Novel features of planar fermions: Anyon superconductivity and the quantum Hall effect.
Item
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Title
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Novel features of planar fermions: Anyon superconductivity and the quantum Hall effect.
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Identifier
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AAI9510709
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identifier
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9510709
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Creator
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Ray, Rashmi.
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Contributor
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Adviser: Bunji Sakita
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Date
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1994
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics, General | Physics, Elementary Particles and High Energy | Physics, Condensed Matter
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Abstract
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In this work we have discussed some remarkable features associated with systems where the particles are permitted to move only along a plane, the third degree of freedom having been effectively frozen out. From a theoretical point of view, the restriction of the dimensionality of space to two is interesting in the sense that anyons, particles with any spin and any statistics may exist in planar systems. Anyons, as may be expected, have some rather novel features which are absent in higher dimensions. In this work, we have dwelt on one such feature: the superfluidity of a gas of anyonic particles. We have further demonstrated that if the anyons are coupled minimally to electromagnetism, the magnetic field is expelled from within the system, resulting in superconductivity. This is the so-called anyon superconductivity, which is one of the candidates for explaining the properties of planar superconductors. Further, planar fermionic systems subjected to strong magnetic fields normal to the plane support the various quantum Hall effects. The single-particle spectrum for such a system consists of the equi-spaced Landau levels, the gap between two successive levels being the cyclotron frequency. If the applied magnetic field is strong enough, the system is projected to the lowest Landau level and hence the development of a field theory of fermions in the lowest Landau levels becomes of more than cursory interest. In this work, we have developed the field theory of such fermions, coupled to external perturbative electromagnetic fields, when the system is projected onto the lowest Landau level. If we further confine the fermions to a finite portion of the plane through some suitably chosen confining potential, the field theory that we develop enables us to discuss the excitations associated with the boundary of the system. These excitations, dubbed as the edge-excitations in the literature, are shown to be important in the maintenance of the original electromagnetic gauge invariance of the system. In summary, the main thrust of this work is in the discussion of anyon superconductivity and the development of a field theory for fermions in the lowest Landau level, the unifying theme being the physics of planar fermions.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
