874 resultados para Symmetries groups
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Page 68 of the "American Jewish Cavalcade" scrapbook of Leo Baeck in New York found in ROS 10 Folder 3
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Page 12 of the "American Jewish Cavalcade" scrapbook of Leo Baeck in New York found in ROS 10 Folder 3
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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.
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In Tanzania, indigenous forests can still be found whose existence is based on the management systems of precolonial society. This study covers material from over 900 forests. There are similar types of forests elsewhere in Africa, and similar forests can also be found in indigenous cultures on every continent. In this study they are called traditionally protected forests (TPFs). They have a high level of endemism and a rich biodiversity. The field study was carried out during the years 1997-2003 using participatory methods. An active debate is going on concerning the capacity of local communities to manage their environment. The role of indigenous people and their institutions in the development of the physical environment is a central issue in the debate. This study discusses the opportunities that the local people have had to decide on how to conserve, maintain, utilise, and manage their environment during different political periods. The study explains what kinds of changes have taken place in these forests and institutions in northeastern Tanzania among the matrilinear Zigua and patrilinear Gweno ethnic groups. About 2% of the land area of the communities was still protected by the precolonial structures. The communities have established their protection systems for different reasons, not only because of their beliefs but also because of different secular and clearly environmentally motivated reasons. There are different TPF types. Less than half of them are directly related to spirituality, and more than half are not. In earlier research elsewhere, it has been commonly understood that spiritual reasons played the main role in the protection of these environments. This study is also part of the postcolonial geographical discussion on the precolonial landscape and environmental management which was started by Carl Sauer. In the Zigua case study villages, only two out of five first comer clans have performed rain rituals in the past 30 years. Many of the most respected sacred sites do not have a ritual maker or even a person who knows how to perform rituals any longer. The same is happening with male initiation rites. In all case study villages there have been illegal cuts in the TPFs, but variations can be seen between the communities. The number of those who neither respect indigenous regulations nor accept indigenous penalties is growing. Positive developments have also taken place. Nowadays, the Forest Act of 2002 is in effect, which works as a cornerstone of community-based land ownership and also allows elders to protect TPFs, and by-laws are created with the support of different projects. Moreover, during the field study it was found that many young people are ignorant about their village's TPF sites, but interested in learning about their history and values.