TIME-DEPENDENT AND TIME-INDEPENDENT APPROACHES TO STUDY EFFECTS OF DEGENERATE ELECTRONIC STATES

Two types of phases are discussed in this article: (1) The topological phase as introduced by Berry [Proc. R. Sec. London, Ser. A 392, 35(19 84)] and Aharonov and Anandan [Phys. Rev. Lett. 58, 1593 (1987)] and ( 2) the Longuet-Higgins phase [Proc. R. Sec. London, Ser. A 344, 147 (1 975)]. The two types of phases have a common origin, namely the multiv aluedness of the electronic adiabatic basis, a phenomenon associated w ith the existence of a degeneracy in configuration space. It will be s hown, by studying an electronic model Hamiltonian that arises from a t wo-state approximation to the Mathieu equation, that the two phases di ffer from each other substantially, coinciding only in the adiabatic l imit ripen completion of a cycle. (C) 1998 American Institute of Ph, s ics. [S0021-9606(98)30440-7].