Theoretical foundations of quantum hydrodynamics for plasmas

TL;DR

This paper derives and refines the theoretical foundations of quantum hydrodynamics for plasmas, including new non-local potentials and exchange-correlation effects, enhancing the model's accuracy and applicability.

Contribution

It introduces a fully non-local Bohm potential linked to the electron polarization function and incorporates dynamic exchange-correlation potentials within the QHD framework.

Findings

Revised and improved Fermi pressure and Bohm potential derivations.

Introduction of a non-local Bohm potential based on the electron polarization function.

Discussion on the applicability range of quantum hydrodynamics.

Abstract

Beginning from the semiclassical Hamiltonian, the Fermi pressure and Bohm potential for the quantum hydrodynamics application (QHD) at finite temperature are consistently derived in the framework of the local density approximation with the first order density gradient correction. Previously known results are revised and improved with a clear description of the underlying approximations. A fully non-local Bohm potential, which goes beyond of all previous results and is linked to the electron polarization function in the random phase approximation, for the QHD model is presented. The dynamic QHD exchange correlation potential is introduced in the framework of local field corrections, and considered for the case of the relaxation time approximation. Finally, the range of applicability of the QHD is discussed.