Browsing by discipline "Theoretical Physics"

As a full-grown science, cosmology is relatively young. Even though man has pondered the existence and structure of the universe throughout his history, the lack of actual observational data has prevented analytical research. Observational cosmology can be seen to have born in the 1920’s when Edwin Hubble discovered that the galaxies surrounding us are receding in all directions. This led to the conclusion that the universe around us is itself actually expanding. Expansion occurring isotropically in all directions indicates that the universe was once much denser and hotter. So hot that the matter in it has been completely ionized plasma. The decrease in temperature caused by the expansion is calculated to have caused the neutralizing of the plasma, recombination, over thirteen billion years ago. The instant is cosmologically remarkable, since light that until that moment scattered frequently from the charged particles now began to propagate freely. Initially at three thousand Kelvin temperature, the radiation has cooled down due to expansion and is now observed as the three Kelvin cosmic microwave background radiation (CMB). First observations of the existence of the CMB date back to 1965. Since the background radiation has traveled its long journey relatively unchanged, its study can yield direct information on the conditions of the early universe. Theoretically it was expected, well before observational confirmation in 1992, that the CMB should have a structure that reflects those inhomogeneities, that have now undergone their ten billion years of evolution, to become the large scale structure we observe: galaxies, galaxy clusters and the evermore larger entities. In this thesis we examine, how the effects of two cosmological parameters, the matter and baryon densities of the universe, manifest in the pre-recombination dynamics and how these effects are reflected in the structure of the observed CMB anisotropy. Baryons are the “ordinary” matter all around us, protons and neutrons. The concept of “matter” is extended to include the unknown dark matter, the existence of which is only known through its gravitational effects. We will review the equations that are necessary to track the evolution of the primordial perturbations. By a computer program based on those equations we display how the early universe dynamics change with the values of the density parameters. Finally we will show how these effects are reflected in the angular power spectrum that describes the structure of the microwave background.

The best renormalizable theory in particle physics is the Standard Model. According to this model, neutrinos must be massless. We know that neutrinos have three different flavors. Owing to the observations, it is seen that there are oscillations between different flavors of neutrinos. This fact forces us to go beyond the Standard Model of Particle Physics, because neutrino oscillations can only happen if the neutrinos are massive. The first solution is to define three mass eigenstates and claim that the flavor eigenstates are superpositions of the mass eigenstates. However, due to some problems it is concluded that physical states must be replaced with fields. In this thesis we study neutrino oscillations. We begin our work with reviewing fermion fields before the Standard Model. Then the Standard Model and experiments which confirm the existence of different neutrino flavors are shortly discussed. Moreover, we present the observations that show neutrino oscillations phenomenon and after that, the Dirac and Majorana neutrinos are discussed. Finally, oscillations are described theoretically. First, quantum mechanical oscillations are discussed and we find the phase and probability of the flavor transitions. Then due to the problems of this approach, oscillations in quantum field theory are presented. It is seen that, again, the results derived with the quantum mechanical treatment are accepted in the quantum field theory approach.

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

There exists various suggestions for building a functional and a fault-tolerant large-scale quantum computer. Topological quantum computation is a more exotic suggestion, which makes use of the properties of quasiparticles manifest only in certain two-dimensional systems. These so called anyons exhibit topological degrees of freedom, which, in principle, can be used to execute quantum computation with intrinsic fault-tolerance. This feature is the main incentive to study topological quantum computation. The objective of this thesis is to provide an accessible introduction to the theory. In this thesis one has considered the theory of anyons arising in two-dimensional quantum mechanical systems, which are described by gauge theories based on so called quantum double symmetries. The quasiparticles are shown to exhibit interactions and carry quantum numbers, which are both of topological nature. Particularly, it is found that the addition of the quantum numbers is not unique, but that the fusion of the quasiparticles is described by a non-trivial fusion algebra. It is discussed how this property can be used to encode quantum information in a manner which is intrinsically protected from decoherence and how one could, in principle, perform quantum computation by braiding the quasiparticles. As an example of the presented general discussion, the particle spectrum and the fusion algebra of an anyon model based on the gauge group S_3 are explicitly derived. The fusion algebra is found to branch into multiple proper subalgebras and the simplest one of them is chosen as a model for an illustrative demonstration. The different steps of a topological quantum computation are outlined and the computational power of the model is assessed. It turns out that the chosen model is not universal for quantum computation. However, because the objective was a demonstration of the theory with explicit calculations, none of the other more complicated fusion subalgebras were considered. Studying their applicability for quantum computation could be a topic of further research.

