Phd records
https://feeds.library.caltech.edu/people/McGraw-Patrick-Neal/Phd.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:26:54 +0000Dynamics of non-Abelian Aharonov-Bohm systems
https://resolver.caltech.edu/CaltechTHESIS:02182016-092822106
Authors: {'items': [{'email': 'patrick_n_mcgraw@hotmail.com', 'id': 'McGraw-Patrick-Neal', 'name': {'family': 'McGraw', 'given': 'Patrick Neal'}, 'show_email': 'YES'}]}
Year: 1996
DOI: 10.7907/CGWP-HF33
This thesis examines several examples of systems in which non-Abelian magnetic
flux and non-Abelian forms of the Aharonov-Bohm effect play a role. We consider
the dynamical consequences in these systems of some of the exotic phenomena associated
with non-Abelian flux, such as Cheshire charge holonomy interactions and
non-Abelian braid statistics. First, we use a mean-field approximation to study a
model of U(2) non-Abelian anyons near its free-fermion limit. Some self-consistent
states are constructed which show a small SU(2)-breaking charge density that vanishes
in the fermionic limit. This is contrasted with the bosonic limit where the SU(2)
asymmetry of the ground state can be maximal. Second, a global analogue of Chesire
charge is described, raising the possibility of observing Cheshire charge in condensedmatter
systems. A potential realization in superfluid He-3 is discussed. Finally, we
describe in some detail a method for numerically simulating the evolution of a network
of non-Abelian (S<sub>3</sub>) cosmic strings, keeping careful track of all magnetic fluxes
and taking full account of their non-commutative nature. I present some preliminary
results from this simulation, which is still in progress. The early results are suggestive
of a qualitatively new, non-scaling behavior.https://thesis.library.caltech.edu/id/eprint/9563