Dynamics of Non-Abelian Aharonov-Bohm Systems

Details Dynamics of Non-Abelian Aharonov-Bohm Systems Dynamics of Non-Abelian Aharonov-Bohm Systems

Jan 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996phdt.........8m&link_type=abstract

Thesis (PH.D.)--CALIFORNIA INSTITUTE OF TECHNOLOGY, 1996.Source: Dissertation Abstracts International, Volume: 57-05, Section: B

Statistics

Cosmic Strings

Scientific paper

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 Cheshire charge is described, raising the possibility of observing Cheshire charge in condensed-matter 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_3 ) 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.

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