Quantum plasmas are an important topic in astrophysics and high pressure laboratory physics for more than 50 years. In addition, many condensed matter systems, including the electron gas in metals, metallic nanoparticles, or electron-hole systems in semiconductors and heterostructures, exhibit—to some extent—plasmalike behavior. Among the key theoretical approaches that have been applied to these systems are quantum kinetic theory, Green function theory, quantum Monte Carlo, semiclassical and quantum molecular dynamics, and more recently, density functional theory simulations. These activities are in close contact with the experiments and have firmly established themselves in the fields of plasma physics, astrophysics, and condensed matter physics. About two decades ago, a second branch of quantum plasma theory emerged that is based on a quantum fluid description and has attracted a substantial number of researchers. The focus of these studies has been on collective oscillations and linear and nonlinear waves in quantum plasmas. Even though these papers pretend to address the same physical systems as the more traditional papers mentioned above, the former appear to form a rather closed community that is largely isolated from the rest of the field. The quantum hydrodynamics (QHD) results have—with a few exceptions—not found application in astrophysics or in experiments in condensed matter physics. Moreover, these results practically did not have any impact on the former quantum plasma theory community. One reason is the unknown accuracy of the QHD for dense plasmas. In this paper, we present a novel derivation, starting from reduced density operators that clearly point to the deficiencies of QHD, and we outline possible improvements. It is also to be noted that some of the QHD results have attracted negative attention being criticized as unphysical. Examples include the prediction of “novel attractive forces” between protons in an equilibrium quantum plasma, the notion of “spinning quantum plasmas,” or the new field of “quantum dusty plasmas.” In the present article, we discuss the latter system in some detail because it is a particularly disturbing case of formal theoretical investigations that are detached from physical reality despite bold and unproven claims of importance for, e.g., dense astrophysical plasmas or microelectronics. We stress that these deficiencies are not a problem of QHD itself, which is a powerful and efficient method, but rather are due to ignorance of its properties and limitations. We analyze the common flaws of these works and come up with suggestions to improve the situation of QHD applications to quantum plasmas.

Quantum hydrodynamics for plasmas—Quo vadis?

Applying the separate spin evolution-quantum hydrodynamic model incorporating Coulomb exchange interaction, the instabilities of upper hybrid mode and beam driven mode due to passing of electron beam in a spin polarized degenerate plasma are studied. It is found that the electron spin not only changes the growth rate of these modes but also gives birth to a new spin-dependent wave (spin electron acoustic wave) in the real frequency spectrum. Further, the Bohm potential and exchange interaction effects significantly affect the frequency spectra of upper hybrid mode. Other parameters like streaming speed of beam electron and beam density are also found to influence the growth rate of these modes. These consequential effects may have a strong bearing on the wave and instability phenomena in the solid state plasmas.

On the upper hybrid wave instability in a spin polarized degenerate plasma

An investigation of nonlinear dust-acoustic cnoidal waves in a magnetized quantum dusty plasma consisting of inertial dust, inertialess electrons and ions is presented. The Korteweg–de Vrie...

Dust-acoustic cnoidal waves in a magnetized quantum dusty plasma

We have discussed energy densities and energy flow speed in a spin polarized plasma when longitudinal waves [Spin electron acoustic wave (SEAW) and Langmuir wave] propagate through the plasma. Employing the separate spin evolution quantum hydrodynamic model, we have derived the expression for energy densities and energy flow speed. It is found that the spin polarization changes the profiles of various energy densities. Specifically, we find that the spin polarization broadens the profile of the electrostatic energy density retaining the same peak value. In the case of kinetic and quantum energy densities, the profiles become narrower with the decrease in the peak value for the former case and increase for the latter. On the other hand, in the case of Langmuir waves, the spin polarization effect is similar for electrostatic energy density but opposite to the peak values of kinetic and quantum energy densities. The corresponding profiles become narrower as in the case of SEAW. Furthermore, energy flow speed associated with the SEAW and Langmuir wave is reduced for higher values of spin polarization. It is also noted that the contribution of Bohm potential in the dispersion compensates the reduction of energy flow due to spin polarization. The results are graphically analyzed for the choice of solid state plasma parameters.

Separate spin evolution of electrostatic energy flow in a degenerate quantum plasma

The nonlinear propagation of magnetosonic waves in a magnetized strongly coupled dusty plasma consisting of inertialess electrons and ions as well as strongly coupled inertial charged dust particles is presented. A generalized viscoelastic hydrodynamic model for the strongly coupled dust particles and a quantum hydrodynamic model for electrons and ions are considered. In the kinetic regime, we derive a modified Kadomstev-Petviashvili (KP) equation for nonlinear magnetosonic waves of which the amplitude changes slowly with time due to the effect of a small amount of dust viscosity. The approximate analytical solutions of the modified KP equations are obtained with the help of a steady state line-soliton solution of the second type KP equation in a frame with a constant velocity. The dispersion relationship in the kinetic regime shows that the viscosity is no longer a dissipative effect.The nonlinear propagation of magnetosonic waves in a magnetized strongly coupled dusty plasma consisting of inertialess electrons and ions as well as strongly coupled inertial charged dust particles is presented. A generalized viscoelastic hydrodynamic model for the strongly coupled dust particles and a quantum hydrodynamic model for electrons and ions are considered. In the kinetic regime, we derive a modified Kadomstev-Petviashvili (KP) equation for nonlinear magnetosonic waves of which the amplitude changes slowly with time due to the effect of a small amount of dust viscosity. The approximate analytical solutions of the modified KP equations are obtained with the help of a steady state line-soliton solution of the second type KP equation in a frame with a constant velocity. The dispersion relationship in the kinetic regime shows that the viscosity is no longer a dissipative effect.

Nonlinear dusty magnetosonic waves in a strongly coupled dusty plasma

The influence of quantum effects on the excitation of two instabilities, namely quantum dust-acoustic and quantum dust-lower-hybrid waves due to the free streaming of ion/dust particles in uniformly magnetized dusty plasmas has been investigated using a quantum hydrodynamic model. We have obtained dispersion relations under some particular conditions applied on streaming ions and two contrastreaming dust particle beams at equilibrium and have analyzed the growth rates graphically. We have shown that with the increase of both the electron number density and the streaming speed of ion there is enhancement in the instability due to the fact that the dense plasma particle system with more energetic species having a high speed results in the increase of the growth rate in the electrostatic mode. The application of this work has been pointed out for laboratory as well as for space dusty plasmas.

J. Saman

Papers

Low frequency waves in streaming quantum dusty plasmas