Ling, Stephen (2011)
Ph.D. thesis, University of Birmingham.
In this thesis we will discuss the effects of Weak Localisation, Aharonov-Bohm oscillations and sample-to-sample fluctuations in the context of Mesoscopic systems
and also introduce an interesting concept indicating the possibility of local regions of negative superfluid densities. These normal state phenomena will be rigorously
calculated using Green’s functions and Diagrammatic techniques to help understand their underlying properties. The AC sample-to-sample fluctuations will be evaluated using an original diagrammatic calculation and will be used to show that there are an interesting set of cancellations when taking the DC limit, known as the wrong-sign cancellations.
The second half of this thesis will deal with these mesoscopic effects in the superconducting limit. This will help to understand and develop the useful diagrammatic
techniques needed in the superconducting limit. In the final section we will derive the superconducting mesoscopic fluctuations in an original calculation which will help to understand whether or not there is the possibility of regions of local negative superfluid density as suggested in 1991 by Spivak and Kivelson .
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