The accuracy of a popular quantum hydrodynamic plasma model

Recently, researchers have had a growing interest in plasmas with low temperatures and high densities, motivated by applications such as quantum wells, spintronics and plasmonics. In this regime, well-established classical plasma models are not accurate due to the significance of quantum properties like exchange and particle dispersion.

A new article investigates the accuracy of a popular quantum hydrodynamic plasma model that accounts for the effects of both exchange interactions and electron correlations. While the model is straightforward to apply, its exchange potential is derived from time-independent density functional theory rather than its time-dependent counterpart. The researchers found that the hydrodynamical theory is applicable only within a limited regime, at best, and otherwise gives misleading results.

The study used a quantum kinetic model derived from the density matrix, keeping first-order corrections in the quantum equivalent of many-particle dynamics while neglecting correlations in order to focus on exchange effects. They compared this model with the much-used hydrodynamic expression based on time-independent density function theory.

In both the low-frequency and the combined short-wavelength/high-frequency regimes, the hydrodynamic plasma model proves to be inaccurate. Wave-particle interaction leads to a strong enhancement of the exchange correction, and the result given by the model is smaller by an order of magnitude. The only instance where this model can be used is the high-frequency/long-wavelength regime.

The findings suggest that exchange effects can be larger than previously assumed, and the accurate modeling of these effects can be crucial for high-density plasmas. More work needs to be done to get a clearer picture of the applicability of current density functional theories, however, the researchers conclude that hydrodynamic models based on time-independent density functional theory must be applied with caution.

Source: “Do hydrodynamic models based on time-independent density functional theory misestimate exchange effects? Comparison with kinetic theory for electrostatic waves,” by Gert Brodin, Robin Ekman, and Jens Zamanian, Physics of Plasmas (2019). The article can be accessed at http://doi.org/10.1063/1.5104339 .