Non-linear electrostatic waves in degenerate quantum plasmas: two-tone waves and self-beats

The authors reviewed theoretical gas-dynamic models of nonlinear electrostatic (Langmuir and ion-acoustic) waves in degenerate quantum unmagnetized uniform plasmas. The models take into account the Bohm quantum force, equations of state of plasma components in the form of an equation of state of fully or partially degenerate Fermi gases, as well as exchange interaction. A new fundamental result has been discovered and explained within the framework of these models: electrostatic waves are shown always to have a two-tone form or a form of self-beats. The reason for the appearance of these forms is the Bohm quantum force, which bends the dispersion curve upward. The fundamental significance of the discovered forms is related to the descriptions of wave phenomena in compact astrophysical objects such as white dwarfs and neutron stars. The significance of the forms in applied sciences is related with the creation of new solid-state devices.