Quasi-Adiabatic Approximation for Slowly-Changing Quantum System and Berry's Phase Factors

Abstract：

By analyzing the symmetry of a quantum system in terms of the method of the group theory, a quasi-adiabatic approximate method for solving a Schrodinger equation is presented. The method is to study the transition problem of the quantum system with the Hamiltonian that changes slowly but finitely. As a result of zeroth-order approximate, the quantum adiabatic theorem for the degenerate case is proved strictly, and the topological Berry's phase factors are introduced. A geometrical interpretation of the violation in the adiabatic condition is given, and it is demonstrated that the Berry^ phase factors exist generally in the quantum processes with the time scale which is comparable with the pericxJ of the Hamiltonian. Finally, a possible observable effect is pointed out of the Berry's phase factor in a slowly changing process where the adiabatic condition is violated.