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Full-Text Articles in Physical Sciences and Mathematics
Theoretical And Numerical Studies Of Phase Transitions And Error Thresholds In Topological Quantum Memories, Pejman Jouzdani
Theoretical And Numerical Studies Of Phase Transitions And Error Thresholds In Topological Quantum Memories, Pejman Jouzdani
Electronic Theses and Dissertations
This dissertation is the collection of a progressive research on the topic of topological quantum computation and information with the focus on the error threshold of the well-known models such as the unpaired Majorana, the toric code, and the planar code. We study the basics of quantum computation and quantum information, and in particular quantum error correction. Quantum error correction provides a tool for enhancing the quantum computation fidelity in the noisy environment of a real world. We begin with a brief introduction to stabilizer codes. The stabilizer formalism of the theory of quantum error correction gives a well-defined description …
Deriving The Density Of States For Granular Contact Forces, Philip Metzger
Deriving The Density Of States For Granular Contact Forces, Philip Metzger
Electronic Theses and Dissertations
The density of single grain states in static granular packings is derived from first principles for an idealized yet fundamental case. This produces the distribution of contact forces P_f(f) in the packing. Because there has been some controversy in the published literature over the exact form of the distribution, this dissertation begins by reviewing the existing empirical observations to resolve those controversies. A method is then developed to analyze Edwards' granular contact force probability functional from first principles. The derivation assumes Edwards' flat measure -- a density of states (DOS) that is uniform within the metastable regions of phase space. …
Statistical Mechanics Of Farey Fraction Spin Chain Models, Jan Fiala
Statistical Mechanics Of Farey Fraction Spin Chain Models, Jan Fiala
Electronic Theses and Dissertations
This thesis considers several statistical models defined on the Farey fractions. Two of these models, considered first, may be regarded as "spin chains", with long-range interactions, another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle-Perron-F'robenius operator), which is defined using the maps (presentation functions) generating the Farey "tree". The spectrum of this operator was completely determined by Prellberg. It follows that all these models have a second-order phase transition with a specific …