that there were no other fundamental forces. The main contributors were Gunnar Nordstrom, Hermann Weyl, Arthur Eddington, Theodor Kaluza, Oskar Klein (See Theory of Kaluza-Klein, 1921) and most notably the many attempts by Einstein and his collaborators. No attempt went through. In the first half of the twentieth century quantum mechanics was consolidated, an instrument capable of overcoming the inadequacy of classical mechanics to explain phenomena and properties such as blackbody radiation, the photoelectric effect, the specific heat of solids, the atomic spectra, the stability of atoms, the Compton effect, .... When in the thirties Fermi and Yukawa ’s studies led to the discovery of nuclear forces, the quantum formalism proved to be appropriate for the description of the new phenomena and, in 1967-68, Sheldon Glashow, Steven Weinberg and Abdus Salam showed how the weak nuclear force and the electromagnetism were simply different manifestations of the same force (electroweak). Since then, proposals have been done to include in a single grand unification theory also the strong nuclear force, and some of them (GTU SU(5) and SO(10)) have provided testable predictions as the quantization of electric charge. At classical level there is an extension of the Kaluza-Klein theory on a 11-dimensional space M4 × S1 × S2 × CP2. It corresponds to Einstein’s General Relativity with 7 extra dimensions, and considers all four forces as different expressions of a “mega†gravitational field. The forces are unified at the classical level but, once quantized, the theory turns out to be inconsistent and therefore unusable. This is because the nuclear forces have range of 10−15 m for strong force and of 10−18 m for weak force, distances at which classical physics loses its meaning. Ultimately, it seems that quantum mechanics is compatible with electroweak and strong interactions only if we limit ourselves to spaces of dimensionality less than or equal to 4. In addition, it is inconsistent with General Relativity for spaces with more of 3 dimensions. For these reasons, the theory of Kaluza-Klein fails doubly. Really, the incompatibility is not between general relativity and quantum mechanics in its entirety, but rather between General Relativity and the method of calculation used in quantum mechanics: perturbative expansion whose terms, in the cases indicted above, become . To get around this problem two different approaches have been taken: String Theory and Loop Quantum Gravity. The first has completely changed the wording of quantum theory, from considering local interactions, where the phenomena occur at specific points (of Feynman graphs), to interactions “extended†, where the phenomena are distributed along one limited dimension (string), open or closed. This system has eliminated the divergences in the terms of perturbative expansion, but has developed other anomalies, eliminated only by building up the theory on a space of 11 dimensions. Unfortunately, the extra dimensions introduce a huge number of arbitrariness, such as the theory can predict everything and nothing. The scientific community hopes to identify some potential whose minimum make a selection between these arbitrariness, but we are still far from such a result. The alternative discussed in this thesis is the Loop Quantum Gravity. This is simply the union of GR and quantum mechanics, without modifying the basic axioms of both. It can be made only in spaces of dimensionality equal to 4 and it surrenders completely the perturbative expansion. This produces fascinating predictions, such as the inflation of early universe, and the lack of singularities in the black holes and in the big bang. It also provides the picture of a “combinatorial†universe, described by nodes connected by paths, whose only necessary variables are integer numbers associated with nodes and paths. This last point in particular escapes the string theory which, whilst losing the locality, is however concentrated within the “very small†. The Loop Quantum Gravity, by contrast, is able to describe the universe as a whole, and to deal with transitions between universes of different topology. The downside is that the calculations are so complex that they are impracticable. Strategies have been developed to introduce a different perturbative expansion that makes the calculations feasible, but this introduces important changes to the initial structure of the theory, in a way that eliminate the beautiful cosmological predictions. Nevertheless, we tried to calculate the graviton propagator in this new “modified framework†, and the result is compatible with linearized quantum GR . For this reason, this framework has not been abandoned. It also seems that this formalism can easily be extended to include extra-dimensions and adapted to the unified theory of Kaluza Klein. This thesis has been developed in an attempt to contribute to the desire for simplification and connection to the essence that has always been in the natural sciences. In particular, it was given a demonstration of how the †modified framework†of Loop Quantum Gravity is derivable from a classical formulation of the GR of Palatini type. Finally, we give suggestions for extending the model to 11 dimensions, because 11 is the number suggested by String theory, by the classical theory of Kaluza Klein, and by the GTU SO(10). Probably the truth lies somewhere in between, maybe an action of a 4-dimensional brane immersed in a 11-dimensional universe would be the right compromise between String Theory and Loop Quantum Gravity. A 4-dimensional brane represents our universe, and any contact with other branes of a much smaller scale put small pieces of it in vibration. Depending on the number of dimensions in which contact is, the part could be a vibrating string or a two- or three-brane (with probability decreasing rapidly moving from string to the three-brane). So, we even lose the distinction between the notions of particles and universes, making the first totally unnecessary. The action of a 4-brane is equivalent to the action of Loop Quantum Gravity, with the coordinate-fields which assume the role of gauge fields, and the indexes in the 11-dimensional space that would become similar to the indexes of internal gauge. This thesis focuses on two specific problems: the calculation of the graviton propagator in Loop Quantum Gravity and the derivation of the “modified framework†from the Palatini formulation of GR (Chapter 8). While the first it was simply supported with a minimum contribution, the second is a problem undertaken by the student in a completely independent way that, while waiting for more in-depth audits, has not yet shown any inconsistency and for now can be hailed a success. A small space is reserved for some inedited consideration undertaken by the student on the “physical†projector. This operator is intended to project the Hilbert space of kinematic states in the subspace of physical states. The conclusion of the argument is simple and somewhat disturbing: the Loop Quantum Gravity is not an unitary theory!