In this thesis we give a self-sufficient introduction to the trace anomaly and its applications in the problem of cosmological constant. We begin by revising the renormalization of quantum electrodynamics in flat space and the Lagrangian formalism of general relativity. Then we discuss shortly about the renormalizability of quantum general relativity, after which we turn our attention to a semiclassical theory of quantum gravitation. We review the construction and renormalization of the semiclassical theory, and discuss shortly the stability of it. We then proceed to examine the trace anomaly of the semiclassical theory, and begin by reviewing Weyl cohomology in n-dimensions. We use the Weyl cohomology to construct the Wess-Zumino action, from which we derive a non-local action for the trace anomaly. The non-local action is then rendered local by introducing new auxiliary fields, in which the non-local behaviour of the action is contained. After all these theoretical considerations we finally examine the non-trivial cosmological consequences of the trace anomaly. At first we review shortly the Friedman-Robertson-Walker -model and its classical perturbations, after which we examine the linear perturbations of the trace anomaly action in de Sitter space. We find that when the auxiliary fields of the action are quantized, the cosmological constant becomes dependent on the border conditions at the horizon scale of de Sitter space. We then conclude that the small but non-zero value of the cosmological constant could be a physical consequence of the presence of the horizon.

The purpose of this thesis is to study the asymmetric simple exclusion process, its asymptotics and some connections to other stochastic models. The text begins by giving some results on random matrix theory, such as the distribution function of the largest eigenvalue of a given random matrix. This is followed by a short section on the totally asymmetric simple exclusion process, which is a stochastic model of fermionic particles jumping only in one direction on a one-dimensional lattice. The probability that a given particle has jumped m times is then shown to be equal to the distribution of the largest eigenvalue of a specific type of a random matrix analyzed earlier. As this hints at some kind of universality, the particle model is then generalized to the asymmetric simple exclusion process, in which the particles can jump left or right. It turns out this model does not have the simple determinantal structure the earlier models had. The asymptotics of the model will then be analyzed, and it turns out there is a large universality class that encompasses all the models analyzed in the text. The reader is expected to be familiar with basic measure theory and complex analysis.

Entanglement entropy is a proposal to quantify quantum entanglement of two disjoint regions in a pure system. It is a relatively new topic and is developing rapidly. The current main motives to study it are its applications to studying quantum gravity, thermalization and phase transitions in condensed matter systems. Mutual information is a related quantity and it can be used to measure the amount of information two disjoint regions share. The purpose of this thesis is to give an introduction to the general results of the field without considering specific systems. The two prominent approaches used are two-dimensional conformal field theory and the holographic entanglement entropy conjecture. The first approach is to calculate entanglement entropy using conformal field theory, the results of which are known to be exact although technically more difficult to derive and only available for 1+1 dimensional systems. Both static and dynamic systems will be discussed. The results are reproduced and generalized to higher dimensions using holography. As a more recent topic, the holographic approach is used to rederive the entanglement entropy of systems with a Fermi surface using AdS/Vaidya metric with Lifshitz scaling and hyperscaling violation. The final chapter of the thesis discusses mutual information in various static and dynamic cases considered in the previous chapters. For the first time, the evolution of mutual information is calculated in AdS/Vaidya metric with Lifshitz scaling and hyperscaling violation in the critical theta=d-1 case.

Water-ethanol mixtures are commonly used in industry and house holds. However, quite surprisingly their molecular-level structure is still not completely understood. In particular, there is evidence that the local intermolecular geometries depend significantly on the concentration. The aim of this study was to gain information on the molecular-level structures of water-ethanol mixtures by two computational methods. The methods are classical molecular dynamics (MD), where the movement of molecules can be studied, and x-ray Compton scattering, in which the scattering cross section is sensitive to the electron momentum density. Firstly, the water-ethanol mixtures were studied with MD simulations, with the mixture concentration ranging from 0 to 100%. For the simulations well-established force fields were used for the water and ethanol molecules (TIP4P and OPLS-AA, respectively). Moreover, two models were used for ethanol, rigid and non-rigid. In the rigid model the intramolecular bond lengths are fixed, whereas in the non-rigid model the lengths are determined by harmonic potentials. Secondly, mixtures with three different concentrations employing both ethanol models were studied by calculating the experimentally observable x-ray quantity, the Compton profile. In the MD simulations a slight underestimation in the density was observed as compared to experiment. Furthermore, a positive excess of hydrogen bonding with water molecules and a negative one with ethanol was quantified. Also, the mixture was found more structured when the ethanol concentration was higher. Negligible differences in the results were found between the two ethanol models. In contrast, in the Compton scattering results a notable difference between the ethanol models was observed. For the rigid model the Compton profiles were similar for all the concentrations, but for the non-rigid model they were distinct. This leads to two possibilities of how the mixing occurs. Either the mixing is similar in all concentrations (as suggested by the rigid model) or the mixing changes for different concentrations (as suggested by the non-rigid model). Either way, this study shows that the choice of the force field is essential in the microscopic structure formation in the MD simulations. When the sources of uncertainty in the calculated Compton profiles were analyzed, it was found that more statistics needs to be collected to reduce the statistical uncertainty in the final results. The obtained Compton scattering results can be considered somewhat preliminary, but clearly indicative of the behaviour of the water-ethanol mixtures when the force field is modified. The next step is to collect more statistics and compare the results with experimental data to decide which ethanol model describes the mixture better. This way, valuable information on the microscopic structure of water-ethanol mixtures can be found. In addition, information on the force fields in the MD simulations and on the ability of the MD simulations to reproduce the microscopic structure of binary liquids is obtained.