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Dynamics of non-Abelian Aharonov-Bohm systems


McGraw, Patrick Neal (1996) Dynamics of non-Abelian Aharonov-Bohm systems. Dissertation (Ph.D.), California Institute of Technology. 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 (S3) 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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:cosmic strings, topological defects, nonabelian Aharonov‐Bohm effect
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Group:Caltech Theory
Thesis Committee:
  • Unknown, Unknown
Defense Date:31 May 1996
Non-Caltech Author Email:patrick_n_mcgraw (AT)
Record Number:CaltechTHESIS:02182016-092822106
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9563
Deposited By: Benjamin Perez
Deposited On:19 Feb 2016 21:10
Last Modified:09 Nov 2022 19:19

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