The aim of this work is to investigate the both, some mathematical and physical general aspect of modified gravity, and, more specifically, the proprieties of viable, realistic models of modified gravity which can be used to reproduce the inflation and the dark energy epoch of universe today.

One of the most interesting problems in string theory is to understand how the background space-time on which the string propagates arises in a self-consistent way. For open strings, there are two main approaches to this problem, boundary string field theory (BSFT) and cubic string field theory (CSFT). In the first part of this Thesis we deal with the construction of the spacetime tachyon effective action in BSFT. Renormalization fixed points are solutions of classical equations of motion and should be viewed as solutions of classical string field theory. We have constructed the Witten-Shatashvili (WS) space-time action S and shown that some solitonic solutions are lower dimensional D-branes for which the finite value of S provides a quite accurate prediction of the D-brane tension. We have derived the explicit relation between the CSFT and WS action as a field redefinition which is nonsingular on-shell only when the normalization factor in the WS action coincides with the tension of the D25-brane, in agreement with the conjectures involving tachyon condensation. We have also found a time-dependent solution of CSFT whose evolution is driven by a diffusion equation that makes the equations of motion local with respect to the time variable. The analysis here proposed has attracted a good deal of attention for its potential cosmological applications. The profile can be expressed in terms of a series in powers of exponentials of the time coordinate, and gives evidence of a well-defined but wildly oscillatory behavior. The tachyon rolls well past the minimum of the potential, then turns around and begins to oscillate with ever increasing amplitude. Furthermore, we have derived an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude. From such a solution we computed the exact coefficient of the quartic effective action relevant for time-dependent solutions and we derived the exact coefficient of the quartic tachyon coupling. We studied the rolling tachyon solution expressed as a series of exponentials of the time coordinate both using level-truncation computations and the exact 4-tachyon amplitude. The results for the level-truncated coefficients converge to those derived using the exact string amplitude and confirm the wild oscillatory behavior. In the second part of the Thesis we consider the extension of the gauge/gravity correspondence to systems with reduced and hence more realistic supersymmetry, which is one of the main steps towards a non-perturbative description of confining, QCD-like, gauge theories in terms of gravitational backgrounds. If string theory on AdS5xS5 is integrable, the theory on simple orbifolds of that space would also be expected to be integrable. We have computed the planar finite size corrections to the spectrum of the dilatation operator acting on states of a certain limit of conformal N = 2 quiver gauge field theory which is a ZM-orbifold of N = 4 SYM theory. We matched the result to the string dual, IIB superstrings on a pp-wave background with a periodically identified null coordinate. Up to two loops, we have shown that the computations done by using an effective Hamiltonian technique and a twisted Bethe Ansatz agree with each other and also agree with a computation of the analogous quantity in string theory. Our results are consistent with integrability of the N = 2 theory.

