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Chapter 1 contains the general background of our work. We briefly discuss important aspects of quantum chromodynamics (QCD) and introduce the concept of the chiral condensate as an order parameter for the chiral phase transition. Our focus is on the concept of universality and the arguments why the O(4) model should fall into the same universality class as the effective Lagrangian for the order parameter of (massless) two-flavor QCD. Chapter 2 pedagogically explains the CJT formalism and is concerned with the WKB method. In chapter 3 the CJT formalism is then applied to a simple Z2 symmetric toy model featuring a one-minimum classical potential. As for all other models we are concerned with in this thesis, we study the behavior at nonzero temperature. This is done in 1+3 dimensions as well as in 1+0 dimensions. In the latter case we are able to compare the effective potential at its global minimum (which is minus the pressure) with our result from the WKB approximation. In chapter 4 this program is also carried out for the toy model with a double-well classical potential, which allows for spontaneous symmetry breaking and tunneling. Our major interest however is in the O(2) model with the fields treated as polar coordinates. This model can be regarded as the first step towards the O(4) model in four-dimensional polar coordinates. Although in principle independent, all subjects discussed in this thesis are directly related to questions arising from the investigation of this particular model. In chapter 5 we start from the generating functional in cartesian coordinates and carry out the transition to polar coordinates. Then we are concerned with the question under which circumstances it is allowed to use the same Feynman rules in polar coordinates as in cartesian coordinates. This question turns out to be non-trivial. On the basis of the common Feynman rules we apply the CJT formalism in chapter 6 to the polar O(2) model. The case of 1+0 dimensions was intended to be a toy model on the basis of which one could more easily explore the transition to polar coordinates. However, it turns out that we are faced with an additional complication in this case, the infrared divergence of thermal integrals. This problem requires special attention and motivates the explicit study of a massless field under topological constraints in chapter 8. In chapter 7 we investigate the cartesian O(2) model in 1+0 dimensions. We compare the effective potential at its global minimum calculated in the CJT formalism and via the WKB approximation. Appendix B reviews the derivation of standard thermal integrals in 1+0 and 1+3 dimensions and constitutes the basis for our CJT calculations and the discussion of infrared divergences. In chapter 9 we discuss the so-called path integral collapse and propose a solution of this problem. In chapter 10 we present our conclusions and an outlook. Since we were interested in organizing our work as pedagogical as possible within the narrow scope of a diploma thesis, we decided to make extensive use of appendices. Appendices A-H are intended for students who are not familiar with several important concepts we are concerned with. We will refer to them explicitly to establish the connection between our work and the general context in which it is settled.
Of central importance in the whole thesis is the concept of the generating functional and the partition function, respectively. In appendix A.1 we present the general context in which the partition function appears and its general definition within the operator formalism of second quantization. Alternatively, this definition can be rewritten via the path integral formalism. We restrict ourselves to scalar fields in this case. Furthermore, the understanding of the CJT formalism is based on knowledge about n-point functions (connected or disconnected, in the presence or in the absence of sources) and the context in which they arise. In appendix A.2 we give their definition taking account of the different modifications in which these quantities occur in this thesis, i.e., scalar field theory at zero or at nonzero temperature, respectively. From a didactic point of view, we believe that it is helpful if one can establish a relation between special cases and a general framework. Therefore, in appendix A.3 we want to keep an eye on the overall picture. We discuss the general concept of the generating functional for correlation functions, which also covers the partition function. We also briefly comment on the general concept of Feynman rules and we clarify the meaning of the terms Green’s function and propagator.
Neuronal activity in the brain is often investigated in the presence of stimuli, termed externally driven activity. This stimulus-response-perspective has long been focussed on in order to find out how the nervous system responds to different stimuli. The neuronal response consists of baseline activity, so called spontaneous activity1, and activity which is caused by the stimulus. The baseline activity is often considered as constant over time which allows the identification of the stimulus-evoked part of the neuronal response by averaging over a set of trials.
However, during the last years it has been recognized that own dynamics of the nervous system plays an important role in information processing. As a consequence, spontaneous activity is no longer regarded only as background ’noise’ and its role in cortical processing is reconsidered. Therefore, the study of spontaneous firing pattern gains more importance as these patterns may shape neuronal responses to a larger extent as previously thought. For example, recent findings suggest that prestimulus activity can predict a person’s visual perception performance on a single trial basis (Hanslmayr et al., 2007). In this context, Ringach (2009) remarks that one can learn much about even the quiescent state of the brain which “underlies the importance of understanding cortical responses as the fusion of ongoing activity and sensory input”.
