Time evolution and Aharonov-Anandan phase for system with dynamical semisimple Lie algebra (Q1801738)

A class of systems with dynamical semisimple Lie algebra is studied. The Hamiltonian of such systems is a linear combination of the generators of a semisimple Lie algebra. The nonadiabatic cyclic evolution of the systems is studied by using the Lewis-Riesenfeld invariant theory. Then, the Aharonov-Anandan geometric phase is obtained and the non-cyclic evolution of the systems is discussed. Finally, it is pointed out that the method given in this work can be applied not only to the study of the systems with dynamical semisimple algebra, but also to the systems with \(SU(1,1)\oplus_ sh(4)\) or \(E_ 2\) Hamiltonians.