This thesis is devoted to the study of the hydrodynamic behavior of the unitary Fermi gas trapped by a highly elongated harmonic potential. Propagation of sound is one of the most exciting features exhibited by interacting many-body systems. It provides crucial information on the dynamic behavior of the system as well as on key thermodynamic quantities. The propagation of sound is particularly interesting in superfluids where two-fluid hydrodynamic theory predicts the occurrence of two different sounds: first sound, where the normal and superfluid component oscillate in phase, and second sound, where the two components oscillate with opposite phase. In the thesis, we investigate the propagation of sound waves of the unitary Fermi gas in a cylindrical geometry by solving the equations of two-fluid hydrodynamics in the `1D' scenario at finite temperature. The relevant thermodynamic functions entering the hydrodynamic equations are discussed in the superfluid and normal regimes in terms of universal scaling functions. Both the first sound and second sound solutions are calculated as a function of temperature and the role of the superfluid density is explicitly pointed out. The density fluctuations in the second sound wave are found to be large enough to be measured as a consequence of the finite thermal expansion coefficient of the gas, which is the strategy used in a recent experiment carried out at Innsbruck where second sound was detected in the unitary Fermi gas. We also provide an investigation of the temperature dependence of the collective oscillations of first sound nature exhibited by a highly elongated harmonically trapped Fermi gas at unitarity, including the region below the critical temperature for superfluidity. Differently from the lowest axial breathing mode, the hydrodynamic frequencies of the higher-nodal excitations show a temperature dependence, which is calculated starting from Landau two-fluid theory and using the available experimental knowledge of the equation of state.

Neste trabalho foi estudado como a materia escura pode ser capturada por corpos celestes e como a ela pode se comunicar com o Modelo Padrao atraves de sua aniquilacao em quarks e leptons. Os hadrons e leptons gerados podem decair em neutrinos que podem ser detectados por experimentos na Terra. Como tres tipos de neutrinos de autoestados de sabor ja foram observados experimentalmente e que diversos dados experimentais evidenciam oscilacao de sabor entre esses neutrinos, e preciso levar essa fenomenologia em consideracao ao estudar os neutrinos produzidos pela materia escura. O formalismo que permite considerar oscilacoes de neutrinos e ao mesmo tempo colisoes elasticas e inelasticas na materia e o formalismo de matriz densidade. Com ele estudamos o fluxo de muons gerados por neutrinos provenientes da aniquilacao da materia escura no interior do sol e como utilizar esse resultado para testes de modelos de particulas para materia escura. / In this work was studied how dark matter can be captured by celestial bodies and how it can communicate with the Standard Model through its annihilation in quarks and leptons. The hadrons and leptons generated can decay in to neutrinos which can be detected by experiments in Earth. As three types of neutrino flavor eigenstates have been observed experimentally and many experimental data have shown the flavor neutrino oscillate, it is necessary use this phenomenology when studying neutrinos produced by Dark Matter. The formalism that allows considering neutrino oscillations and, at same time, elastic and inelastic matter collisions is the density matrix formalism. With this formalism we studied the muons flux produced by neutrinos coming from dark matter annihilation inside the sun and how to use these results to test particle models for dark matter.