Taking into account that spontaneous activity reflects anything else but noise, new challenges arise when analysing neuronal data. In this thesis one of these problems related to the analysis of neuronal activity will be adressed, namely the nonstationarity of firing rates.
The present work consists of four chapters. First of all the introduction gives neurophysiological background information to get an idea of neuronal information processing. Afterwords the theory of point processes is provided which forms the basis for modeling neuronal spiking data. In the last section of the introduction a statement of the problem is given. Chapter 2 proposes an easily applicable statistical method for the detection of nonstationarity. It is applied to simulations and to real data in order to show its capabilities. Thereafter, four other approaches are presented which provide useful illustrations concerning the nonstationarity of the firing rate but share the problem that one cannot make objective statements on the basis of their results. They were developed in the course of establishing a suitable method. In chapter 4 the results are discussed and suggestions for further study are given.
A study on the impact of mobile telecommunication on the welfare of sub saharan african countries
(2010)
Africa: A continent is waking up. Not through aid or wealth from the exploitation of natural resources, but through a technological revolution. The access to affordable mobile telecommunication. Inspired by deregulation and pioneered by local champions who have taken a lead in what is today's fastest growing mobile market in the world. There is money to be made in these markets, attracting more and more operators from the northern hemisphere.
However positive the short term impact of this revolution may be, governments should try hard to assure a market of continued competition among network operators, as this competition is the source of a self propelled creation of welfare and new opportunities, motivated from within Africa.
Chapter 1 of this thesis highlights the positive impact of mobile telecommunication on the social and economic life in Sub Saharan Africa. Chapter 2 builds on the static as well as the dynamic version of the Network Pricing Game, a model developed by Dr. Carolyn Gideon, to stress the immanent threat of network markets turning into a monopoly. This theses ends in Chapter 3 with an brief outlook on further drivers of economic growth and opportunities awaiting Sub Saharan Africa in the coming decade.
Production of neutral strange hadrons with high transverse momentum in Pb+Pb collisions at 158 A GeV
(2006)
The motivation for studying ultrarelativistic heavy ion collisions is to search for signatures of a transition from hadronic matter to a partonic phase, the Quark-Gluon plasma. The bulk of the particles produced in these collisions possesses transverse momenta of pT < 2 GeV/c and evidence for the production of a Quark-Gluon plasma at SPS energies has been found in the properties of particles from this pT range. The rare particles seen in the higher pT domain can complete the picture of the produced matter. Examples for such high pT signatures include the properties of the baryon/meson ratios and the elliptic flow in the region 2 < pT < 4 GeV/c observed at RHIC. They can be explained by quark coalescence models. This phase space range can also be accessed for analysis at the highest SPS beam energy of 158 A GeV. A study of the pT dependence of baryon/meson ratios here can help to answer the question which hadron production mechanisms are relevant in this energy range. In the NA49 large acceptance hadron spectrometer, K0S and Lambda are identified via the V 0 topology of their decay into charged hadrons and the determination of their invariant mass. The reach in pT of this method is only limited by the statistics of the available data. An important part of the analysis presented in this thesis is to select potential V 0 candidates by adequate cuts. Optimisation for the high pT domain requires careful cuts in order to retain the signal there. A challenge implicated by this approach is the large combinatorial background left over by the loose cuts. A reliable signal extraction method was found that can deal with this possible difficulty and provide raw spectra.The fraction of particles that cannot be detected because of the geometrical acceptance of the detector and analysis inefficiencies was determined in simulations. Correction factors are extracted from this simulation for each phase space bin and applied to the raw spectra. The spectra corrected in this way reach pT = 3.6 GeV/c (for K0 S) and pT = 3.8 GeV/c (Lambda), respectively. The whole analysis method has been checked to be self-consistent and was compared to existing data on kaon and ... production, that is only available in the lower pT range. While the Lambda spectra agree with an earlier analysis [44], a disagreement remains between the results for K0 S presented here and charged kaon data published in [42]. The Lambda/K0 S ratio calculated from the corrected spectra qualitatively agrees with the results for the higher collision energy at RHIC [8]. A saturation of the ratio for pT >= 2 GeV/c clearly indicates that the hydrodynamical picture is not valid in the higher range any more. Unfortunately, no calculations from coalescence models are available for the SPS energy range so far.