Dynamics of Degenerate Electron Gas in a Magnetic Field

Abstract

Some aspects of the correlations between interacting electrons in a magnetic field are studied by a quantum kinetic approach, taking into account the quantization of the orbital motion of the electrons. The treatment is based on the introduction of an hierarchy of equations of motion for the $s$-body density matrices and employing a decoupling scheme, valid in the self-consistent field approximation. In this way the dielectric function is introduced "naturally," and the response of the system to an applied field is calculated. The dielectric function reflects the two main effects of the correlations, i.e., the collective excitations of the system and the dynamical shielding. The dielectric function plays a role also in the "dressing" of the interacting electrons. This is shown by calculating the spectrum of the density fluctuations and the equation which governs the approach to equilibrium of the system. The method is not limited to systems in thermal equilibrium, but also applies to systems in other stationary equilibrium states.