Neste trabalho é investigado o papel de defeitos no processo de nucleação martensitica em monocristais de zirconia (Zr02), submetidos a altas pressões, e é feita uma revisão da teoria sobre nucleação martensitica. As amostras foram submetidas a diferentes tratamentos (irradiação. microindentação. envelhecimento à temperatura ambiente), para geração de defeitos, sendo estudados os seus efeitos na pressão de transformação monoclinica/ortorrombica dos cristais. A pressão foi gerada através de uma câmara de bigornas de diamante e as transições foram detectadas pela observação. via microscopia óptica, de mudanças na birrefringéncia dos cristais. As características da transição (velocidade, deformações associadas, formação de geminamentos) e a observação da formação da interface em uma direção cristalográfica definida confirmam a natureza martensitica da transformação. A redução da força motriz necessária para a transição, em monocristais nos quais foram gerados defeitos eminentemente pontuais, indica que o processo de nucleação é não clássico, de acordo com o modelo de modos macios localizados.

No description available.

E’ stato affrontato in modo approfondito lo studio dei campi gravitazionali della relatività generale (RG) che producono un’accelerazione uniforme, e si è confrontato tale studio con i sistemi si riferimento (SR) accelerati della relatività ristretta (RR). Nel corso di quest’analisi sono stati trovati alcuni aspetti non evidenziati in precedenza nella letteratura scientifica, di cui il più rilevante è il fatto che la metrica di Rindler produce un campo che, osservato con misure di tipo radar, appare uniforme a un osservatore solidale con il campo stesso. Si è inoltre trovata più di una metrica cui corrisponde un’accelerazione che non dipende dalla coordinata di partenza. Per il campo di Rindler è stata eseguita anche un’analisi approfondita, tramite un’applicazione diretta del principio di equivalenza (PE). La metodologia utilizzata e i risultati sono un contributo originale di questa tesi e sono di interesse da un punto di vista didattico. Nel corso dell’analisi delle proprietà del campo di Rindler sono stati analizzati in modo operativo: il confronto del ritmo di marcia di due orologi che si trovano a una quota differente, la deflessione dei raggi luminosi e la traiettoria di un corpo in caduta libera. Infine si è indagato sulla forma della metrica di una distribuzione di massa a simmetrica planare.

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Este trabalho trata o problema genérico da obtenção analítica exata das variedades algébricas que definem domínios de estabilidade e multiestabilidade para sistemas dinâmicos dissipativos com equações de movimento definidas por funções racionais. Apresentamos um método genérico, válido para qualquer sistema dinâmico, que permite reduzir a análise de sistemas multidimensionais arbitrários à análise de um sistema unidimensional equivalente. Este método é aplicado ao mapa de Hénon, o exemplo paradigmático de sistema multidimensional, para estudar a estrutura aritmética imposta pela dinâmica das órbitas de períodos 4, 5, e 6, bem como seus domínios de estabilidade no espaço de parâmetros. Graças à obtençao de resultados analíticos exatos, podemos explorar pela primeira vez as peculariedades de cada um dos períodos mencionados. Algumas das novidades mais marcantes encontradas são as seguintes: Para período 4, encontramos um domínio de multiestabilidade caracterizado pela coexistência de duas órbitas definidas em corpos algébricos distintos. Observamos a existência de discontinuidades na dinâmica simbólica quando os parâmetros são mudados adiabáticamente ao longo de circulações fechadas no espaço de parâmetros e explicamos sua origem algébrica. Publicamos tais resultados em dois artigos: Physica A, 295, 285-290(2001) e Physical Review E, 65, 036231 (2002). Para período 5, obtivemos a variedade algébrica que define o "camarão" (shrimp) característico, obtemos uma expressão analítica para todas as órbitas de período 5, classificamos todas as singulariedades presentes no espaço de parâmetros e analisamos todas as mudanças que ocorrem ao circular-se em torno de tais singulariedades. Para período 6, da expressão analítica que fornece todas as órbitas, encontramos um resultado muito surpreendente, o mais notável desta dissertação: a possibilidade de coexistência de órbitas reais e complexas estáveis, para valores reais dos parâmetros físicos. Resultados preliminares parecem indicar serem tais órbitas complexas uma espécie de órbitas fantasmas, com semelhanças as órbitas encontradas por Gutzwiller para sistemas Hamiltonianos (não- dissipativos).