Nonadiabatic Transition in the Quantum Hall Effect

We analyze the nonadiabatic transition in a 2D electron system with a periodic potential in the quantum Hall regime. We obtain corrections to the Chern-number term of the Hall conductance and a non-vanishing diagonal conductance. We treat the electric field as a time-dependent vector potential in the Hamiltonian. We calculate the time evolution of the density operator taking account of the first order of the electric field, and thereby study the electric conduction when the system evolves nonadiabatically. We thus obtain analytical expressions of the diagonal and off-diagonal conductances and calculate them numerically.