Construction of a more complete quantum fluid model from Wigner-Boltzmann Equation with all higher order quantum corrections

TL;DR

This paper develops a comprehensive quantum fluid model from the Wigner-Boltzmann equation, incorporating all higher order quantum corrections to improve accuracy at low temperatures and high densities.

Contribution

It introduces a novel closure method using a momentum-shifted, all-order quantum corrected solution, extending the model's applicability in quantum hydrodynamics.

Findings

Extended the quantum fluid model to low temperature and high density regimes.

Retained correlation and exchange effects via the Kohn-Sham equation.

Achieved closure of the moment equations with a new quantum correction approach.

Abstract

A semiclassical Quantum Hydrodynamic model has been derived by taking the moments of the Wigner-Boltzmann equation. For the first time, the closure has been achieved by the use of the momentum shifted version of all order quantum corrected solution of the Wigner-Boltzmann equation and that has considerably extended the applicability of the model towards the low temperature and high density limit. In this context, the importance of the correlation and exchange effects have been retained through the Kohn-Sham equation in the construction of the Wigner-Boltzmann equation. The validity of the approach is subject to the existence of the Taylor's expansion of the associated Kohn-Sham potential.