TIME-DEPENDENT LANDAU SYSTEM AND NON-ADIABATIC BERRY PHASE IN TWO DIMENSIONS

By applying the time-independent unitary transformation, the time-dependent Landau system is transformed into a product of a time-independent Landau system's Hamiltonian and a factor only depending on time, which can be solved exactly. Both the invariant operator and the eigenstate are obtained. In the periodical time-dependent case, the non-adiabatic Berry's phase is also presented.