Fractional Statics and Topological Defects in Quantum Field Systems

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9414509 Incera Since 1911, it has been known that certain materials, like, for instance, mercury, lose all their resistance at some low critical temperature. The state with zero resistance persists at temperatures below the critical one. This property is called superconductivity. Until 1986, the highest critical temperature ever observed was of the order of -418 F. In that year a new class of superconducting materials were discovered. For them the superconducting state appears at critical temperatures around - 244 F. This discovery has great technological implications. If scientists obtain a enough high superconducting temperature, the superconductors could be used for many energy saving applications. However, the theoretical model known as the Bardeen Cooper Schrieffer (BCS) theory, which in 1957 explained the phenomenon of supersonductivity at low temperatures, is unable to give a satisfactory explanation for the behavior of the modern high- temperature superconductors. Without a thorough understanding of the physical mechanism that produces this impressive phenomenon, its practical implementation will be very limited. It has been shown that a zero temperature a system formed by particles with fractional statistics, known as anyons, is superconductor. This property has encouraged the idea that the anyons could serve to modeling the high-Temperature superconductivity. However, it is still unclear if an anyon system superconducts at finite temperature. This proposal intends to address this problem by investigating the effects of topological defects in models of anyons at finite temperature and density. ***