Quantum Hall effect in alternating electric field

In two-dimensional systems, the influence of external alternating electric field on the quantum Hall effect is studied within the theory of open quantum systems. Charge carriers are treated as quantum particles interacting with the environment through a one-body (mean-field) mechanism. The dynamics of charge carriers is limited by the average collision time, which takes effectively into account two-body effects. The functional dependencies of average collision time on temperature and magnetic field are phenomenologically treated. Taking into consideration one-body, two-body, and non-Markovian effects, the electrical conductivity tensor is analytically derived in terms of cyclotron frequency and frequency of the external electric field. The theory is applied to describe the real and imaginary parts of the dynamic conductivity in GaAs/$\mathrm{Al}{}_{x}\mathrm{Ga}{}_{1\ensuremath{-}x}\mathrm{As}$ heterojunctions at various alternating electric fields. The dependence of magnetic moment of two-dimensional systems on the magnetic field is predicted at various temperatures and frequencies of the external electric field.