Some New Aspects of Degenerate Quantum Plasma

Answers to some salient questions, which arise in quantum plasmas, are given. Starting from the Schr\"{o}dinger equation for a single particle it is demonstrated how the Wigner-Moyal equation can be derived. It is shown that the Wigner-Moyal type of equation also exists in the classical field theory. As an example, from the Maxwell equations the Wigner-Moyal type of equation is obtained for a dense photon gas, which is classical, concluding that the Wigner-Moyal type of equation can be derived for any system, classical or quantum. A new type of quantum kinetic equations are presented. These novel kinetic equations allow to obtain a set of quantum hydrodynamic equations, which is impossible to derive by the Wigner-Moyal equation. The propagation of small perturbations and instabilities of these perturbations are then discussed, presenting new modes of quantum plasma waves. In the case of low frequency oscillations with ions, a new Bogolyubov type of spectrum is found. Furthermore, the Korteweg-de Vries (KdV) equation is derived and the contribution of the Madelung term in the formation of the KdV solitons is discussed.