5 research outputs found
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.Comment: 15 pages, no figures. Accepted by J.Phys.
Projective planes, Severi varieties and spheres
A classical result asserts that the complex projective plane modulo complex
conjugation is the 4-dimensional sphere. We generalize this result in two
directions by considering the projective planes over the normed real division
algebras and by considering the complexifications of these four projective
planes.Comment: 28 pages, 1 figure, Late