Dynamics of non-Abelian Aharonov-Bohm systems

cosmic strings, topological defects, nonabelian Aharonov‐Bohm effect

McGraw, Patrick Neal ; Preskill, John P.

University:California Institute of Technology

Department:Physics, Mathematics and Astronomy

关键词: cosmic strings, topological defects, nonabelian Aharonov‐Bohm effect;   

Others  :  https://thesis.library.caltech.edu/9563/8/McGraw_pn_1996.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

This thesis examines several examples of systems in which non-Abelian magneticflux and non-Abelian forms of the Aharonov-Bohm effect play a role. We considerthe dynamical consequences in these systems of some of the exotic phenomena associatedwith non-Abelian flux, such as Cheshire charge holonomy interactions andnon-Abelian braid statistics. First, we use a mean-field approximation to study amodel of U(2) non-Abelian anyons near its free-fermion limit. Some self-consistentstates are constructed which show a small SU(2)-breaking charge density that vanishesin 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 Chesirecharge is described, raising the possibility of observing Cheshire charge in condensedmattersystems. A potential realization in superfluid He-3 is discussed. Finally, wedescribe in some detail a method for numerically simulating the evolution of a networkof non-Abelian (S₃) cosmic strings, keeping careful track of all magnetic fluxesand taking full account of their non-commutative nature. I present some preliminaryresults from this simulation, which is still in progress. The early results are suggestiveof a qualitatively new, non-scaling behavior.