Field theoretical treatment of plasma modes in coupled two-dimensional systems

We investigate an assembly of two-dimensional electron systems, separated spatially but coupled by Coulomb interaction. The acoustic and the optical plasma modes are studied using a field theoretical method. It is found that a certain approximation in treating one class of diagrams gives an effective exchange potential equal to that calculated using the method of Kohn and Sham 1]. For small wave-vector, expressions equivalent to Boltzmann equations are obtained. Numerical results are finally obtained for the dependence of the frequency on wave vector and densities of the electron systems.