Topological structures of adiabatic phase for multi-level quantum   systems
  The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) have a monopole structure, the curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures. 
Zheng-Xin Liu, Xiao-Ting Zhou, Xin Liu, Xiong-Jun Liu, Jing-Ling Chen